Constraints on Deep-seated Zonal Winds Inside Jupiter and Saturn

TL;DR

This paper investigates the depth of zonal winds inside Jupiter and Saturn, using magnetic and dynamical constraints, and concludes that winds are likely confined to shallow, stably stratified layers rather than penetrating deep into the planets.

Contribution

It combines Ohmic dissipation constraints and dynamical analysis to provide new limits on the depth of zonal winds in giant planets, suggesting they are shallow.

Findings

Zonal winds cannot penetrate below regions where electrical conductivity is much lower.

Maximum wind penetration radii are approximately 0.96R_J for Jupiter and 0.86R_S for Saturn.

Strong winds are likely confined to shallow layers, not deep convective zones.

Abstract

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. 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.