Modelling the zonal winds of the giant planets

The surface zonal winds (i.e. flows independent of longitude) observed in the giant planets form a complex jet pattern with alternating eastward and westward direction. While the main equatorial band is prograde on Jupiter and Saturn, both Uranus and Neptune have a pronounced retrograde equatorial jet. The depth of these zonal winds remains however poorly known. Theoretical scenarios range from "shallow models", that assume that these zonal flows are restricted to a very thin layer close to the surface; to "deep models" that suppose that the jets are maintained by deep-seated convective motions that involve the whole molecular envelope. The latter idea is supported by fully 3-D numerical simulations using the so-called "Boussinesq approximation", that assumes the reference state (temperature, density, ...) to be constant with radius. While this approximation is suitable for the liquid iron cores of terrestrial planets, it becomes rather dubious in the envelopes of the four giant planets where density increases by several orders of magnitude. The so-called "anelastic approximation" thus provides a more realistic framework to simulate the dynamics of the zonal flows in such planets as it allows compressibility effects while filtering out fast acoustic waves. Recent anelastic models in fact suggest that including compressibility effects yields interesting differences to the classical Boussinesq approaches. Here, we therefore adopt an anelastic formulation to simulate 3-D compressible flows in rapidly rotating spherical shells. I will present the results of a parameter study on the effects of background density stratification and discuss the influences on both convective flows and zonal jets.