Fast Tides in Slow Stars: the Efficiency of Eddy Viscosity

Abstract

The turbulent viscosity of convection is believed to circularize the orbits of close binary stars. When the tidal period is shorter than the turnover time of the largest eddies, turbulent viscosity is believed to be suppressed. The degree of suppression is disputed. We re-examine these beliefs via direct perturbative calculations, linearizing the fluid equations on a turbulent background, and by numerical integration of a chaotic dynamical system subject to periodic forcing. We find that (i) dissipation of rapid tides is severely suppressed; and (ii) turbulent convection does not circularize binaries while the stars are on the main sequence. The latter conclusion seems secure (though weaker) even without the former.