Modeling convection and zonal winds in giant planets

Three basic modeling approaches have been used to numerically simulate fluid turbulence and the banded zonal winds in the interiors and atmospheres of giant planets: shallow-water models, deep-shell Boussinesq models and deep-shell anelastic models. We review these models and discuss the approximations and assumptions upon which they are based. All three can produce banded zonal wind patterns at the surface. However, shallow-water models produce a retrograde (i.e., westward) zonal jet in the equatorial region, whereas strong prograde (i.e., eastward) equatorial jets exist on Jupiter and Saturn. Deep-shell Boussinesq models maintain prograde equatorial jets by the classic method of vortex stretching of convective columnar flows; however, they neglect the effects of the large density stratification in these giant planets. Deep-shell anelastic models account for density stratification and maintain prograde equatorial jets by generating vorticity as rising fluid expands and sinking fluid contracts, without the constraint of long thin convective column

Heat transport in 3D anelastic simulations of the internal dynamics of giant planets without cores

Differential rotation, similar to that seen on our gas giants, is manifested at the surface of three-dimensional (3D) computer simulations of thermal convection in density-stratified rotating planets without solid cores. Below the surface, the flow forms short axially-aligned vortices, generated by fluid expanding as it rises and contracting as it sinks. The convergence of the nonlinear Reynolds stresses resulting from the vorticity generated by fluid flowing through the density stratification maintains the surface banded zonal flow without the classical vortex stretching of Taylor columns. These preliminary simulations demonstrate that large non-convecting cores are not required to obtain multiple zonal jets at the surface, and show greater convective heat flux towards the poles relative to that seen at the equator. This result could help explain the nearly uniform with latitude thermal emission observed at the surface of Jupite

The Effects of Rotation Rate on Deep Convection in Giant Planets with Small Solid Cores

We study how the pattern of thermal convection and differential rotation in the interior of a giant gaseous planet is affected by the presence of a small solid core as a function of the planetary rotation rate. We show, using 2D anelastic, hydrodynamic simulations, that the presence of a small solid core results in significantly different flow structure relative to that of a fully convective interior only if there is little or no planetary rotation.Comment: 12 pages, 3 figure

Differential rotation in giant planets maintained by density-stratified turbulent convection

The zonal winds on the surfaces of giant planets vary with latitude. Jupiter and Saturn, for example, have several bands of alternating eastward (prograde) and westward (retrograde) jets relative to the angular velocity of their global magnetic fields. These surface wind profiles are likely manifestations of the variations in depth and latitude of angular velocity deep within the liquid interiors of these planets. Two decades ago it was proposed that this differential rotation could be maintained by vortex stretching of convective fluid columns that span the interiors of these planets from the northern hemisphere surface to the southern hemisphere surface. This now classic mechanism explains the differential rotation seen in laboratory experiments and in computer simulations of, at best, weakly turbulent convection in rotating constant-density fluid spheres. However, these experiments and simulations are poor approximations for the density-stratified strongly-turbulent interiors of giant planets. The long thin global convective columns predicted by the classic geostrophic theory for these planets would likely not develop. Here we propose a much more robust mechanism for maintaining differential rotation in radius based on the local generation of vorticity as rising plumes expand and sinking plumes contract. Our high-resolution two-dimensional computer simulations demonstrate how this mechanism could maintain either prograde or retrograde surface winds in the equatorial region of a giant planet depending on how the density scale height varies with depth.Comment: Geophysical and Astrophysical Fluid Dynamics, in pres

Gravity Waves in the Sun

We present numerical simulations of penetrative convection and gravity wave excitation in the Sun. Gravity waves are self-consistently generated by a convective zone overlying a radiative interior. We produce power spectra for gravity waves in the radiative region as well as estimates for the energy flux of gravity waves below the convection zone. We calculate a peak energy flux in waves below the convection zone to be three orders of magnitude smaller than previous estimates for m=1. The simulations show that the linear dispersion relation is a good approximation only deep below the convective-radiative boundary. Both low frequency propagating gravity waves as well as higher frequency standing modes are generated; although we find that convection does not continually drive the standing g-mode frequencies.Comment: 22 pages, 14 figures, submitted to MNRA

A note on "Constraints on deep-seated zonal winds inside Jupiter and Saturn"

Liu et al. 2008 discuss an important consideration for models of zonal winds deep within giant planets. However, the constraints they propose for the depth of the winds are based on their prescriptions for the internal structures of the magnetic field and zonal winds. The same kinematic analysis applied to other plausible configurations would produce no constraint on the depth to which the winds extend.Comment: accepted for publication in Icaru

Effects of multiple phase transitions in a three-dimensional spherical model of convection in Earth's mantle

Numerical models of mantle convection that incorporate the major mantle phase changes of the transition zone reveal an inherently three-dimensional flow pattern, with cylindrical features and linear features that behave differently in their ability to penetrate the 670-km discontinuity. The dynamics are dominated by accumulation of cold linear downwellings into rounded pools above the endothermic phase change at 670 km depth, resulting in frequent “avalanches” of upper mantle material into the lower mantle. The effect of the exothermic phase transition at 400 km depth is to reduce the overall degree of layering by pushing material through the 670-km phase change, resulting in smaller and more frequent avalanches, and a wider range of morphologies. Large quantities of avalanched cold material accumulate above the coremantle boundary (CMB), resulting in a region of strongly depressed mean temperature at the base of the mantle. The 670-km phase change has a strong effect on the temperature field, with three-distinct regions being visible: (1) the upper mantle, containing linear downwellings and pools of cold material in the transition zone and characterized by a high amplitude long wavelength spectrum; (2) the midmantle, containing quasi-cylindrical avalanche conduits and characterized by a low amplitude, broad spectrum; and (3) the deep mantle, containing large pools of cold, avalanched material and characterized by a high amplitude, ultra-red (i.e., long wavelength) spectrum. The effect on the velocity field is very different. Flow penetration across the 670-km phase change is strongly wavelength-dependent, with easy penetration at long wavelengths but strong inhibition at short wavelengths. Thus, when comparing numerical models with long wavelength seismic tomography, diagnostics based on the density field, such as the radial correlation function, are much more sensitive to the effects of phase transitions than those based on the velocity field. The amplitude of the geoid is not significantly affected by the partial layering, because the contribution from the strong heterogeneity in the transition zone is almost perfectly balanced by the contribution from deflection of the 670-km discontinuity. Avalanches are associated with geoid lows. However, a more complex viscosity structure is required to correctly match the sign of the geoid over slabs in Earth

Evolution of progenitor stars of Type Ibc supernovae and long gamma-ray bursts

We discuss how rotation and binary interactions may be related to the diversity of type Ibc supernovae and long gamma-ray bursts. After presenting recent evolutionary models of massive single and binary stars including rotation, the Tayler-Spruit dynamo and binary interactions, we argue that the nature of SNe Ibc progenitors from binary systems may not significantly differ from that of single star progenitors in terms of rotation, and that most long GRB progenitors may be produced via the quasi-chemically homogeneous evolution at sub-solar metallicity. We also briefly discuss the possible role of magnetic fields generated in the convective core of a massive star for the transport of angular momentum, which is potentially important for future stellar evolution models of supernova and GRB progenitors.Comment: 6 pages, 4 figures, to appear in IAU Symp. 250, Massive Stars as Cosmic Engines, Kauai (HI), 12/2007, ed. F. Bresolin, P. Crowther, & J. Pul

The Los Alamos General Circulation Model hydrologic cycle

As the global population has increased, so have human influences on the global environment. ... How can we better understand and predict these natural and potential anthropogenic variations? One way is to develop a model that can accurately describe all the components of the hydrologic cycle, rather than just the end result variables such as precipitation and soil moisture. If we can predict and simulate variations in evaporation and moisture convergence, as well as precipitation, then we will have greater confidence in our ability to at least model precipitation variations. Therefore, we describe here just how well we can model relevant aspects of the global hydrologic cycle. In particular, we determine how well we can model the annual and seasonal mean global precipitation, evaporation, and atmospheric water vapor transport