Zonal jets in rotating convection with mixed mechanical boundary conditions

Large-scale zonal flows, as observed on the giant planets, can be driven by thermal convection in a rapidly rotating spherical shell. Most previous models of convectively-driven zonal flow generation have utilized stress-free mechanical boundary conditions (FBC) for both the inner and the outer surfaces of the convecting layer. Here, using 3D numerical models, we compare the FBC case to the case with a stress free outer boundary and a non-slip inner boundary, which we call the mixed case (MBC). We find significant differences in surface zonal flow profiles produced by the two cases. In low to moderate Rayleigh number FBC cases, the main equatorial jet is flanked by a strong, high-latitude retrograde jets in the northern and southern hemispheres. For the highest Rayleigh number FBC case, the equatorial jet is flanked by strong reversed jets as well as two additional large-scale alternating jets at higher latitudes. The MBC cases feature stronger equatorial jets but, much weaker, small-scale alternating zonal flows are found at higher latitudes. Our high Rayleigh number FBC results best compare with the zonal flow pattern observed on Jupiter, where the equatorial jet is flanked by strong retrograde jets as well as small-scale alternating jets at high latitude. In contrast, the MBC results compare better with the observed flow pattern on Saturn, which is characterized by a dominant prograde equatorial jet and a lack of strong high latitude retrograde flow. This may suggest that the mechanical coupling at the base of the jovian convection zone differs from that on Saturn.     

The effects of vigorous mixing in a convective model of zonal flow on the ice giants

Previous studies have used models of three-dimensional (3D) Boussinesq convection in a rotating spherical shell to explain the zonal flows on the gas giants, Jupiter and Saturn. In this paper we demonstrate that this approach can also generate flow patterns similar to those observed on the ice giants, Uranus and Neptune. The equatorial jets of Uranus and Neptune are often assumed to result from baroclinic cloud layer processes and have been simulated with shallow layer models. Here we show that vigorous, 3D convection in a spherical shell can produce the retrograde (westward) equatorial flows that occur on the ice giants as well as the prograde (eastward) equatorial flows of the gas giants. In our models, the direction of the equatorial jet depends on the ratio of buoyancy to Coriolis forces in the system. In cases where Coriolis forces dominate buoyancy, cylindrical Reynolds stresses drive prograde equatorial jets. However, as buoyancy forces approach and exceed Coriolis forces, the cylindrical nature of the flow is lost and 3D mixing homogenizes the fluid's angular momentum; the equatorial jet reverses direction, while strong prograde jets form in the polar regions. Although the results suggest that conditions involving strong atmospheric mixing are responsible for generating the zonal flows on the ice giants, our present models require roughly 100 and 10 times the internal heat fluxes observed on Uranus and Neptune, respectively.     

Compressible convection in the deep atmospheres of giant planets

Fast rotating giant planets such as Jupiter and Saturn possess alternate prograde and retrograde zonal winds which are stable over long periods of time. We consider a compressible model of convection in a spherical shell with rapid rotation, using the anelastic approximation, to explore the parameter range for which such zonal flows can be produced.We consider models with a large variation in density across the layer. Our models are based only on the molecular H/He region above the metallic hydrogen transition at about 2 Mbar, and we do not include the hydromagnetic effects which may be important if the electrical conductivity is significant. We find that the convective velocities are significantly higher in the low density regions of the shell, but the zonal flow is almost independent of the z-coordinate parallel to the rotation axis. We analyse how this behaviour is consistent with the Proudman-Taylor theorem.We find that deep prograde zonal flow near the equator is a very robust feature of our models. Prograde and retrograde jets alternating in latitude can occur inside the tangent cylinder in compressible as well as Boussinesq models, particularly at lower Prandtl numbers. However, the zonal jets inside the tangent cylinder are suppressed if a no-slip condition is imposed at the inner boundary. This suggests that deep high latitude jets may be suppressed if there is significant magnetic dissipation.Our compressible calculations include the viscous dissipation in the entropy equation, and we find this is comparable to, and in some cases exceeds, the total heat flux emerging from the surface. For numerical reasons, these simulations cannot reach the extremely low Ekman number found in giant planets, and they necessarily also have a much larger heat flux than planets. We therefore discuss how our results might scale down to give solutions with lower dissipation and lower heat flux.     

Generation of equatorial jets by large-scale latent heating on the giant planets

Three-dimensional numerical simulations show that large-scale latent heating resulting from condensation of water vapor can produce multiple zonal jets similar to those on the gas giants (Jupiter and Saturn) and ice giants (Uranus and Neptune). For plausible water abundances (3-5 times solar on Jupiter/Saturn and 30 times solar on Uranus/Neptune), our simulations produce ∼20 zonal jets for Jupiter and Saturn and 3 zonal jets on Uranus and Neptune, similar to the number of jets observed on these planets. Moreover, these Jupiter/Saturn cases produce equatorial superrotation whereas the Uranus/Neptune cases produce equatorial subrotation, consistent with the observed equatorial-jet direction on these planets. Sensitivity tests show that water abundance, planetary rotation rate, and planetary radius are all controlling factors, with water playing the most important role; modest water abundances, large planetary radii, and fast rotation rates favor equatorial superrotation, whereas large water abundances favor equatorial subrotation regardless of the planetary radius and rotation rate. Given the larger radii, faster rotation rates, and probable lower water abundances of Jupiter and Saturn relative to Uranus and Neptune, our simulations therefore provide a possible mechanism for the existence of equatorial superrotation on Jupiter and Saturn and the lack of superrotation on Uranus and Neptune. Nevertheless, Saturn poses a possible difficulty, as our simulations were unable to explain the unusually high speed (∼) of that planet’s superrotating jet. The zonal jets in our simulations exhibit modest violations of the barotropic and Charney-Stern stability criteria. Overall, our simulations, while idealized, support the idea that latent heating plays an important role in generating the jets on the giant planets.     

Instability of Zonal Flows in Rotating Spherical Shells: An Application to Jupiter

Measurements from the Galileo probe suggest that the zonal winds are deep rooted. Jupiter's high rotation rate makes it likely that the whole outer molecular H/He layer is involved in these long-lived jet flows. Assuming that the primary flows are geostrophic, and that the banded surface structure stretches right through the molecular H/He layer, we examine the conditions for such flows to be stable. As a first step, the linear stability of some prescribed banded zonal flows in a rotating spherical shell is explored. Incompressibility is assumed for simplicity, and the boundary condition is stress-free. We compare solutions for two aspect ratios, appropriate for the molecular H/He layers of Jupiter and Saturn, and two Ekman numbers (E=10⁻² and E=10⁻⁴). Convective and shear flow instabilities compete in our system. The convective instabilities are of the well-known columnar structure. Shear flow instabilities for the larger Ekman number are similar to the Taylor-Couette instability in rotating annuli. At the lower Ekman number, shear flow instabilities adopt a geostrophic character, assuming the form of rotating columns, similar to the convective instabilities. While the convective instability always sets in outside the tangent cylinder, shear instability can become unstable inside the tangent cylinder. If even a weak zonal flow is present inside the tangent cylinder, the flow is unstable to shear instability. This offers an explanation why the jovian zonal jet structure is much weaker at the higher latitudes that correspond to locations inside the tangent cylinder.     

Hadley circulations and Kelvin wave-driven equatorial jets in the atmospheres of Jupiter and Saturn

We propose a dynamical mechanism that can plausibly explain the origin of the broad prograde equatorial winds observed on Jupiter and Saturn, and examine the feasibility of this mechanism using two- (2D) and three-dimensional (3D) numerical simulation models. The idea is based on combining a narrow Gaussian jet peaking at the equator, which is induced by the momentum transfer from an upward propagating equatorial Kelvin-wave, and a pair of off-equatorial jets due to a meridional-vertical circulation similar to the tropical Hadley circulation on Earth. We employ for this feasibility study a 2D mechanistic mean-flow model which incorporates the influence of prescribed waves, and a 3D general circulation model, based on the generalised primitive equations of atmospheric motion. We then confirm that the dynamical models of both kinds can successfully reproduce theoretically expected flows of a reasonable magnitude, and that when two mechanisms are combined, a broad super-rotating jet is produced with off-equatorial maxima in zonal velocity for both Jupiter and Saturn, approximately in accordance with observations.     

Deep jets on gas-giant planets

Three-dimensional numerical simulations of the atmospheric flow on giant planets using the primitive equations show that shallow thermal forcing confined to pressures near the cloud tops can produce deep zonal winds from the tropopause all the way down to the bottom of the atmosphere. These deep winds can attain speeds comparable to the zonal jet speeds within the shallow, forced layer; they are pumped by Coriolis acceleration acting on a deep meridional circulation driven by the shallow-layer eddies. In the forced layer, the flow reaches an approximate steady state where east-west eddy accelerations balance Coriolis accelerations acting on the meridional flow. Under Jupiter-like conditions, our simulations produce 25 to 30 zonal jets, similar to the number of jets observed on Jupiter and Saturn. The simulated jet widths correspond to the Rhines scale; this suggests that, despite the three-dimensional nature of the dynamics, the baroclinic eddies energize a quasi-two-dimensional inverse cascade modified by the β effect (where β is the gradient of the Coriolis parameter). In agreement with Jupiter, the jets can violate the barotropic and Charney-Stern stability criteria, achieving curvatures ^∂2u/∂y² of the zonal wind u with northward distance y up to 2β. The simulations exhibit a tendency toward neutral stability with respect to Arnol'd's second stability theorem in the upper troposphere, as has been suggested for Jupiter, although deviations from neutrality exist. When the temperature varies strongly with latitude near the equator, our simulations can also reproduce the stable equatorial superrotation with wind speeds greater than . Diagnostics show that barotropic eddies at low latitudes drive the equatorial superrotation. The simulations also broadly explain the distribution of jet-pumping eddies observed on Jupiter and Saturn. While idealized, these simulations therefore capture many aspects of the cloud-level flows on Jupiter and Saturn.     

Interaction of moist convection with zonal jets on Jupiter and Saturn

Observations suggest that moist convection plays an important role in the large-scale dynamics of Jupiter's and Saturn's atmospheres. Here we use a reduced-gravity quasigeostrophic model, with a parameterization of moist convection that is based on observations, to study the interaction between moist convection and zonal jets on Jupiter and Saturn. Stable jets with approximately the same width and strength as observations are generated in the model. The observed zonal jets violate the barotropic stability criterion but the modeled jets do so only if the flow in the deep underlying layer is westward. The model results suggest that a length scale and a velocity scale associated with moist convection control the width and strength of the jets. The length scale and velocity scale offer a possible explanation of why the jets of Saturn are stronger and wider than those of Jupiter.     

Stability of jets on Jupiter and Saturn

The linear stability of a zonal jet that decays with depth is investigated under the assumption that the thermal stratification is very small. A westerly cosine jet is found to be more stable than it is in a thin fluid shell with two-dimensional flow. This is in agreement with observations of Jupiter and Saturn, where jet curvature exceeds the barotropic stability criterion. This result constitutes an alternative hypothesis to that of Ingersoll and Pollard [Icarus 52 (1982) 62], who showed that deep jets extending through the interior are also more stable than thin shell jets. The flow regime assumed in the present work requires that a small stratification can exist and persist even in the presence of horizontal temperature gradients. Further work will be needed to test whether this is realistic.     

Constraints on deep-seated zonal winds inside Jupiter and Saturn

The atmospheres of Jupiter and Saturn exhibit strong and stable zonal winds. How deep the winds penetrate unabated into each planet is unknown. Our investigation favors shallow winds. It consists of two parts. The first part makes use of an Ohmic constraint; Ohmic dissipation associated with the planet's magnetic field cannot exceed the planet's net luminosity. Application to Jupiter (J) and Saturn (S) shows that the observed zonal winds cannot penetrate below a depth at which the electrical conductivity is about six orders of magnitude smaller than its value at the molecular-metallic transition. Measured values of the electrical conductivity of molecular hydrogen yield radii of maximum penetration of 0.96RJ and 0.86RS, with uncertainties of a few percent of R. At these radii, the magnetic Reynolds number based on the zonal wind velocity and the scale height of the magnetic diffusivity is of order unity. These limits are insensitive to difficulties in modeling turbulent convection. They permit complete penetration along cylinders of the equatorial jets observed in the atmospheres of Jupiter and Saturn. The second part investigates how deep the observed zonal winds actually do penetrate. As it applies heuristic models of turbulent convection, its conclusions must be regarded as tentative. Truncation of the winds in the planet's convective envelope would involve breaking the Taylor-Proudman constraint on cylindrical flow. This would require a suitable nonpotential acceleration which none of the obvious candidates appears able to provide. Accelerations arising from entropy gradients, magnetic stresses, and Reynolds stresses appear to be much too weak. These considerations suggest that strong zonal winds are confined to shallow, stably stratified layers, with equatorial jets being the possible exception.     

Scaling laws for convection and jet speeds in the giant planets

Three dimensional studies of convection in deep spherical shells have been used to test the hypothesis that the strong jet streams on Jupiter, Saturn, Uranus, and Neptune result from convection throughout the molecular envelopes. Due to computational limitations, these simulations must be performed at parameter settings far from jovian values and generally adopt heat fluxes 5-10 orders of magnitude larger than the planetary values. Several numerical investigations have identified trends for how the mean jet speed varies with heat flux and viscosity in these models, but no previous theories have been advanced to explain these trends. Here, we show using simple arguments that if convective release of potential energy pumps the jets and viscosity damps them, the mean jet speeds split into two regimes. When the convection is weakly nonlinear, the equilibrated jet speeds should scale approximately with F/ν, where F is the convective heat flux and ν is the viscosity. When the convection is strongly nonlinear, the jet speeds are faster and should scale approximately as (F/ν)^1/2. We demonstrate how this regime shift can naturally result from a shift in the behavior of the jet-pumping efficiency with heat flux and viscosity. Moreover, both Boussinesq and anelastic simulations hint at the existence of a third regime where, at sufficiently high heat fluxes or sufficiently small viscosities, the jet speed becomes independent of the viscosity. We show based on mixing-length estimates that if such a regime exists, mean jet speeds should scale as heat flux to the 1/4 power. Our scalings provide a good match to the mean jet speeds obtained in previous Boussinesq and anelastic, three-dimensional simulations of convection within giant planets over a broad range of parameters. When extrapolated to the real heat fluxes, these scalings suggest that the mass-weighted jet speeds in the molecular envelopes of the giant planets are much weaker—by an order of magnitude or more—than the speeds measured at cloud level.     

Effects of compressibility on driving zonal flow in gas giants

The banded structures observed on the surfaces of the gas giants are associated with strong zonal winds alternating in direction with latitude. We use three-dimensional numerical simulations of compressible convection in the anelastic approximation to explore the properties of zonal winds in rapidly rotating spherical shells. Since the model is restricted to the electrically insulating outer envelope, we therefore neglect magnetic effects.A systematic parametric study for various density scaleheights and Rayleigh numbers allows to explore the dependence of convection and zonal jets on these parameters and to derive scaling laws.While the density stratification affects the local flow amplitude and the convective scales, global quantities and zonal jets properties remain fairly independent of the density stratification. The zonal jets are maintained by Reynolds stresses, which rely on the correlation between zonal and cylindrically radial flow components. The gradual loss of this correlation with increasing supercriticality hampers all our simulations and explains why the additional compressional source of vorticity hardly affects zonal flows.All these common features may explain why previous Boussinesq models were already successful in reproducing the morphology of zonal jets in gas giants.     

Saturn eddy momentum fluxes and convection: First estimates from Cassini images

We apply an automated cloud feature tracking algorithm to estimate eddy momentum fluxes in Saturn's southern hemisphere from Cassini Imaging Science Subsystem near-infrared continuum image sequences. Voyager Saturn manually tracked images had suggested no conversion of eddy to mean flow kinetic energy, but this was based on a small sample of <1000 wind vectors. The automated procedure we use for the Cassini data produces an order of magnitude more usable wind vectors with relatively unbiased sampling. Automated tracking is successful in and around the westward jet latitudes on Saturn but not in the vicinity of most eastward jets, where the linearity and non-discrete nature of cloud features produces ambiguous results. For the regions we are able to track, we find peak eddy fluxes and a clear positive correlation between eddy momentum fluxes and meridional shear of the mean zonal wind, implying that eddies supply momentum to eastward jets and remove momentum from westward jets at a rate . The behavior we observe is similar to that seen on Jupiter, though with smaller eddy-mean kinetic energy conversion rates per unit mass of atmosphere (). We also use the appearance and rapid evolution of small bright features at continuum wavelengths, in combination with evidence from weak methane band images where possible, to diagnose the occurrence of moist convective storms on Saturn. Areal expansion rates imply updraft speeds of over the convective anvil cloud area. As on Jupiter, convection preferentially occurs in cyclonic shear regions on Saturn, but unlike Jupiter, convection is also observed in eastward jet regions. With one possible exception, the large eddy fluxes seen in the cyclonic shear latitudes do not seem to be associated with convective events.     

Emergence of polar-jet polygons from jet instabilities in a Saturn model

Voyager flybys of Saturn in 1980-1981 revealed a circumpolar wave at ≈78° north planetographic latitude. The feature had a dominant wavenumber 6 mode, and has been termed the Hexagon from its geometric appearance in polar-projected mosaics. It was also noted for being stationary with respect to Saturn’s Kilometric Radiation (SKR) rotation rate. The Hexagon has persisted for over 30 years since the Voyager observations until now. It has been observed from ground based telescopes, Hubble Space Telescope and multiple instruments onboard Cassini in orbit around Saturn. Measurements of cloud motions in the region reveal the presence of a jet stream whose path closely follows the Hexagon’s outline. Why the jet stream takes the characteristic six-sided shape and how it is stably maintained across multiple saturnian seasons are yet to be explained. We present numerical simulations of the 78.3°N jet using the Explicit Planetary Isentropic-Coordinate (EPIC) model and demonstrate that a stable hexagonal structure can emerge without forcing when dynamic instabilities in the zonal jet nonlinearly equilibrate. For a given amplitude of the jet, the dominant zonal wavenumber is most strongly dependent on the peak curvature of the jet, i.e., the second north-south spatial derivative of the zonal wind profile at the center of the jet. The stable polygonal shape of the jet in our simulations is formed by a vortex street with cyclonic and anticyclonic vortices lining up towards the polar and equatorial side of the jet, respectively. Our result is analogous to laboratory experiments of fluid motions in rotating tanks that develop polygonal flows out of vortex streets. However, our results also show that a vortex street model of the Hexagon cannot reproduce the observed propagation speed unless the zonal jet’s speed is modified beyond the uncertainties in the observed zonal wind speed, which suggests that a vortex street model of the Hexagon and the observed zonal wind profile may not be mutually compatible.     

Constraints on Saturn’s tropospheric general circulation from Cassini ISS images

An automated cloud tracking algorithm is applied to Cassini Imaging Science Subsystem high-resolution apoapsis images of Saturn from 2005 and 2007 and moderate resolution images from 2011 and 2012 to define the near-global distribution of zonal winds and eddy momentum fluxes at the middle troposphere cloud level and in the upper troposphere haze. Improvements in the tracking algorithm combined with the greater feature contrast in the northern hemisphere during the approach to spring equinox allow for better rejection of erroneous wind vectors, a more objective assessment at any latitude of the quality of the mean zonal wind, and a population of winds comparable in size to that available for the much higher contrast atmosphere of Jupiter. Zonal winds at cloud level changed little between 2005 and 2007 at all latitudes sampled. Upper troposphere zonal winds derived from methane band images are ～10 m s^?1 weaker than cloud level winds in the cores of eastward jets and ～5 m s^?1 stronger on either side of the jet core, i.e., eastward jets appear to broaden with increasing altitude. In westward jet regions winds are approximately the same at both altitudes. Lateral eddy momentum fluxes are directed into eastward jet cores, including the strong equatorial jet, and away from westward jet cores and weaken with increasing altitude on the flanks of the eastward jets, consistent with the upward broadening of these jets. The conversion rate of eddy to mean zonal kinetic energy at the visible cloud level is larger in eastward jet regions (5.2 × 10^?5 m² s^?3) and smaller in westward jet regions (1.6 × 10^?5 m² s^?3) than the global mean value (4.1 × 10^?5 m² s^?3). Overall the results are consistent with theories that suggest that the jets and the overturning meridional circulation at cloud level on Saturn are maintained at least in part by eddies due to instabilities of the large-scale flow near and/or below the cloud level.     

A dynamo driven by zonal jets at the upper surface: Applications to giant planets

We present a dynamo mechanism arising from the presence of barotropically unstable zonal jet currents in a rotating spherical shell. The shear instability of the zonal flow develops in the form of a global Rossby mode, whose azimuthal wavenumber depends on the width of the zonal jets. We obtain self-sustained magnetic fields at magnetic Reynolds numbers greater than 10³. We show that the propagation of the Rossby waves is crucial for dynamo action. The amplitude of the axisymmetric poloidal magnetic field depends on the wavenumber of the Rossby mode, and hence on the width of the zonal jets. We discuss the plausibility of this dynamo mechanism for generating the magnetic field of the giant planets. Our results suggest a possible link between the topology of the magnetic field and the profile of the zonal winds observed at the surface of the giant planets. For narrow Jupiter-like jets, the poloidal magnetic field is dominated by an axial dipole whereas for wide Neptune-like jets, the axisymmetric poloidal field is weak.     

Jupiter and Saturn rotation periods

Anderson and Schubert [2007. Saturn's Gravitational field, internal rotation, and interior structure. Science 317, 1384-1387 (paper I)] proposed that Saturn's rotation period can be ascertained by minimizing the dynamic heights of the 100 mbar isosurface with respect to the geoid; they derived a rotation period of 10 h 32 m 35 s. We investigate the same approach for Jupiter to see if the Jovian rotation period is predicted by minimizing the dynamical heights of its isobaric (1 bar pressure level) surface using zonal wind data. A rotation period of 9 h 54 m 29.7 s is found. Further, we investigate the minimization method by fitting Pioneer and Voyager occultation radii for both Jupiter and Saturn. Rotation periods of 9 h 55 m 30 s and 10 h 32 m 35 s are found to minimize the dynamical heights for Jupiter and Saturn, respectively. Though there is no dynamical principle requiring the minimization of the dynamical heights of an isobaric surface, the successful application of the method to Jupiter lends support to its relevance for Saturn.We derive Jupiter and Saturn rotation periods using equilibrium theory to explain the difference between equatorial and polar radii. Rotation periods of 9 h 55 m 20 s and 10 h 31 m 49 s are found for Jupiter and Saturn, respectively. We show that both Jupiter's and Saturn's shapes can be derived using solid-body rotation, suggesting that zonal winds have a minor effect on the planetary shape for both planets.The agreement in the values of Saturn's rotation period predicted by the different approaches supports the conclusion that the planet's period of rotation is about 10 h 32 m.     

Dust on the Outskirts of the Jovian System

The outer region of the jovian system between ∼50 and 300 jovian radii from the planet is found to be the host of a previously unknown dust population. We used the data from the dust detector aboard the Galileo spacecraft collected from December 1995 to April 2001 during Galileo's numerous traverses of the outer jovian system. Analyzing the ion amplitudes, calibrated masses and speeds of grains, and impact directions, we found about 100 individual events fully compatible with impacts of grains moving around Jupiter in bound orbits. These grains have moderate eccentricities and a wide range of inclinations—from prograde to retrograde ones. The radial number density profile of the micrometer-sized dust is nearly flat between about 50 and 300 jovian radii. The absolute number density level (∼10 km⁻³ with a factor of 2 or 3 uncertainty) surpasses by an order of magnitude that of the interplanetary background. We identify the sources of the bound grains with outer irregular satellites of Jupiter. Six outer tiny moons are orbiting the planet in prograde and fourteen in retrograde orbits. These moons are subject to continuous bombardment by interplanetary micrometeoroids. Hypervelocity impacts create ejecta, nearly all of which get injected into circumjovian space. Our analytic and numerical study of the ejecta dynamics shows that micrometer-sized particles from both satellite families, although strongly perturbed by solar tidal gravity and radiation pressure, would stay in bound orbits for hundreds of thousands of years as do a fraction of smaller grains, several tenths of a micrometer in radius, ejected from the prograde moons. Different-sized ejecta remain confined to spheroidal clouds embracing the orbits of the parent moons, with appreciable asymmetries created by the radiation pressure and solar gravity perturbations. Spatial location of the impacts, mass distribution, speeds, orbital inclinations, and number density of dust derived from the data are all consistent with the dynamical model.     

Nonradial stellar oscillations excited by turbulent convection

The resonant excitation of the large-scale nonradial oscillations of a star by turbulent convection is considered. In the case of an incompressible inhomogeneous liquid sphere and a spherical shell we have demonstrated the excitation of oscillations and have obtained the explicit analytic expressions for the oscillation amplitudes. The effect of uniform axial rotation of a star upon the oscillations has also been considered. The estimates of the r.m.s. velocities of the excited quadrupole oscillations based on solar parameters do not contradict the observations of the 160 min. solar oscillations. Results are briefly discussed and applications are also made to the case of nonradial oscillations of outer convection zones of white dwarfs, Jupiter and Saturn.