Rotating fluids

We are used to spinning solid tops moving in surprising ways. The dynamics of a rotating body certainly do not become simpler if it is liquid. The hydrodynamics of rotating fluids is a well worn subject of relevance to astrophysics, geophysics, oceanography and meteorology alike. In recent years, inertial oscillations have received renewed interest. Rotating fluids support wave motions, the so called inertial waves. These oscillations have in general a complex structure and contain internal shear layers. Whether and where these layers appear depends on the geometry of the container. The figure shows an axisymmetric inertial oscillation in a spherical shell at different Ekman numbers (10-5, 10-6, 10-7, 10-8). The rotation axis is pointing upwards, the upper section of each panel shows meridional streamlines, whereas the lower section shows contour plots of azimuthal velocity. Internal shear layers become increasingly evident as the Ekman number decreases. The notion of an attractor borrowed from dynamical systems theory has proved useful in determining the location of these shear layers.



Large Reynolds stresses, or equivalently, large momentum transfer occurs in the internal shear layers. The non-linear self-interaction of inertial modes drives zonal flows, similar to the banded structure of surface velocity known from the giant planets. According to a perturbation calculation, it is plausible that for example the tidally excited inertial modes in Jupiter contribute significantly to the surface winds observed on Jupiter. More pictures are found in the references.