ALBERT

Description: Recent observations of Jupiter and Saturn suggest that heavy elements may be diluted in the gaseous envelope, providing a compositional gradient that could stabilize ordinary convection and produce a stably stratified layer near the core of these planets. This region could consist of semiconvective layers with a staircase-like density profile, which have multiple convective zones separated by thin stably stratified interfaces, as a result of double-diffusive convection. These layers could have important effects on wave propagation and tidal dissipation that have not been fully explored. We analyse the effects of these layers on the propagation and transmission of internal waves within giant planets, extending prior work in a local Cartesian model. We adopt a simplified global Boussinesq planetary model in which we explore the internal waves in a non-rotating spherical body. We begin by studying the free modes of a region containing semiconvective layers. We then analyse the transmission of internal waves through such a region. The free modes depend strongly on the staircase properties, and consist of modes with both internal and interfacial gravity wave-like behaviour. We determine the frequency shifts of these waves as a function of the number of steps to explore their potential to probe planetary internal structures. We also find that wave transmission is strongly affected by the presence of a staircase. Very large wavelength waves are transmitted efficiently, but small-scale waves are only transmitted if they are resonant with one of the free modes. The effective size of the core is therefore larger for non-resonant modes.

Description: We investigate the linear response to longitudinal and latitudinal libration of a rapidly rotating fluid-filled sphere. Asymptotic methods are used to explore the structure of resonant modes in both cases, provided that the nondimensional libration frequency is in the range 0〈ω〈2. High-resolution numerics are then used to map out this entire frequency range, picking out both the resonant peaks as well as the non-resonant troughs in between. The kinetic energy is O(1) at the peaks, and O(E1/2) at the troughs. As the Ekman number is reduced, down to E=1e-10 for longitudinal libration and E=1e-9 for latitudinal libration, the frequency response also exhibits an increasingly fractal structure, with more and more peaks and troughs emerging. The spacing between peaks is seen to follow an self-similarity factor. However, detailed examinations of some of the more prominent troughs shows that their widths follow anE〈sup〉~0.23〈/sup〉 self-similarity factor.