Abstract

We propose a new formalism to calculate the exchange of energy between tides and a convective flow when the turnover timescale is larger than the tidal period. We argue that the standard picture, in which the tides are described as a mean shear flow which is damped by fluctuating convective eddies, is inconsistent and should be reversed. In other words, the fluctuations are the tidal oscillations and the mean shear flow is provided by the largest convective eddies. The rate at which energy is exchanged between the tides and convection is then given by the coupling of the Reynolds stress associated the tidal velocity to the shear associated with the convective velocity. We further argue that, even if energy is intermittently transferred from convection to the tides, it must ultimately return to the convective flow and transported efficiently to the stellar surface on the convective timescale. This is consistent with assuming that energy is locally transferred from the tides to the convective flow. Using this assumption, we obtain values for the tidal dissipation Q factor of Jupiter and Saturn, for the circularization periods of late-type binaries (taking into account the full time evolution of the stellar structure) and for hot Jupiters in good overall agreement with observations.