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 lengthwhere Ω is the angular velocity, H −1 ρ 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.

Onset of rotating and non-rotating convection in compressible and anelastic ideal gases

“…For N ρ → 0, the critical parameters are the same as those for non-rotating convection (Ra c ≈ 658, k c ≈ 2.22) since the resulting fluid motions of N S rolls are everywhere perpendicular to the rotation axis. The effect of stratification at this colatitude has been discussed in detail by Glatzmaier and Gilman (1981b) and more recently by Verhoeven and Stellmach (2014); as fluid moves outward (inward) it expands (contracts) resulting in a local spin-down (spin-up) and the cumulative effect is a positively propagating compressible Rossby wave. We note that this compressional β-effect occurs for all cases in which the gravity and rotation vector are not aligned, but is strongest at the equator (θ = 90 • ).…”

“…Previous work has shown that one effect of fluid compressibility on convection dynamics is the occurrence of asymmetric flows with respect to the midplane of the fluid layer in the case of plane layer geometries (Spiegel 1965, Heard 1973, Gough et al 1976, Mizerski and Tobias 2011; analagous effects occur in spherical geometries (e.g., Gilman 1981a, Jones et al 2009). Another important consequence of compressibility is the excitation of convective Rossby waves in rotating convection when the gravity and rotation vectors are not antiparallel (Glatzmaier and Gilman 1981b); the resulting vortex stretching mechanism may be an important process for generating mean flows in gaseous atmospheres (Glatzmaier et al 2009, Verhoeven andStellmach 2014). Although previous work has determined the stability criteria in the plane layer geometry for both non-rotating (Spiegel 1965, Gough et al 1976) and upright rotating compressible convection (Heard 1973), to date no studies have examined the linear stability of compressible convection on the tilted f -plane geometry.…”

Rotating convective turbulence in Earth and planetary cores

“…Such effects are likely of relevance in gas planets (e.g., Glatzmaier et al, 2009;Kaspi et al, 2009), and may be relevant in Earth-sized terrestrial cores as well (cf. Anufriev et al, 2005;Verhoeven and Stellmach, 2014). The effects of self-compression in liquid metal cores are not, however, considered here, but can be accurately incorporated via fully-compressible models (Calkins et al, 2014;Calkins et al, 2015a).…”

Validity of sound-proof approaches in rapidly-rotating compressible convection: marginal stability versus turbulence

“…The numerical approaches for solving the nonlinear fully compressible and anelastic equations given in Appendix A are described in Verhoeven and Stellmach (2014), Verhoeven et al (2015).…”