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Toomre, J.

Publications and source records attributed to Toomre, J..

At least 37 records · Page 2
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NASA NTRS1983

Nonlinear anelastic modal theory for solar convection

Solar envelope models are developed using single-mode anelastic equations as a description of turbulent convection which provide estimates for the variation with depth of the largest convective cellular flows, with horizontal sizes comparable to the total depth of the convection zone. These models can be used to describe compressible motions occurring over many density scale heights. Single-mode anelastic solutions are obtained for a solar envelope whose mean stratification is nearly adiabatic over most of its vertical extent because of the enthalpy flux explicitly carried by the big cell, while a subgrid scale representation of turbulent heat transport is incorporated into the treatment near the surface. It is shown that the single-mode equations allow two solutions for the same horizontal wavelength which are distinguished by the sense of the vertical velocity at the center of the three-dimensional cell. It is found that the upward directed flow experiences large pressure effects which can modify the density fluctuations so that the sense of the buoyancy force is changed, with buoyancy braking actually achieved near the top of the convection zone. It is suggested that such dynamical processes may explain why the amplitudes of flows related to the largest scales of convection are so weak in the solar atmosphere.

Latour, J.↗
NASA NTRS1983

On the detection of subphotospheric convective velocities and temperature fluctuations

A procedure is outlined for estimating the influence of large-scale convective eddies on the wave patterns of five-minute oscillations of high degree. The method is applied to adiabatic oscillations, with frequency omega and wave number k, of a plane-parallel polytropic layer upon which is imposed a low-amplitude convective flow. The distortion to the k-omega relation has two constituents: one depends on the horizontal component of the convective velocity and has a sign which depends on the sign of omega/k; the other depends on temperature fluctuations and is independent of the sign of omega/k. The magnitude of the distortion is just at the limit of present observational sensitivity. Thus there is reasonable hope that it will be possible to reveal some aspects of the large-scale flow in the solar convection zone.

Gough, D. O.↗
NASA NTRS1983

Variability in the power spectrum of solar five-minute oscillations

It is noted that two-dimensional power spectra of solar five-minute oscillations exhibit prominent ridge structures in (k, omega) space, k being the horizontal wavenumber and omega the temporal frequency. The positions of these ridges in k and omega can be used in probing temperature and velocity structures in the subphotosphere. The progress made in a program to establish whether power spectra taken on separate days show shifts in ridge locations is surveyed, noting that these may arise from different velocity and temperature patterns having been brought into the sampling region by solar rotation. Power spectra are obtained for six days of observations of Doppler velocities using the Mg I 5173 A and Fe I 5434 A spectral lines. Each data set encompasses 8 to 11 hr in time and samples a region 256 x 1024 arcsec in spatial extent, with a spatial resolution of 2 arcsec and temporal sampling of 65 s. Statistically significant shifts are detected in ridge locations between certain data sets. When analyzed in terms of eastward and westward propagating waves, the character of these displacements is seen as implying that changes have occurred in both temperature and horizontal velocity fields underlying the observing window. The velocity changes are estimated to be of the order of 100 m/s.

Hill, F.↗
NASA NTRS1982

Internal gravity waves in the solar atmosphere. II - Effects of radiative damping

In the solar photosphere, temperature fluctuations associated with acoustic-gravity waves may be rapidly smoothed by the transfer mechanism of radiation between hotter and cooler regions. The present investigation of the radiative effects on internal gravity waves takes into account the parameterization of the radiative energy, employing the Newtonian cooling approximation. A linear analysis of the propagation of internal gravity waves is carried out in a model of the solar atmosphere which is taken to be homogeneous in the horizontal coordinates. Linear wave properties both with and without radiative cooling are summarized, and the variation with height of energy fluxes and of nonlinearities in the waves is discussed. Attention is given to the significance of the obtained results in terms of energy balance in the chromosphere and in relation to spectral line observations.

Mihalas, B. W.↗
NASA NTRS1982

Time-dependent solutions of multimode convection equations

Truncated modal equations are used to study the time evolution of thermal convection. In the Boussinesq approximation these nonlinear equations are obtained by expanding the fluctuating velocity and temperature fields in a finite set of planforms of the horizontal coordinates. Numerical studies dealing with two or three modes with triad interactions are discussed. Rich time dependence was found in these cases: periodic and aperiodic solutions can be obtained, along with various steady solutions. Three-mode solutions reproduce the qualitative appearance of spoke-pattern convection as observed in experiments at high Prandtl numbers. Though the values of the periods of the time-dependent solutions do not agree with those of the experiments, their variation with Rayleigh number compares favorably. Except at the highest Rayleigh number considered (10,000,000), the theoretical Nusselt numbers agree well with experiment.

Toomre, J.↗
NASA NTRS1982

Single-mode theory of diffusive layers in thermohaline convection

A two-layer configuration of thermohaline convection is studied, with the principal aim of explaining the observed independence of the buoyancy-flux ratio on the stability parameter when the latter is large. Temperature is destabilizing and salinity is stabilizing, so diffusive interfaces separate the convecting layers. The convection is treated in the single-mode approximation, with a prescribed horizontal planform and wavenumber. Surveys of numerical solutions are presented for a selection of Rayleigh numbers R, stability parameters lambda and horizontal wavenumbers. The solutions yield a buoyancy flux ratio chi that is insensitive to lambda, in accord with laboratory experiments. However chi increases with increasing R, in contradiction to laboratory observations.

Gough, D. O.↗
NASA NTRS1982

Vertical flows of supergranular and mesogranular scale observed on the sun with OSO 8

A program of observations was carried out in order to study the penetration of supergranular flows over a broad range of heights in the solar atmosphere. Steady Doppler velocities are determined from observations of a Si II spectral line using the Ultraviolet Spectrometer on the Orbiting Solar Observatory 8 (OSO 8) satellite and Fe I and Mg I lines with the diode-array instrument on the vacuum telescope at Sacramento Peak Observatory (SPO). The heights of formation of these spectral lines span about 1400 km or nearly 11 density scale heights from the photosphere to the middle chromosphere. Steady vertical flows on spatial scales typical of supergranulation and mesogranulation have been detected in the middle chromosphere with OSO 8. The patterns of intensity and steady velocity of granular scale are reproducible in successive data sets. The patterns appear to evolve slowly over the 9 hr period spanned by six orbits.

November, L. J.↗
NASA NTRS1982

Nonlinear modal analysis of penetrative convection

It is pointed out that thermal convection in many astrophysical and geophysical settings occurs in an unstable layer bounded above and below by regions which are stably stratified. The convective motions may extend a substantial distance into the adjacent stable zones. If the motions have little direct effect upon the mean stratification of the stable zone, then they are usually referred to as convective overshooting. The primary objective of the present investigation is to study the dynamics of overshooting at very large Rayleigh numbers, mainly with stellar applications in mind. Numerically this is only feasible if severe simplifications are made in the description of what are likely to be turbulent motions. The approach employed in the investigation utilizes nonlinear modal equations in which the vertical and temporal structure of the convection is described accurately at the expense of the horizontal structure. A summary of the salient properties of penetrative convection is provided on the basis of the results of the conducted studies.

Zahn, J.-P.↗
NASA NTRS1981

Steady flows in the solar transition region observed with SMM

Steady flows in the quiet solar transition region have been observed with the Ultraviolet Spectrometer and Polarimeter experiment on the Solar Maximum Mission (SMM) satellite. The persistent vertical motions seen at disk center have spatial rms amplitudes of 1.4 km/s in the C II line, 3.9 km/s in Si IV, and 4.2 km/s in C IV. The amplitudes of the more horizontal flows seen toward the limb tend to be somewhat higher. Plots of steady vertical velocity versus intensity seen at disk center in Si IV and C IV show two distinct branches.

Gebbie, K. B.↗
NASA NTRS1981

Internal gravity waves in the solar atmosphere. I - Adiabatic waves in the chromosphere

The properties of adiabatic and linear internal gravity waves propagating in a solar wind model are discussed, using nonlinearity criteria unique to gravity waves to estimate wave-breaking heights. The results are used to deduce information on the possible role of gravity waves in the chromospheric energy balance. Maximum vertical velocity amplitudes for gravity waves are estimated to be on the order of 2 km/sec or less, and maximum horizontal velocity amplitudes are less than 6 km/sec, with temperature perturbations as large as 1000-2000 K. It is also estimated that gravity waves with an incident energy flux of one million ergs/sq cm-sec can propagate upward to a maximum height of 900-1000 km above the visible surface before nonlinearities lead to wave breaking, while those with an energy flux of 100,000 ergs/sq cm-sec can reach maximum heights of 1400-1600 km.

Mihalas, B. W.↗
NASA NTRS1981

Stellar convection theory. III - Dynamical coupling of the two convection zones in A-type stars by penetrative motions

The thermal convection occurring over many density scale heights in an A-type star outer envelope, encompassing both the hydrogen and helium convectively unstable zones, is examined by means of anelastic modal equations. The single-mode anelastic equations for such compressible convection display strong overshooting of the motions into adjacent radiative zones, which would preclude diffusive separation of elements in the supposedly quiescent region between the two unstable zones. In addition, the anelastic solutions reveal that the two zones of convective instability are dynamically coupled by the overshooting motions. The two solutions that the nonlinear single-mode equations admit for the same horizontal wavelength are distinguished by the sense of the vertical velocity at the center of the three-dimensional cell. It is suggested that strong horizontal shear flows should be present just below the surface of the star, and that the large-scale motions extending into the stable atmosphere would appear mainly as horizontal flows.

Latour, J.↗
NASA NTRS1981

The detection of mesogranulation on the sun

Time averages of velocity measurements at disk center on the quiet sun reveal the presence of a fairly stationary pattern of cellular flow with a spatial scale of 5-10 Mm. Such mesogranulation has a spatial rms vertical velocity amplitude of about 60 m/s superposed on the larger scale supergranular flows. The lifetimes of mesogranules appear to be at least 2 hr.

November, L. J.↗
NASA NTRS1980

Scientific management and implementation of the geophysical fluid flow cell for Spacelab missions

Scientific support for the spherical convection experiment to be flown on Spacelab 3 was developed. This experiment takes advantage of the zero gravity environment of the orbiting space laboratory to conduct fundamental fluid flow studies concerned with thermally driven motions inside a rotating spherical shell with radial gravity. Such a system is a laboratory analog of large scale atmospheric and solar circulations. The radial body force necessary to model gravity correctly is obtained by using dielectric polarization forces in a radially varying electric field to produce radial accelerations proportional to temperature. This experiment will answer fundamental questions concerned with establishing the preferred modes of large scale motion in planetary and stellar atmospheres.

Hart, J.↗
NASA NTRS1980

Convective instability when the temperature gradient and rotation vector are oblique to gravity. II - Real fluids with effects of diffusion

The linear stability analysis of Hathaway et al. (1979) is repeated for Boussinesq fluids with viscous and thermal diffusion. The fluid is confined between plane parallel boundaries and the rotation vector is oblique to gravity; this tilted rotation vector introduces a preference for roll-like disturbances whose axes are oriented north-south. The presence of a latitudinal temperature gradient produces a thermal wind shear which favors axisymmetric convective rolls if the gradient exceeds some critical value. The axisymmetric rolls are similar in many respects to the cloud bands on Jupiter provided they extend to a depth of about 15,000 km.

Hathaway, D. H.↗
NASA NTRS1979

The height variation of supergranular velocity fields determined from simultaneous OSO 8 satellite and ground-based observations

Results are reported for simultaneous satellite and ground-based observations of supergranular velocities in the sun, which were made using a UV spectrometer aboard OSO 8 and a diode-array instrument operating at the exit slit of an echelle spectrograph attached to a vacuum tower telescope. Observations of the steady Doppler velocities seen toward the limb in the middle chromosphere and the photosphere are compared; the observed spectral lines of Si II at 1817 A and Fe I at 5576 A are found to differ in height of formation by about 1400 km. The results show that supergranular motions are able to penetrate at least 11 density scale heights into the middle chromosphere, that the patterns of motion correlate well with the cellular structure seen in the photosphere, and that the motion increases from about 800 m/s in the photosphere to at least 3000 m/s in the middle chromosphere. These observations imply that supergranular velocities should be evident in the transition region and that strong horizontal shear layers in supergranulation should produce turbulence and internal gravity waves.

November, L. J.↗
NASA NTRS1979

Convective instability when the temperature gradient and rotation vector are oblique to gravity. I - Fluids without diffusion

A linear stability analysis of fluid layers under uniform rotation (generally oblique to gravity) which possess both vertical and horizontal temperature gradients is made by considering ideal fluids without diffusion within a Boussinesq approximation. This simplified configuration is used to assess the preferred convective modes as a function of latitude on a planet like Jupiter. The tilted rotation vector introduces a preference for roll-like disturbances with north-south orientations, while the horizontal temperature gradient produces a thermal wind shear which favors convective rolls oriented parallel to the flow in an east-west direction. It is found that the horizontal temperature gradient needed to produce a preference for the axisymmetric or east-west rolls increases with an increasing rotation rate and a decreasing latitude. The parameter values for Jupiter are estimated with the use of a simple radiative convective model, indicating a preference for axisymmetric rolls at nearly all latitudes if the convection zone depth is greater than about 200 km below the one atmosphere pressure level and convective roll characteristics which contribute to an equatorial acceleration.

Hathaway, D. H.↗
NASA NTRS1977

Numerical solutions of single-mode convection equations

In the Boussinesq approximation, single-mode equations describing thermal convection are constructed by expanding the fluctuating velocity and temperature fields in a complete set of functions (or planforms) of the horizontal coordinates and retaining just one term. Numerical solutions of the single-mode equations are investigated, chief consideration being given to hexagonal planforms. Extensive surveys of steady solutions are presented for various Rayleigh numbers, Prandtl numbers, and horizontal wavenumbers. The dependences on Rayleigh number and Prandtl number at very large Rayleigh number are in satisfactory agreement with the results of asymptotic expansions.

Toomre, J.↗