Constraints on Deep-seated Zonal Winds Inside Jupiter and Saturn

By Junjun Liu, Peter Goldreich, D. Stevenson. 2007

181 citations recorded by the source corpus.

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 0.96R_J and 0.86R_S, 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.

Subfields: Astronomy and Astrophysics, Geophysics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/c79f5747ba2bd0a7ffb5d7f502b7cd17b0efb334

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Citations in the corpus

ATMOSPHERIC CIRCULATION OF HOT JUPITERS: COUPLED RADIATIVE-DYNAMICAL GENERAL CIRCULATION MODEL SIMULATIONS OF HD 189733b and HD 209458b (2008, unknown): “In the deep interior of gas giants (p & 105 bars), Ohmic dissipation may also provide an important source of drag (Kirk & Stevenson 1987; Liu et al. 2008), although it is unclear whether the atmospheric circulation on hot Jupiters couples to such deep regions.”
Formation of Jets and Equatorial Superrotation on Jupiter (2008, background): “…the conductivity of hydrogen increases with depth, making a continuous transition from very low values in the outer atmosphere to a constant value reached at the depth at which hydrogen becomes metallic, which occurs at ∼1.4 Mbar or ∼0.84 Jupiter radii (Nellis et al. 1996; Liu et al. 2008).”
The Interior Structure, Composition, and Evolution of Giant Planets (2009, background): “…& Trubitsyn (1978) suggest a small correction of 0.5% for J2 and 1% for J4 based on observations of atmospheric winds (see also Hubbard 1982); Liu et al. (2008) predict a penetration depth of deep-zonal winds down only 0.04RJ, supporting an only slight effect on the low-degree gravitational…”
JUPITER MODELS WITH IMPROVED AB INITIO HYDROGEN EQUATION OF STATE (H-REOS.2) (2011, background): “…three-layer models over the two-layer models as they allow to reproduce J4 without invoking the hypothesis of deep-zonal winds because the penetration depth of such winds might have to be much deeper (< 0.96 RJ) than physically allowed in the presence of convective flow motions (Liu et al. 2008).”
The deep wind structure of the giant planets: Results from an anelastic general circulation model (2009, background): “As discussed in the introduction, MHD effects, which we do not include here, might put additional limitations on the dynamics (Liu et al., 2007).”
AB INITIO SIMULATIONS FOR MATERIAL PROPERTIES ALONG THE JUPITER ADIABAT (2012, background): “In contrast, our ab initio results are in excellent agreement with a simple semiconductor model for the conductivity in Jupiter’s outer regions as given by Liu et al. (2008).”