Author name code: wolff ADS astronomy entries on 2022-09-14 author:"Wolff, Charles. L." ------------------------------------------------------------------------ Title: Building the Foundation for Field Research | Interactive Online Training in Instrumentation and Measurement of Atmospheric Parameters Authors: Rockwell, A.; Clark, R. D.; Page, E. M.; Stevermer, A.; Bol, A.; Campos, T. L.; Cooper, W. A.; Haggerty, J. A.; Wolff, C.; Voemel, H. Bibcode: 2020AGUFMSY0020002R Altcode: A series of ten online learning modules on topics related to instrumentation and measurement of atmospheric parameters are now published through a collaborative effort between the National Center for Atmospheric Research Earth Observing Laboratory, The COMET Program, and Millersville University.

These open-source, interactive, multimedia educational modules are positioned to enhance traditional pedagogies and supplement blended instruction on topics such as instrument types, measurement techniques, site selection, and measurement uncertainty. The target audience includes early graduate students and upper-level undergraduates in atmospheric and related sciences fields, but the content is extensible to other disciplines where treatment of these topics is relevant.

Foundations of Meteorological Instrumentation and Measurements

Meteorological Instrument Performance Characteristics

Instrumentation and Measurement of Atmospheric Temperature

Instrumentation and Measurement of Atmospheric Pressure

Instrumentation and Measurement of Atmospheric Humidity

Instrumentation and Measurement of Surface Precipitation

Instrumentation and Measurement of Wind

Instrumentation and Measurement of Atmospheric Trace Gases

Instrumentation and Measurement of Atmospheric Radiation

Instrumentation and Measurement of Clouds and Airborne Particles

The content of these modules is of the highest caliber as it has been developed by subject matter experts who are scientists and engineers at the forefront of the field of observational science. It is expected that this effort will fulfill the expressed need for contemporary, interactive, multimedia guided education and training modules integrating the latest instructional design and assessment tools in observational science. Thousands of undergraduate and graduate students will benefit, while course instructors will value a set of high-quality lessons to use as supplements in their courses. For schools that may lack the resources to stage a field project or offer laboratory-based instrument/measurement experiences, the modules can fill the void and serve as an alternative to observational and laboratory research training. Title: Solar Irradiance Variability, Influenced by r Modes Authors: Wolff, Charles L. Bibcode: 2019ApJ...870...20W Altcode: A spectrum of the four-decade solar irradiance record has a prominent cluster of power for periodicities near 1 yr. Correlating irradiance with a bandpass filter showed that periodicity values were not constant, but varied sinusoidally with each cycle lasting 14 ± 1 yr. The large modulation amplitude makes solar frequencies ≥1 yr-1 hard to detect at the solar surface. After removing the modulation, a Lomb-Scargle spectrum exposed two true periodicities: 1.006 and 0.920 yr. They are interpreted as the synodic rotation periods of r modes of lowest angular degree (ℓ = 1). The first propagates in the stable interior and the second in the convective envelope perturbed by its several flow fields. The rotational beat period of the two modes is about 10.9 yr. This is close to the average length of a solar cycle and possibly controls this average. The 1.006 yr periodicity dominates most of the filtered irradiance record but an abrupt change to about 0.8 yr occurs in mid-2010. Also found was evidence for higher-degree r modes (ℓ = 2 to 8) and a curious sawtooth modulation with a recurrence period of 2.6 yr. Title: Are Pulsing Solitary Waves Running inside the Sun? Authors: Wolff, Charles L. Bibcode: 2012ApJ...756..125W Altcode: A precise sequence of frequencies—detected four independent ways—is interpreted as a system of solitary waves below the Sun's convective envelope. Six future observational or theoretical tests of this idea are suggested. Wave properties (rotation rates, radial energy distribution, nuclear excitation strength) follow from conventional dynamics of global oscillation modes after assuming a localized nuclear term strong enough to perturb and hold mode longitudes into alignments that form "families." To facilitate future tests, more details are derived for a system of two dozen solitary waves 2 <= l <= 25. Wave excitation by 3He and 14C burning is complex. It spikes by factors M 1 <= 103 when many waves overlap in longitude but its long-time average is M 2 <= 10. Including mixing can raise overall excitation to ~50 times that in a standard solar model. These spikes cause tiny phase shifts that tend to pull wave rotation rates toward their ideal values vprop[l(l + 1)]-1. A system like this would generate some extra nuclear energy in two spots at low latitude on opposite sides of the Sun. Each covers about 20° of longitude. Above a certain wave amplitude, the system starts giving distinctly more nuclear excitation to some waves (e.g., l = 9, 14, and 20) than to neighboring l values. The prominence of l = 20 has already been reported. This transition begins at temperature amplitudes ΔT/T = 0.03 in the solar core for a typical family of modes, which corresponds to δT/T ~ 0.001 for one of its many component oscillation modes. Title: Astrocaching as an Outreach Tool for Schools Authors: Khalisi, E.; Wolff, C. Bibcode: 2011epsc.conf..957K Altcode: 2011DPS....43..957K We tried a scavenger hunt as an outreach tool to inspire 10-13 aged pupils for astronomical issues. The game was inherited from the "Geocaching" activities which employ GPS or other mobile devices to hide and seek repositories anywhere in the world. We altered the rules such that the itinerary was based on astronomical instructions, and the repositories contained related items. The realization was successful, however, some difficulties arose in the specification required from the young students. Title: A New Way that Planets Can Affect the Sun Authors: Wolff, Charles L.; Patrone, Paul N. Bibcode: 2010SoPh..266..227W Altcode: 2010SoPh..tmp..166W We derive a perturbation inside a rotating star that occurs when the star is accelerated by orbiting bodies. If a fluid element has rotational and orbital components of angular momentum with respect to the inertially fixed point of a planetary system that are of opposite sign, then the element may have potential energy that could be released by a suitable flow. We demonstrate the energy with a very simple model in which two fluid elements of equal mass exchange positions, calling to mind a turbulent field or natural convection. The exchange releases potential energy that, with a minor exception, is available only in the hemisphere facing the barycenter of the planetary system. We calculate its strength and spatial distribution for the strongest case ("vertical") and for weaker horizontal cases whose motions are all perpendicular to gravity. The vertical cases can raise the kinetic energy of a few well positioned convecting elements in the Sun's envelope by a factor ≤7. This is the first physical mechanism by which planets can have a nontrivial effect on internal solar motions. Occasional small mass exchanges near the solar center and in a recently proposed mixed shell centered at 0.16Rs would carry fresh fuel to deeper levels. This would cause stars like the Sun with appropriate planetary systems to burn somewhat more brightly and have shorter lifetimes than identical stars without planets. The helioseismic sound speed and the long record of sunspot activity offer several bits of evidence that the effect may have been active in the Sun's core, its envelope, and in some vertically stable layers. Additional proof will require direct evidence from helioseismology or from transient waves on the solar surface. Title: Effects of a Deep Mixed Shell on Solar g-Modes, p-Modes, and Neutrino Flux Authors: Wolff, Charles L. Bibcode: 2009ApJ...701..686W Altcode: A mixed-shell model that reflects g-modes away from the Sun's center is developed further by calibrating its parameters and evaluating a mixing mechanism: buoyancy. The shell roughly doubles g-mode oscillation periods and would explain why there is no definitive detection of their periods. But the shell has only minor effects on most p-modes. The model provides a mechanism for causing short-term fluctuations in neutrino flux and makes plausible the correlations between this flux and solar activity levels. Relations are derived for a shell heated asymmetrically by transient increases in nuclear burning in small "hot spots." The size of these spots and the timing of a heating event are governed by sets(ell) of standing asymptotic g-modes, coupled by a maximal principle that greatly enhances their excitation and concentrates power toward the equator, assisting the detection of higher-ell sets. Signals from all sets, except one, in the range 2 <= ell <= 8 are identified by difference periods between consecutive radial states using the method of Garcia et al. and reinterpreting their latest spectrum. This confirms two detections of sets in a similar range of ell by their rotation rates. The mean radius of shell mixing is rm = 0.16 R sun, which improves an earlier independent estimate of 0.18 by the author. The shell may cause the unexplained dip in measured sound speed at its location. Another sound speed error, centered near 0.67 R sun, and reversing flows in the same place with a period originally near 1.3 yr suggest that the g-modes are depositing there about 3% of the solar luminosity. That implies the shell at rm is receiving a similar magnitude of power, which would be enough energy to mix the corresponding shell in a standard solar model in Lt107 yr. Title: Correspondence between Solar Variability (0.6 - 7.0 Years) and the Theoretical Positions of Rotating Sets of Coupled g Modes Authors: Juckett, David A.; Wolff, Charles L. Bibcode: 2009SoPh..257...13J Altcode: Recently, Juckett and Wolff (Solar Phys.252, 247, 2008) showed that the timing and longitude of sunspot patterns has some correspondence with a model based on coupled g modes. The model maximizes the nonlinear coupling of those g modes sharing harmonic degree ℓ to generate a "set(ℓ)" that assists its own excitation by locally enhancing nuclear burning. Each set(ℓ) has oscillatory power concentrated at two longitudes, on opposite sides of the Sun and drifts slowly retrograde within the radiative zone (RZ) at a rate that depends on ℓ. When the strong longitudes of two or more sets overlap, wave dissipation adds extra energy to that locality at the base of the convective envelope increasing convection and then sunspot activity. We compare the main subdecadal sunspot frequencies with the intersections of sets derived from ℓ=2 - 11 and G, where G represents unresolvable high-ℓ modes that rotate similarly to the RZ. After determining the set(ℓ) spatial phases, we show that 17 subdecadal oscillations with periods in the range 0.6 to 7.0 years (4.5 to 50 nHz), generated by 23 unique intersections of the 11 sets, are synchronous with 17 corresponding frequencies in the sunspot time series. After optimizing parameters, we find a mean correlation of 0.96 for synchrony among the 17 waveform pairs. These 17 frequencies constitute the bulk of the non-noise subdecadal frequency domain of the sunspot variation. We conclude that the sunspot series contains oscillatory components with the same temporal phases and frequencies as various set(ℓ) intersections spanning the past ≈ 100 years. This additional evidence for the role of coupled g modes in sunspot dynamics suggests that more of sunspot variability can be understood with nonmagnetic fluid mechanics than popularly thought. Title: Evidence for Long-term Retrograde Motions of Sunspot Patterns and Indications of Coupled g-mode Rotation Rates Authors: Juckett, David A.; Wolff, Charles L. Bibcode: 2008SoPh..252..247J Altcode: 2008SoPh..tmp..168J Solar g-modes are global oscillations that would exist primarily in the radiative zone (RZ) and would be excited by either convective overshoot or nuclear burning in the core. Wolff and O'Donovan (Astrophys. J.661, 568, 2007) proposed a non-linear coupling of g-modes into groups that share the same harmonic degree ℓ. Each group (denoted set(ℓ)) exhibits a unique retrograde rotation rate with respect to the RZ that depends mainly on ℓ. The coupling yields a standing wave (nearly stationary in longitude) that has two angularly defined hot spots offset from the equator on opposite sides of the Sun that would deposit energy asymmetrically in the lower convective envelope (CE). It is anticipated that when two or more groups overlap in longitude, an increase in local heating would influence the distribution of sunspots. In this paper, we scanned a multitude of rotational reference frames for sunspot clustering to test for frames that are concordant with the rotation of these g-modes sets. To achieve this, spherical harmonic filtering of sunspot synoptic maps was used to extract patterns consistent with coalesced g-modes. The latitude band, with minimal differential rotation, was sampled from each filtered synoptic map and layered into a stackplot. This was progressively shifted, line-by-line, into different rotational reference frames. We have detected long-lived longitudinal alignments, spanning 90 years of solar cycles, which are consistent with the rotation rate of the deep solar interior as well as other rotational frames predicted by the coupled g-mode model. Their sidereal rotation rates of 370.0, 398.8, 412.7, 418.3, 421.0, 424.2 and 430.0 nHz correspond, respectively, to coupled g-modes for ℓ = 2 through 7 and G, where G is a set with high ℓ values or a group of such sets (unresolved) that rotate almost as fast as the RZ. While the clustering in these reference frames offers new approaches for studying the longitudinal behavior of solar activity, it tentatively leads to the more profound conclusion that a portion of the driving force for sunspot occurrence is linked to energy extracted from the solar core and deposited at the top of the RZ by solar g-modes. Title: The QBO as potential amplifier and conduit to lower altitudes of solar cycle influence Authors: Mayr, H. G.; Mengel, J. G.; Wolff, C. L.; Huang, F. T.; Porter, H. S. Bibcode: 2007AnGeo..25.1071M Altcode: In several papers, the solar cycle (SC) effect in the lower atmosphere has been linked observationally to the Quasi-biennial Oscillation (QBO) of the zonal circulation. Salby and Callaghan (2000) in particular analyzed the QBO wind measurements, covering more than 40 years, and discovered that they contain a large SC signature at 20 km. We present here the results from a study with our 3-D Numerical Spectral Model (NSM), which relies primarily on parameterized gravity waves (GW) to describe the QBO. In our model, the period of the SC is taken to be 10 years, and the relative amplitude of radiative forcing varies exponentially with height, i.e., 0.2% at the surface, 2% at 50 km, and 20% at 100 km and above. Applying spectral analysis to identify the SC signature, the model generates a relatively large modulation of the QBO, which reproduces the observations qualitatively. The numerical results demonstrate that the QBO modulation, closely tracking the phase of the SC, is robust and persists at least for 70 years. The question is what causes the SC effect, and our analysis shows that four interlocking processes are involved: (1) In the mesosphere at around 60 km, the solar UV variations generate in the zonal winds a SC modulation of the 12-month annual oscillation, which is hemispherically symmetric and confined to equatorial latitudes like the QBO. (2) Although the amplitude of this equatorial annual oscillation (EAO) is relatively small, its SC modulation is large and extends into the lower stratosphere under the influence of, and amplified by, wave forcing. (3) The amplitude modulations of both EAO and QBO are essentially in phase with the imposed SC heating for the entire time span of the model simulation. This indicates that, due to positive feedback in the wave mechanism, the EAO apparently provides the pathway and pacemaker for the SC modulation of the QBO. (4) Our analysis demonstrates that the SC modulations of the QBO and EAO are amplified by tapping the momentum from the upward propagating gravity waves. Influenced and amplified by wave processes, the QBO thus acts as conduit to transfer to lower altitudes the larger SC variations in the UV absorbed in the mesosphere. Our model produces in the temperature variations of the QBO and EAO measurable SC modulations at polar latitudes near the tropopause. The effects are apparently generated by the meridional circulation, and planetary waves presumably, which redistribute the energy from the equatorial region where the waves are very effective in amplifying the SC influence. Title: Soliton Properties of Coupled g-Mode Oscillations Authors: Wolff, Charles L. Bibcode: 2007AAS...210.4505W Altcode: 2007BAAS...39..160W Several features typical of solitons are also exhibited by stellar g-modes when coupled into families that maximize the release of nuclear energy. Each family is held together against dispersion of its members by enhanced nuclear burning in small portions of the stellar core where amplitudes reach nonlinear levels. Since each family has a different rotation rate somewhat slower than the star, its nonlinear regions drift past those of others causing complex interactions (shown in a video). Yet each region emerges from this with its original wave form. Other similarities with solitons are mentioned, including the physical origin of a phase shift in longitude due to the interaction. These similarities suggest that a fully nonlinear derivation of g-mode sets may be able to show that their large amplitude regions approach true solitons. Title: Coupled Groups of g-Modes in a Sun with a Mixed Core Authors: Wolff, Charles L.; O'Donovan, Adam E. Bibcode: 2007ApJ...661..568W Altcode: Groups of linear g-modes can sum to create nonlinear motion in small ``hot volumes'' (diameter ~10 Mm) near the solar center that help drive the modes. We explore the consequences of coupling only in the hot volumes where the time-averaged rate of 3He burning can double if temperature oscillations exceed 10%. Anticipating large local motions in the core, we impose a mixed shell r=(0.10+/-0.03) Rsolar on an otherwise standard solar model before computing g-mode solutions. Mixing is rapid (<<106 yr) in this shell, with slower mixing somewhat beyond. If l is the principal spherical harmonic index, a set of g-modes for any single l<=5 with six consecutive radial harmonics can be excited with nearly linear thermal amplitudes AT<=0.05 throughout the star. But far smaller thresholds for excitation are actually expected when sets for many values of l can be computed simultaneously. This is a new kind of stellar instability whose effectiveness rises with the number of active modes. Each set rotates rigidly and maximizes the release of nuclear energy from its hot volumes. There is some evidence for their rotation rates in the long solar activity record. The upward wave flux powered by the hot volumes has also been suggested to explain the 1.3 yr reversing flows tentatively detected below the Sun's convective envelope. An analog using uncoupled modes is also investigated based on an observation that indicates g-mode activity up to l~=20. If all modes in that range had linear amplitudes of only AT~=0.0015, their combined effect would give positive growth rates to dozens of low harmonic g-modes. Title: QBO as potential amplifier of solar cycle influence Authors: Mayr, Hans G.; Mengel, John G.; Wolff, Charles L.; Porter, Hayden S. Bibcode: 2006GeoRL..33.5812M Altcode: The solar cycle (SC) effect in the lower atmosphere has been linked observationally to the quasi-biennial oscillation (QBO) of the zonal circulation. Salby and Callaghan (2000) in particular analyzed the QBO covering more than 40 years and found that it contains a large SC signature at 20 km. We discuss a 3D study in which we simulate the QBO under the influence of the SC. For a SC period of 10 years, the relative amplitude of radiative forcing is taken to vary with height: 0.2% (surface), 2% (50 km), 20% (100 km and above). This model produces in the lower stratosphere a relatively large modulation of the QBO, which appears to come from the SC and qualitatively agrees with the observations. The modulation of the QBO, with constant phase relative to the SC, is shown to persist at least for 50 years, and it is induced by a SC modulated annual oscillation that is hemispherically symmetric and confined to low latitudes (Mayr et al., 2005). Title: Wave-driven equatorial annual oscillation induced and modulated by the solar cycle Authors: Mayr, Hans G.; Mengel, John G.; Wolff, Charles L. Bibcode: 2005GeoRL..3220811M Altcode: Our 3-D model for the solar cycle (SC) effect on the QBO (H. G. Mayr et al., The QBO as potential amplifier of solar cycle influence, submitted to Geophysical Research Letters, 2005, hereinafter referred to as Mayr et al., submitted manuscript, 2005) produces a hemispherically symmetric 12-month Annual Oscillation (AO) in the zonal winds, which is largely confined to low latitudes. This Equatorial Annual Oscillation (EAO) is generated through nonlinear interaction between the dominant anti-symmetric AO and the anti-symmetric component of the SC response. Due to wave-mean-flow interaction from small-scale gravity waves (GW), the SC-modulated EAO is amplified and propagates down through the stratosphere as does the QBO. The amplitude of the EAO is relatively small, but its SC modulation is large and is in phase with that of the QBO. Although the EAO is concentrated at low latitudes, prominent signatures appear in the polar regions where the SC produces measurable temperature variations. At lower altitudes, the GW-driven downward propagation of the EAO affects the phase of the annual cycle and causes the SC effect to be different in the two hemispheres. Title: The Sun's Reversing Flows and Heat Spike as Caused by g-Modes Authors: Wolff, Charles L.; Mayr, Hans G. Bibcode: 2004ApJ...606L.163W Altcode: The reversing east-west flows centered near 0.675 Rsolar have not been explained by gravity waves from the convection zone because suitable wavelengths do not penetrate deeply enough to drive the observed flow. An alternative is explored using g-modes, many of whose rotation rates have already been detected. Simple formulas for the radial drift of the flow and for angular momentum transfer from asymptotic g-modes are expressed in terms of local oscillation amplitudes and dissipation rates. The main loss mechanism is horizontal turbulence caused by the flow. It exceeds that due to gravity waves for which Schatzman estimated a diffusivity ~108 m2 s-1. Our proposed flow has a peak zonal speed of 50 m s-1, consistent with the observations at current resolving power. An array of g-modes with amplitudes near the detectable limit at the solar surface can cause the flow to replace itself about every 1.3 yr, as observed, if there are ~103 high harmonic modes. Since the flow occupies the same thin layer where the sound speed is anomalous, heat dissipated in driving the flow acts to reduce that solar modeling error. Title: Rotational Sequences of Global Oscillations inside the Sun Authors: Wolff, Charles L. Bibcode: 2002ApJ...580L.181W Altcode: A very simple mathematical sequence is detected in a half-century of thermal radio flux from the Sun. Since the only known solar source for the sequence is global oscillations trapped in the nonconvecting interior, g-modes and probably r-modes are active. If so, their rotation frequencies are detected and some previously reported difference frequencies are confirmed with high confidence. All angular harmonics for 2<=l<=7 are detected as well as some others up to the limit l<=14 resolvable by the observations (a Fourier spectrum of the 10.7 cm flux time series). The mean sidereal rotation rate of the nonconvecting interior is 428.2 nHz as averaged by g-modes and 429.8 nHz by the r-modes, indicating that g-mode energy is a bit more centrally concentrated. Helioseismology measures such rotation rates near 0.36R (R = solar radius), so the global modes would have about half their kinetic energy above and below that level. This, and the known log (r) energy dependence of most modes, implies that these oscillations are significantly reflected near 0.18R, the same level at which sound speed measurements display a maximum departure from theoretical models. Title: Model of Wave Driven Flow Oscillation for Solar Cycle Authors: Mayr, H. G.; Wolff, C. L. Bibcode: 2001AGUSM..SP31A16M Altcode: At low latitudes in the Earth's atmosphere, the observed zonal flow velocities are dominated by the semi-annual and quasi-biennial oscillations with periods of 6 months and 20 to 32 months respectively. These equatorial oscillations, the SAO and QBO respectively, are driven by wave-mean flow interactions due to upward propagating planetary-scale waves (periods of days) and small-scale gravity waves (periods of hours). We are proposing (see also Mayr, Wolff, Hartle, GRL, 28, 2001) that such a mechanism may drive long period oscillations (reversing flows) in stellar and planetary interiors, and we apply it to the Sun. The reversing flows would occur below the convective envelope where waves can propagate. We apply a simplified, one dimensional, analytical flow model that incorporates a gravity wave parameterization due to Hines (1997). Based on this analysis, our estimates show that relatively small wave amplitudes < 10 m/s can produce zonal flow amplitudes of 20 m/s, which should be sufficient to generate the observed variations in the magnetic field. To produce the 22-year period of oscillation, a low buoyancy frequency must be chosen, and this places the proposed flow in a region that is close to (and below) the base of the convective envelope. Enhanced turbulence associated with this low stability should help to generate the dynamo currents. With larger stability at deeper levels in the solar interior, the model can readily produce also oscillations with much longer periods. To provide an understanding of the fluid dynamics involved, we present numerical results from a 2D model for the terrestrial atmosphere that exemplify the non-linear nature of the wave interaction for which a mechanical analog is the escapement mechanism of the clock. Title: Wave driven non-linear flow oscillator for the 22-year solar cycle Authors: Mayr, Hans G.; Wolff, Charles L.; Hartle, Richard E. Bibcode: 2001GeoRL..28..463M Altcode: In the Earth's atmosphere, a zonal flow oscillation is observed with periods between 20 and 32 months, the Quasi Biennial Oscillation. This oscillation does not require an external time dependent source but is maintained by non-linear wave momentum forcing. We propose that such a mechanism also drives long-period oscillations in planetary and stellar interiors, and we apply it here to generate a flow oscillation for the 22-year solar cycle. The oscillation would occur just below the convective envelope—in a region where gravity waves can propagate. We present results from a simplified analytical model that incorporates Hines' gravity wave parameterization. Wave amplitudes <10 m/s can produce reversing zonal flows of 20 m/s that should be sufficient to generate a corresponding oscillation in the poloidal magnetic field. The low buoyancy frequency and associated increase in turbulence help produce the desired oscillation period of the flow and should help generate the currents for the reversing magnetic field. Title: Linear r-Modes below the Sun's Convective Envelope Authors: Wolff, Charles L. Bibcode: 2000ApJ...531..591W Altcode: Theoretical properties of linear r-modes in a standard solar interior are computed, and the excitation of some by convective overshoot is estimated. The modes oscillate in a resonant cavity usually occupying most of the nonconvecting interior. Most modes concentrate their kinetic energy toward the center of the Sun. Over half the energy usually lies below 0.15 Rsolar with an asymptotic limit of 0.11 Rsolar for high radial harmonics (Rsolar is the solar radius). The oscillation frequencies are very close to the well-known toroidal frequency, σt=2Ωm[l(l+1)]-1, deviating by fractional amounts ~10-6+/-1 which are roughly 3 orders of magnitude smaller than deviations found earlier for r-modes in convective layers. An explicit formula for the ratio of divergent motion to curl motion is derived. It shows how rapidly the compressible component changes as a function of r. Compressibility is only ~10-6 of the total motion for low l-modes and declines proportionally to ml-3 for high l. A small subset of modes (the lowest radial harmonic of angular states |m|=l) avoid the core which makes them sensitive to convective overshoot. Just one of the giant convection cells detected by Beck et al. can excite such modes to kilometer-size amplitudes with the possibility that far larger displacement amplitudes can accumulate in the mode over time if the interaction between cells and r-modes is found to be strong. Title: Linear r-Mode Oscillations in a Differentially Rotating Star Authors: Wolff, Charles L. Bibcode: 1998ApJ...502..961W Altcode: Differential rotation of a stellar envelope lifts the degeneracy of r-mode rotation rates and can prohibit some modes. It also reduces the physical distinction between the two branches of r-modes: slow (retrograde) and fast (geostrophic). One mode in each branch is dominated by a given spherical harmonic (l, m), and, for increasing rotational shear in the star, their characteristics approach each other until both modes simultaneously cease to exist. Only about half of the 60 r-modes with l <= 5 and a given radial harmonic can survive as global, linear modes in the Sun. Each of these has at least 70%, and typically 90%, of its energy in a single toroidal component of motion. Among solar survivors are all modes where | m | = l > 1. All results apply to linear, adiabatic oscillations of a spherical fluid shell exhibiting steady, axisymmetric rotation, Ω(r, θ). Since terms ~Ω2 are small in the Sun, spheroidal motions are neglected. A generalization of classical perturbation theory was used to treat ``perturbations'' of large size and to avoid the need for special treatment of oscillation frequencies that are zero or degenerate. Title: Large Convective Events and Their Aftermath in a Rotating Star Authors: Wolff, Charles L. Bibcode: 1997ApJ...486.1058W Altcode: The 35 most exceptional, deep convective events that have occurred since the year 1750 are identified using Fj, an index of solar activity. The average event lasted 38 days and was followed by several years of lesser eruptions in a repeatable time sequence. This contradicts the common assumption that stellar convection is random. Deep convective events, which have lifetimes comparable to the stellar rotation period, will accumulate a net azimuthal motion relative to the ambient fluid. In the Sun, the rising portion of such an event moves in longitude ~1° day-1 as it partially conserves initial angular momentum. Its kinetic energy, ~1029 J, in azimuthal motion amounts to a pulse that is available to excite global oscillations (r-modes). Following the pulse, signatures of r-modes can be traced for 1000 days in the lesser solar eruptions, which is evidence that the r-modes are causing or modulating convection. A successful, nonlinear model of this is constructed in which magnetic fields play no role. Title: Convection: Periodic Due to r-Modes Authors: Wolff, Charles L. Bibcode: 1996ApJ...459L.103W Altcode: Convection in a rotating fluid can acquire a periodic component where the convective timescale becomes comparable to or longer than the rotation period. Then, each local convective event becomes a source of Rossby-like oscillations. They carry off information that, in a spherical shell, can sum much later to stimulate an echo of the initial convective event. The two series of echos most likely to be detectable occur at intervals of six and 30 rotation periods and apply to events of large horizontal size. The waves can also impose other periodicities on the convection, and about a dozen in the range 75--800 days are clearly identified by comparing known regularities in solar activity with theoretical beat frequencies of global oscillations (r-modes). Title: Oscillation-Convection Coupling: Cause of Supergranulation? Authors: Wolff, C. Bibcode: 1995ApJ...443..423W Altcode: A semianalytic method is derived for dealing simultaneously with large numbers of linear stellar oscillation modes trapped in a cavity (a shell) of fluid which is rotating and convecting. A simple generalization of mixing-length theory shows how convection is modulated by weak rotational effects and by the horizontal wind fields of linear r-mode oscillations. The modulated convection is then used to compute the energy lost to turbulent viscosity by a family of nondegenerate oscillations. Viscosity terms of fourth degree in the wind shear can be included if they are a perturbation affecting only a small portion of the r-mode. Viscous energy loss strengthens convection in a narrow layer near the base of the H and He ionization zone. In the Sun, this layer is about 7 Mm thick and centered at 0.932 of a solar radius where convection cells have a typical size of about 20 Mm and a lifetime of 0.3 Ms, both similar to what is observed in supergranules. If the rms velocity of r-modes at the surface exceeds 5 m/s, then energy is deposited inside the Sun at a sufficient rate to power the supergranulation and impose on it a weak latitude dependence. Title: Equidistribution of Energy and Other Quantities in Oscillating Systems Authors: Wolff, Charles L. Bibcode: 1993ApJ...414..892W Altcode: Energy of a high harmonic standing wave tends to be distributed equally over the whole wave even in a stratified medium where the wave's peak amplitude can be much larger near the upper boundary than the lower one. This fact is generalized to the many diverse physical problems which solve second-order differential equations of Sturm-Liouville type. For any such solution y(z) whose sign fluctuates along the z-axis, quantities are found which have the same value between any two neighboring zeros of y. One of the equidistributed quantities for an oscillating fluid sphere is similar to kinetic energy but is identical only in limiting cases. The acoustic midpoint of a cavity can be a unique place where some nonlinear perturbations have extra strength. This may apply to the puzzling solar phenomenon called supergranulation. Title: Solar Supergranulation: Driven by Solar Oscillations Authors: Wolff, C. L. Bibcode: 1993AAS...182.4802W Altcode: 1993BAAS...25..879W No abstract at ADS Title: `Intermittent' solar periodicities Authors: Wolff, Charles L. Bibcode: 1992SoPh..142..187W Altcode: The signal from a stable periodicity can seem to be intermittent when it is partially masked by an unmodelled window function or when the data set is too short to resolve closely spaced periodicities. By taking this into account, short-lived periodicities in solar data can be reinterpreted as evidence for continuously periodic behavior. The periodic sources are located in the solar interior and caused by global oscillation modes. The convective envelope acts as the window for these sources. Recent reports of seven periodicities from 100 to 1000 days are compared with this model. Precise long-term values for the periodicities are predicted and they agree closely with observations. Some elements are suggested that might explain the well-documented 155-day periodicity. Conventional filtering methods to suppress effects of the 11-year cycle are criticized as inadequate. Title: Solar irradiance observed from PVO and inferred solar rotation. Authors: Wolff, Charles L.; Hoegy, Walter R. Bibcode: 1990NASCP3086...57W Altcode: 1990cisv.nasa...57W Solar irradiance in the EUV has been monitored for 11 years by the Pioneer Venus Orbiter (PVO). Since the experiment moves around the Sun with the orbital rate of Venus rather than that of Earth, the measurement gives us a second viewing location from which to begin unravelling which irradiance variations are intrinsic to the Sun, and which are merely rotational modulations whose periods depend on the motion of the observer. The authors confirm an earlier detection, made with only 8.6 years of data, that EUV irradiance is modulated by rotation rates of two families of global oscillation modes. One family is assumed to be r-modes occupying the convective envelope and sharing its rotation, while the other family (g-modes) lies in the radiative interior which has a slower rotation. Measured power in r-modes of low angular harmonic number (l≤7) indicates that the Sun's envelope rotated about 0.7% faster near the last solar maximum (1979 thru 1982) than it did during the next rise to maximum (1986 thru 1989). No change was seen in the g-mode family of lines, as would be expected from the much greater rotational inertia of the radiative interior. Title: A seven-month solar cycle observed with the Langmuir probe on Pioneer Venus Orbiter Authors: Hoegy, W. R.; Wolff, C. L. Bibcode: 1989JGR....94.8663H Altcode: An approximately 7-month solar cycle has been observed in the photoelectron current measured by the Langmuir probe on Pioneer Venus Orbiter over the time period from 1979 through 1987. The probe photoelectron current, Ipe, is obtained when the spacecraft is outside the Venus ionosphere, and the measured current is due to photoelectron emission caused by EUV solar radiation in the wavelength range from about 30 nm to 121.6 nm. About one half of the Ipe is due to solar Lyman alpha emission. The Ipe data from mid-1984 through 1987 are dominated by a 7-month or 216-day cycle. Spectral analysis of the 1980-1988 data shows that this cycle dominates the spectrum for periods less than 300 days; the second most dominant cylce is at 155 days, a 5-month period. The Ipe data were spectrally analyzed with three different methods. The 2800-MHz radio flux, observed from Earth over the same time range, exhibits a similar 7-month cycle at about 234 days which is stronger than a 5-month (158-day) cycle. Solar Mesosphere Explorer (SME) Lyman alpha observations for the time period mid-1981 through mid-1988 also have cycles near 5 and 7 months. Since the 7-month and 5-month cycles are observed from Venus (Ipe) and from Earth (2800-MHz radio flux and SME Lyman alpha), the observations suggest that they are intrinsic frequencies, independent of the orbital frequency of the observer. The 7- and 5-month cycles are believed to be caused by long-lived flux enhancements from nonlinear interactions of global oscillation modes in the Sun's convective envelope (r modes) and radiative interior (g modes). Title: Periodic Solar Extreme Ultraviolet Flux Monitored Near Venus Authors: Wolff, Charles L.; Hoegy, Walter R. Bibcode: 1989SoPh..123....7W Altcode: A detector sharing the orbital rate of Venus has a unique perspective on solar periodicities. Fourier analysis of the 8.6 year record of solar EUV output gathered by the Langmuir probe on Pioneer Venus Orbiter shows the influences of global oscillation modes located in the convective envelope and in the radiative interior. Seven of the eight lowest angular harmonic r-mode families are detected by their rotation rates which differ almost unmeasurably from ideal theoretical values. This determines a mean sidereal rotation rate for the envelope of 457.9 ± 2.0 nHz which corresponds to a period of 25.3 days. Many frequencies are aliased at ± 106 nHz by modulation from the lowest angular harmonic r-mode in the envelope. The rotation of this mode seems slightly retrograde, -1.5 ± 2.0 nHz, but small positive values are not excluded. We confirm that the rotation of the radiative interior, 381 nHz, is slower than the envelope by detecting g-mode frequencies for angular harmonics, 2 ≤ l ≤ 6, and a possible first detection of the rotation rate for the l = 1 case. Solar EUV lacks the sudden darkenings (dips) shown by visible irradiance; vortex cores in the photosphere and below are again suggested as a possible explanation. Title: Angular Momentum of Stellar Oscillations, and Stellar Rotation Authors: Wolff, C. L. Bibcode: 1989BAAS...21..745W Altcode: No abstract at ADS Title: Solar Irradiance Change and Special Longitudes Due to γ -Modes Authors: Wolff, Charles L.; Hickey, John R. Bibcode: 1987Sci...235.1631W Altcode: Sluggish global oscillations, having a periodicity of months and trapped in the sun's convection zone, modulate the amount of energy reaching Earth and seem to impose some large-scale order on the distribution of solar surface features. These recently recognized oscillations (γ -modes) increase the predictability of solar changes and may improve understanding of rotation and variability in other stars. Most of the 13 periodicities ranging from 13 to 85 days that are caused by γ -modes can be detected in Nimbus 7 observations of solar irradiance during 3 years at solar maximum. These modes may also bear on the classical question of persistent longitudes of high solar activity. Title: Multiperiodic Irradiance Changes Caused by R-Modes and G-Modes Authors: Wolff, Charles L.; Hickey, John R. Bibcode: 1987SoPh..109....1W Altcode: More than 20 real periodicities ranging from 20 days to 2 years modulate the solar irradiance data accumulated since November 1978 by Nimbus 7. Many are quite strong during the first three years (solar maximum) and weak after that. There is a high correspondence between periods in irradiance and 28 periods predicted from the rotation and beating of global solar oscillations (r-modes and g-modes). Angular states ℓ = 1, 2, and 3 are detected as well as some unresolved r-mode power at higher ℓ. The prominence of beat periods implies a nonlinear system whose effective nonlinear power was measured to be about 2. This analysis constitutes a detection of r-modes in the Sun and determines from them a mean sidereal rotation rate for the convective envelope of 459 ± 4 nHz which converts to a period of 25.2 days (27.ld, synodic). Title: R-mode oscillations in the sun Authors: Blizard, Jane B.; Wolff, Charles L. Bibcode: 1987LNP...274..318B Altcode: 1987stpu.conf..318B The relationship between solar r-modes (long-period oscillations dominated by the Coriolis force) and solar activity cycles is investigated statistically. FFT power spectra of the daily Zurich sunspot numbers (R) and of the Greenwich Photoheliographic projected whole sunspot area (A) are obtained for the high-activity years of solar cycles 14 through 21. Both R and A are found to exhibit periods of 22 + or - 1 d, 34 + or - 1.5 d, and 43 + or - 2 d, corresponding to r-modes with (l,m) angular harmonics (2,2), (3,1), and (2,1), respectively. Title: Short Periods in the Power Spectrum of Sunspot Number - 16-DAYS to One-Year and R-Mode Oscillations on the Sun Authors: Blizard, J. B.; Wolff, C. L. Bibcode: 1986PASP...98.1100B Altcode: No abstract at ADS Title: r-Modes Influencing the Solar Irradiance Authors: Wolff, C. L. Bibcode: 1986BAAS...18..933W Altcode: No abstract at ADS Title: Properties of R-Modes in the Sun Authors: Wolff, C. L.; Blizard, J. B. Bibcode: 1986SoPh..105....1W Altcode: Global oscillations of the Sun (r-modes) with very long periods ∼ 1 month are reviewed and studied. Such modes would be trapped in an acoustic cavity formed either by most of the convective envelope or by most of the radiative interior. A turning point frequency giving cavity boundaries is defined and the run of eigenvalues for angular harmonics l ≤ 3 are plotted for a conventional solar convection zone. The r-modes show equipartition of oscillatory energy among shells which each contain one antinode in the radial dimension. Toroidal motion is dominant to at least the 14th radial harmonic mode. Viscosity from convective turbulence is strong and would damp any mode in just a few solar rotations if it were the only significant nonadiabatic effect. `Radial fine splitting' which lifts the degeneracy in n is very small (20 nHz or less) for all n ≤ 14 trapped in the envelope. But, if splitting could be detected, we would have a valuable new constraint on solar convection theories. Title: Solar Irradiance &g-modes Authors: Wolff, C. L.; Hickey, J. R. Bibcode: 1984BAAS...16..978W Altcode: No abstract at ADS Title: Solar irradiance changes caused by g-modes and large scale convection Authors: Wolff, C. L. Bibcode: 1984SoPh...93....1W Altcode: Solar irradiance measurements from the ACRIM experiment show a clear response to the rotation periods of g-mode oscillations (l = 1, 2, and 3) and their first harmonics. Peaks in the ACRIM spectrum at 16.6, 18.3, 20.7, 36.5, and ≃- 71 days all lie within about 1% of periods arising from g-mode rotation. This means that the g-modes are a fundamental cause of irradiance fluctuations. On time scales of months and less they modulate the irradiance by means of transient flows of global scale which they stimulate in the Sun's convective envelope. Dimensional arguments indicate that the flows carry up heat at an average rate ∼ 10-3L⊙ which is not in conflict with observed changes in the irradiance. Five additional tests for g-modes and large-scale convection are given. An instability is described which undermines diffusion models of sunspot energy storage. Title: On the clock mechanisms and the implausibility of the 35 day precessing disk in HZ Herculis/Hercules X-1. Authors: Kondo, Y.; van Flandern, T. C.; Wolff, C. L. Bibcode: 1983ApJ...273..716K Altcode: The concept of the precessing accretion disk in HZ Her/Her X-1 in its varied forms, to account for the 35 day periodicity in the X-ray flux, has met many objections from a number of workers on various grounds, but it is still being invoked in current publications. These objections are reviewed and additional arguments are presented against the precessing accretion disk model. The implausibility of the disk models is demonstrated. An alternate clock mechanism, based on nonlinear oscillations in the normal star, which provides the modulation of the mass flow is discussed. Title: Solar Irradiance, g-modes, and Convection Authors: Wolff, C. L. Bibcode: 1983BAAS...15..950W Altcode: No abstract at ADS Title: The rotational spectrum of g-modes in the sun Authors: Wolff, C. L. Bibcode: 1983ApJ...264..667W Altcode: Observations and calculations are presented which strongly suggest that the unique sequence of rotation rates due to g-modes is active in the sun. It is found that all angular harmonics from 1 = 2-11 appear to be resolved, while higher harmonics up to at least 1 = 20 also seem to be active. The extreme narrowness of many of the spectral lines indicates that the g-modes are locked in sets of constant 1 by a local mechanism which excites the modes and possibly regulates the long-term precision of their rotation. These sets act as a system of resonant, or nearly resonant, clocks which impose a degree of periodicity upon solar activity and measure the mean solar interior rotation Title: Turbulent compressible convection in a deep atmosphere. I. Preliminary two-dimensional results. Authors: Chan, K. L.; Sofia, S.; Wolff, C. L. Bibcode: 1982ApJ...263..935C Altcode: The turbulent convection of a compressible fluid in a deep atmosphere is simulated by two-dimensional numerical computations, displaying coexisting 'cells' whose sizes range from the total depth of the convection zone to the smallest scale height at the top. While the largest cells traverse the entire zone, smaller ones are clustered near the top. The vertical correlation length of the vertical velocity is proportional to the local pressure or density scale height, in a way reminiscent of the concept of mixing length. Title: Is the "Mixing Length" Physically Meaningful? Authors: Chan, K. L.; Sofia, S.; Wolff, C. L. Bibcode: 1982BAAS...14Q.665C Altcode: No abstract at ADS Title: Synoptic studies of chromospheric variability in F - K dwarfs with the IUE. Authors: Hallam, K. L.; Wolff, C. L.; Sewall, J. R. Bibcode: 1982NASCP2238..227H Altcode: 1982auva.nasa..227H; 1982NASCP2338..227H; 1982IUE82......227H Time-sequential series of IUE spectra for ten F, G and K dwarfs were obtained in 1980 and 1981 to study the rotational dependence of chromospheric flux in the ultraviolet. An interactive computational method using unbiased estimators was developed to measure emission line fluxes free of arbitrary judgement concerning the behavior of the underlying spectrum and shapes of the line profiles. Due to the limited number of observational samples per star, we have used special techniques to analyze the sparsely and anharmonically sampled emission line flux data. Two different autocorrelation measures were computed for each emission line as a function of temporal frequency. Examples and results of this analysis now in progress are given for several stars. Title: Rotation of dwarf star chromospheres in the ultraviolet. Authors: Hallam, K. L.; Wolff, C. L. Bibcode: 1981ApJ...248L..73H Altcode: Periodic variations in the ultraviolet fluxes of chromospheric emission line multiplets are investigated for F, G and K stars as evidence of rotational modulation. Vacuum ultraviolet spectra were obtained with the IUE spacecraft for six stars as many as 11 times over the period April 23 to December 3, 1980. Variations in the emission fluxes of the hydrogen Lyman-alpha, Si II and Mg II lines are observed with periods up to 47 days. The periodicity, which is identified with rotational modulation, is found to persist over many rotational cycles, although the periods and time dependences of the fluxes from the different ionic species are not identical, probably due to differential rotation and global distributions. The spread of the UV periods is observed to be within 10%, with one or two peaks per cycle and a ratio of modulated to umodulated flux ranging from 1.1 to 3.0, analogous to solar behavior. Title: A variable mixing-length ratio for convection theory Authors: Chan, K. L.; Wolff, C. L.; Sofia, S. Bibcode: 1981ApJ...244..582C Altcode: It is argued that a natural choice for the local mixing length in the mixing-length theory of convection has a value proportional to the local density scale height of the convective bubbles. The resultant variable mixing-length ratio (the ratio between the mixing length and the pressure scale height) of this theory is enhanced in the superadiabatic region and approaches a constant in deeper layers. Numerical tests comparing the new mixing length successfully eliminate most of the density inversion that typically plagues conventional results. The new approach also seems to indicate the existence of granular motion at the top of the convection zone. Title: Large Scale Order in the Sun Authors: Wolff, C. L. Bibcode: 1981BAAS...13..878W Altcode: No abstract at ADS Title: The collective excitation of g-modes in the sun Authors: Wolff, C. L. Bibcode: 1980LNP...125..252W Altcode: 1980nnsp.work..252W Oscillations of the solar interior (linear g-modes) may be strongly driven by the collective influence of all the modes upon the nuclear reactions in the core. This heretofore neglected effect could couple the modes, reduce the effective amplitudes near the center, and spatially concentrate most of the oscillation energy into just a portion of the radiative interior. If operating at sufficient strength, this can reverse the conventional conclusion, drawn from single mode calculations, that almost all solar g-modes are damped. Furthermore, it would put the theory into rough harmony with three otherwise troubling observations: (1) the 'low' neutrino flux measured by Davis (1978), (2) the high correspondence found by Wolff (1976) between recurrence periods in solar activity and the rotational beat periods of g-modes, and (3) the fluctuations in the sun's diameter which imply g-mode activity at high angular harmonics (Hill and Caudell 1979). A nonlinear expression is derived for the local rate of work done on an array of oscillation modes by the nuclear reactions. Three additional tests of the model are suggested. Title: Some simple properties of stellar pulsation modes. Authors: Wolff, C. L. Bibcode: 1979ApJ...227..943W Altcode: Except for the lowest harmonics, small-amplitude stellar pulsation modes possess many simple properties whose evaluation does not require numerical integration of the fourth-order equations of motion. All antinodes tend to have the same total kinetic energy except for those lying near physical or geometric boundaries. However, when kinetic energy per unit volume is considered, order-of-magnitude enhancements are seen in antinodes lying near the center of the star, and factor-of-2 enhancements occur near the polar axis. The nodes are distributed very regularly along the radius. They follow an exponential law in g-regions, and their separation is proportional to the sound travel time in p-regions. A simple graphical procedure is described for surveying the oscillation frequencies of a new stellar model. A precise condition is derived giving the division of energy between radial and angular motion. Another condition gives the fractional contribution to the velocity field of its two sources, the divergence and the curl. Certain simplifying results of weak coupling among the linear modes are briefly described. Title: Hercules X-1 = HZ Herculis: a multiperiod variable? Authors: Wolff, C. L.; Kondo, Y. Bibcode: 1978ApJ...219..605W Altcode: Fundamental rotation properties of the free modes of oscillation of a star are employed to account for the various periodicities observed in the X-ray binary system HZ Her/Her X-1. The various rotation rates may be taken as defining a set of beat periods associated with the quasiregular flareups of HZ Her. This analysis, involving only one free parameter, provides a single physical mechanism to explain five observed periods of the binary system, including periods of 1.7 days, 35 days and 10 to 12 years. Title: White-dwarf variability and the rotation g-modes. Authors: Wolff, C. L. Bibcode: 1977ApJ...216..784W Altcode: The multiperiodic behavior clearly evident after Fourier analysis of many DA white-dwarf light curves is interpreted as arising from outbursts whose timing is regulated by the rotation and oscillation of the star. A model is proposed on the basis of three main assumptions: (1) a broad array of g-mode oscillations is taking place all the time in DA white-dwarf variables; (2) slow rotation permits most of the g-modes to couple and form a small group of nonlinear modes, each characterized by one of the indices of the spherical harmonic functions involved; and (3) the observed brightenings of the star are produced by upwelling of convection on a large horizontal scale when the antinodes of the nonlinear oscillation patterns periodically rotate into alignment and cause a temporary local enhancement of energy per unit volume. This model is used to match precisely almost every strong periodicity observed in the complex light curves of the DA white dwarfs G207-9, G38-29, G29-38, and HL Tau 76. If the model has been applied correctly, the results indicate that all four of these variables are rotating slowly with periods in the range from 250 to 500 sec. Title: White Dwarf Variable Stars and Their Oscillations. Authors: Wolff, C. L. Bibcode: 1976BAAS....8Q.558W Altcode: No abstract at ADS Title: Timing of solar cycles by rigid internal rotations. Authors: Wolff, C. L. Bibcode: 1976ApJ...205..612W Altcode: The so-called 11-year cycle of solar activity is really more complex and contains many periods of greatly different lengths. Periods as long as 178 years and as short as 3.1 years are predicted by a theory based on beats between rigidly rotating, inertially oscillating g-modes inside the sun. Most of the beat periods are then confirmed to about 1 percent accuracy in sunspot observations. Since the agreement is of high statistical significance, one can conclude that approximate alignment of major solar oscillation modes contributes to high solar activity. The theory receives further support when tested against an independent class of observations - the large-scale magnetic sector structure. Predicted rotation rates of at least four solar oscillation modes are detected in the sector data with discrepancies all less than 0.3 percent. As a by-product of these successful fits to observation, the mean rotation of the entire solar mass becomes known. Its rotation frequency is 4.49 by 10 to the -7th power Hz, which is a sidereal period of 25.8 days. Magnetic fields have played no role in calculating the length of any of these solar cycles. Title: Interplanetary gas. XXI. Validity of the Chapman-Enskog description of the solar wind for protons. Authors: Price, J. C.; Brandt, J. C.; Wolff, C. L. Bibcode: 1975ApJ...199..756P Altcode: Measured velocity distribution functions for solar-wind protons are used to estimate the validity of the Chapman-Enskog description, and it is found to be the best description presently in use. Subject headings: interplanetary medium - solar wind Title: An Anticorrelation between Polar and Equatorial Rotation of the Solar Photosphere Authors: Wolff, C. L. Bibcode: 1975SoPh...41..297W Altcode: Published spectroscopic measurements of solar rotation are analyzed to show that when the rotation velocity increases at high latitudes it tends to decrease at low latitudes, and conversely. The high latitude velocities typically vary over only 20% of the range of those near the equator and the smallest variations of all occurred near latitude 60° during the rising portion of the previous solar cycle. The anticorrelation is consistent with a recent suggestion that differential rotation on the sun arises from photospheric wind systems whose strength is determined, ultimately, by oscillations within the Sun. Title: An Anticorrelation Between Polar &Equatorial Rotation Rates Authors: Wolff, C. L. Bibcode: 1975BAAS....7..364W Altcode: No abstract at ADS Title: Rigid and differential rotation driven by oscillations within the sun. Authors: Wolff, C. L. Bibcode: 1974ApJ...194..489W Altcode: Long-period oscillations involving the entire mass of the sun rotate like rigid bodies, and their oscillatory power is distributed nonuniformly across the solar surface. A mostly qualitative theory is constructed showing how the oscillations drive convective flows of global scale, which then organize photospheric and coronal magnetic fields into patterns which rotate rigidly. The convection rises along long graceful curves, creating the magnetic-arcade structures in the corona and unipolar photospheric regions on each side by dynamo action. These are thought to be the origin of the sector structure in the solar wind. The rigid patterns of convective upwelling also force nonrigid horizontal winds on the solar surface. Under the action of the Coriolis force, the main horizontal motions are converted into polar and equatorial wind currents which have the proper directions to drive the differential rotation long observed on the sun's surface. Title: Distinctive patterns on the surface of two slowly rotating stars whose oscillations are nonlinearly coupled. Authors: Wolff, C. L. Bibcode: 1974ApJ...193..721W Altcode: Slowly rotating stars which are oscillating at small amplitude in a broad spectrum of g-modes should display strong surface nonuniformities if even weak nonlinear coupling exists between the modes. Oscillatory power will be concentrated into distinctive patterns which rotate rigidly in spite of differential rotation in the outer stellar layers. Each pattern rotates at a constant rate slower than the star as a whole according to a very simple law of rotation. Virtually all the rotation rates are within 9 per cent of the stellar rate. Evidence is cited that the sun may be oscillating, so other stars along the main sequence may be oscillating, also. If zones obeying the predicted rotation law can be detected in a star, then the rotation rate of the stellar interior becomes known, and differential rotation is negligible over most of the stellar mass. Title: What is the Horizontal Scale of the 5-min Oscillations? Authors: Wolff, Charles L. Bibcode: 1973SoPh...32...31W Altcode: If wrong, all the early reports of a small horizontal scale (≈ 2000 km) for the 5-min oscillations may be due to unfortunate similarities between the velocity and overturning time of the solar granule convection and the corresponding velocity and period typical of the oscillations. A large horizontal scale (≈ 30000 km) for the oscillations seems consistent with the old data and almost required by more recent measurements. The large scales recently measured would imply that a sizeable fraction of the solar volume is involved in the oscillation and would cast some doubt on all the old theories of the 5-min oscillations which were based on plane parallel atmospheres. Title: Interplanetary Gas. XVIII. The Mean Free Path of Protons at i Astronomical Unit Authors: Brandt, John C.; Nichols Thayer, Nina; Wolff, Charles L.; Hundhausen, A. J. Bibcode: 1973ApJ...183.1037B Altcode: Velocity distribution functions of solar-wind protons obtained by the Vela 3 satellites have been analyzed to obtain a microscopic determination of the momentum flux along magnetic field lines with respect to a reference frame moving at the bulk speed. The determination from macroscopic parameters allows the calculation of an effective mean free path for protons at 1 a.u. which averages 0.06 a.u. and is relatively independent of solar-wind velocity w. For quiet times when 300 km 1 < w < 400 km s ', the experimental mean free path is 2 to 3 times smaller than the value from plasma theory. For w > 400 km s', the experimental value is 10 to 100 times smaller than the theoretical value. The shorter mean free path for quiet times has been incorporated into the model by Wolff, Brandt, and Southwick by use of a coefficient of viscosity reduced by a factor of 3 at Earth. The resulting model is in better agreement with the values of the quiet solar wind at Earth suggested by Hundhausen than is the model with full viscosity. Subject headings: interplanetary medium - solar wind Title: A Theory for the 5-Minute Oscillations of Large Horizontal Scale. Authors: Wolff, C. L. Bibcode: 1973BAAS....5...20W Altcode: No abstract at ADS Title: Comments on Paper by E. Leer and T. E. Holzer, ‘Collisionless solar wind protons: A comparison of kinetic and hydrodynamic descriptions’ Authors: Brandt, John C.; Wolff, Charles L. Bibcode: 1973JGR....78.3197B Altcode: No abstract at ADS Title: The Five-Minute Oscillations as Nonradial Pulsations of the Entire Sun Authors: Wolff, Charles L. Bibcode: 1972ApJ...177L..87W Altcode: Calculations of the stability coefficient show that the Sun should be pulsating as a unit in nonradial modes of high order. The pulsations are driven by the superadiabatic gradient of the low photosphere and by the same sensitive changes in opacity that are known to be iniportant in variable stars. The existence of solar pulsations can explain many of the large scale features observed in the well known 5-ininute oscillations of the solar atmosphere. Title: Free Oscillations of the Sun and Their Possible Stimulation by Solar Flares Authors: Wolff, Charles L. Bibcode: 1972ApJ...176..833W Altcode: A large solar flare can raise the temperature of the underlying photosphere by 10 percent. The resulting thermal expansion exerts upon the solar interior a mechanical impulse whose kinetic energy is 1025 ergs. This will stimulate free modes of oscillation of the entire Sun, and the initial amplitudes of the more easily observable modes are calculated. Preliminary estimates of the effects of radiation damping and turbulent viscosity indicate that damping times will typically he longer than 1 day for the modes of most interest. Title: Solar wind heating. Authors: Barnes, A.; Brandt, J. C.; Hartle, R. E.; Wolff, C. L. Bibcode: 1972CosEl...3..254B Altcode: No abstract at ADS Title: Gegenschein-Moulton Region Photography from Lunar Orbit Authors: Dunkelman, L.; Wolff, C. L.; Mercer, R. D. Bibcode: 1972NASSP.315..161D Altcode: No abstract at ADS Title: Theoretical Oscillations of the Entire Sun. Authors: Wolff, Charles L. Bibcode: 1971BAAS....3..462W Altcode: No abstract at ADS Title: A Two-Component Model of the Quiet Solar Wind with Viscosity, Magnetic Field, and Reduced Heat Conduction Authors: Wolff, Charles L.; Brandt, John C.; Southwick, Robert G. Bibcode: 1971ApJ...165..181W Altcode: Previous models of the quiet solar wind based on steady-state plasma theory do not satisfactorily reproduce the observed properties at Earth. The addition of non thermal heating cannot provide agreement. Most earlier models neglected viscosity, and we find that viscosity plays the major role in heating the protons. We present a model, including viscosity, in which steady-state theory is altered only by the reduction of the electron mean free path-a semiempirical method for including the effects of plasma instabilities. At 1 a.u., this model has radial and azimuthal velocities of about 300 and 2 km sec ', respectively; the electron and proton temperatures are 200000 and 40000 K; the electron density is 9 All are in good agreement with quiet-time observations. Title: Gegenschein-Moulton Region Photography from Lunar Orbit Authors: Dunkelman, L.; Wolff, C. L.; Mercer, R. D.; Roosa, S. A. Bibcode: 1971NASSP.272..249D Altcode: No abstract at ADS Title: Are the Libration Clouds Real? Authors: Roosen, R. G.; Wolff, C. L. Bibcode: 1969Natur.224..571R Altcode: IT is disconcerting that the existence of dust cloud satellites at the L4 and L5 libration points in the Earth-Moon system, first reported by Kordylewski1, is so widely accepted2-6, in view of negative radar results3, and optical results7-11, some of which report no clouds even to a limit twenty to thirty times fainter than the brightness claimed by Kordylewski. Other discussions12,13 have also argued against the existence of libration clouds. While there undoubtedly exist patches of brightness in the night sky, their connexion with the libration points is unproven. Title: A Solar-Wind Model with Two Temperatures, Viscosity, Rotation, and Magnetic Field Authors: Wolff, C. L.; Brandt, J. C.; Southwick, R. G. Bibcode: 1969BAAS....1S.369W Altcode: No abstract at ADS Title: Interplanetary Gas. XVI. a Calculation of the Angular Momentum of the Solar Wind Authors: Brandt, John C.; Wolff, Charles; Cassinelli, Joseph P. Bibcode: 1969ApJ...156.1117B Altcode: A model of the quiet solar wind with magnetic field has been calculated numerically using the momen- tum equations developed by Weber and Davis, but with energy transport governed by the first law of thermodynamics with heat conduction. The model is close to observed densities of coronal electrons for r > 2 Ro. Near the Earth, the model has N. = 6 cm3, w = 315 km sec', T = 325000° K, and a garden- hose angle of 55°; the Alfvén point is at r = 31.4 Ro, and the angular momentum per unit mass in the solar equator is L = 1.4 X 1019 cm2 sec', a value which gives an e-folding time for solar rotational braking of 5 X 1O~ yr. The azimuthal velocity (w~) of the plasma near Earth is 2.5 km sec', and this value is consistent with the determination for quiet times from Type I comet tails Title: A Calculation of the Angular Momentum of the Solar Wind Authors: Brandt, John C.; Wolff, Charles; Cassinelli, Joseph P. Bibcode: 1969BAAS....1T.183B Altcode: No abstract at ADS Title: Optical Environment about the OGO-III Satellite Authors: Wolff, Charles Bibcode: 1967Sci...158.1045W Altcode: An upper limit to the brightness of the daytime sky near a large unmanned satellite has been obtained; it is some 30 times less than the darkest daytime sky yet reported by an astronaut. However, there still remains the danger that this background light (less than 5 × 10-13 as bright as the sun) will interfere with observations of the solar corona and zodiacal light. Title: Brightness of Possible Cloud Surrounding the OGO-IlI Satellite. Authors: Wolff, C. L. Bibcode: 1967AJ.....72R.838W Altcode: The fact that orbiting astronauts have great difficulty seeing stars in the daytime has been discussed in the literature (Xey, E. P., and Huch, W. F., Sc?ence 153, 297,1966; Roach, Dunkelman, Gill, and Mercer, NASA Pubi. SP-121, Gemini Mid-Program Conference, 1966, p. 315) and has led to speculation about a possible cloud of material surrounding the spacecraft and scattering sunlight. Experience with a well-shielded photometer on the OGO-IlI satellite cannot rule out the possibility of there being a similar problem of daytime background light near large unmanned satellites; however, if there is, the brightness is 30 times less than the darkest daytime sky yet reported by an astronaut. A measured upper limit of 1000 visual tenth magnitude stars per square degree can be set upon the brightness, in full sunlight, of any cloud of debris that might surround OGO-I I I. Any such high background of scattered sunlight will be of concern to some astronomers. G. Xewkirk (Planetary Space Sc?., to be published) has studied the problem of a cloud about the Gemini spacecraft and this is compared, here, with what might be expected for an unmanned satellite. Title: Photography of the Earth's Cloud Satellites from an Aircraft Authors: Wolff, C.; Dunkelman, L.; Haughney, L. C. Bibcode: 1967Sci...157..427W Altcode: Under astronomically favorable circumstances, photographs do not reveal excess light near the triangular libration points of the earth-moon system. We find that the visible surface brightness of anomalous dust populations, if these populations do exist, is less than 10-9 candela per square centimeter. Title: Schreiben des Herrn Wolff an den Herausgeber Authors: Wolff Bibcode: 1873AN.....82..279W Altcode: No abstract at ADS Title: Beobachtung der Sonnenfinsterniß vom 15ten May 1836 von den Herren Clüver und Wolff zu Bremen Authors: Clüver; Wolff Bibcode: 1836AN.....13..381C Altcode: No abstract at ADS