On a new formulation for energy transfer between convection and fast tides with application to giant planets and solar type stars

Abstract

All the studies of the interaction between tides and a convective flow assume that the large-scale tides can be described as a mean shear flow that is damped by small-scale fluctuating convective eddies. The convective Reynolds stress is calculated using mixing length theory, accounting for a sharp suppression of dissipation when the turnover time-scale is larger than the tidal period. This yields tidal dissipation rates several orders of magnitude too small to account for the circularization periods of late-type binaries or the tidal dissipation factor of giant planets. Here, we argue that the above description is inconsistent, because fluctuations and mean flow should be identified based on the time-scale, not on the spatial scale, on which they vary. Therefore, the standard picture should be reversed, with the fluctuations being the tidal oscillations and the mean shear flow provided by the largest convective eddies. We assume that energy is locally transferred from the tides to the convective flow. Using this assumption, we obtain values for the tidal Q factor of Jupiter and Saturn and for the circularization periods of pre-main-sequence binaries in good agreement with observations. The time-scales obtained with the equilibrium tide approximation are however still 40 times too large to account for the circularization periods of late-type binaries. For these systems, shear in the tachocline or at the base of the convective zone may be the main cause of tidal dissipation.