The compressional beta effect: a source of zonal winds in planets?

Abstract

Giant planets like Jupiter and Saturn feature strong zonal wind patterns on their surfaces. Although several different mechanisms that may drive these jets have been proposed over the last decades, the origin of the zonal winds is still unclear. Here, we explore the possibility that the interplay of planetary rotation with the compression and expansion of the convecting fluid can drive multiple deep zonal jets by a compressional Rhines-type mechanism, as originally proposed by Ingersoll and Pollard (1982). In a certain limit, this deep mechanism is shown to be mathematically analogous to the classical Rhines mechanism possibly operating at cloud level. Jets are predicted to occur on a compressional Rhines length $l_R=(2\Omega ⟨H_{\rho }^{-1}⟩v_{jet}^{-1}{)}^{-1/2}$, where $\Omega$ is the angular velocity, $⟨H_{\rho }^{-1}⟩$ is the mean inverse density scale height and $v_{jet}$ is the typical jet velocity. Two-dimensional numerical simulations using the anelastic approximation reveal that this mechanism robustly generates jets of the predicted width, and that it typically dominates the dynamics in systems deeper than $O(l_R)$. Potential vorticity staircases are observed to form spontaneously and are typically accompanied by unstably stratified buoyancy staircases. The mechanism only operates at large rotation rates, exceeding those typically reached in three-dimensional simulations of deep convection in spherical shells. Applied to Jupiter and Saturn, the compressional Rhines scaling reasonably fits the available observations. Interestingly, even weak vertical density variations such as those in the Earth core can give rise to a large number of jets, leading to fundamentally different flow structures than predicted by the Boussinesq models typically used in this context.

arXiv comment19 pages, 11 figures, 2 tables, accepted for publication in Icarus

References in corpus (15)

• Shock Compression of Deuterium and the Interiors of Jupiter and Saturn
• Ab initio Equation of State data for hydrogen, helium, and water and the internal structure of Jupiter
• Constraints on Deep-seated Zonal Winds Inside Jupiter and Saturn
• Effects of compressibility on driving zonal flow in gas giants
• Generation of equatorial jets by large-scale latent heating on the giant planets
• The Effect of Small-Scale Forcing on Large-Scale Structures in Two-Dimensional Flows
• Simulations of turbulent convection in rotating young solar-like stars: Differential rotation and meridional circulation
• Zonal flow scaling in rapidly-rotating compressible convection
• Differential rotation in giant planets maintained by density-stratified turbulent convection
• Patterns of convection in rotating spherical shells
• A note on "Constraints on deep-seated zonal winds inside Jupiter and Saturn"
• The role of density stratification in generating zonal flow structures in a rotating fluid
• The Effects of Rotation Rate on Deep Convection in Giant Planets with Small Solid Cores
• On the necessary conditions for bursts of convection within the rapidly rotating cylindrical annulus
• A dynamo driven by zonal jets at the upper surface: Applications to giant planets

Cited by in corpus (16)

• Effect of shear and magnetic field on the heat-transfer efficiency of convection in rotating spherical shells
• Zonal flow scaling in rapidly-rotating compressible convection
• Theory of solar oscillations in the inertial frequency range: Linear modes of the convection zone
• Turbulent transport by diffusive stratified shear flows: from local to global models. Part I: Numerical simulations of a stratified plane Couette flow
• Anelastic Versus Fully Compressible Turbulent Rayleigh-Bénard Convection
• Theory of solar oscillations in the inertial frequency range: Amplitudes of equatorial modes from a nonlinear rotating convection simulation
• Multiple zonal jets and convective heat transport barriers in a quasi-geostrophic model of planetary cores
• Mean flow generation in rotating anelastic two-dimensional convection
• pizza: An open-source pseudo-spectral code for spherical quasi-geostrophic convection
• Convective Differential Rotation in Stars and Planets I: Theory
• The compressional beta effect: Analytical solution, numerical benchmark, and data analysis
• Validity of Sound-Proof Approaches in Rapidly-Rotating Compressible Convection: Marginal Stability vs. Turbulence
• An assessment of implicit-explicit time integrators for the pseudo-spectral approximation of Boussinesq thermal convection in an annulus
• Impacts of small-scale dynamo on rotating columnar convection in stellar convection zones
• Generation of shear flows and vortices in rotating anelastic convection
• The effect of magnetic field on mean flow generation by rotating two-dimensional convection