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Tidal dissipation due to convective turbulent viscosity shapes the evolutionof a variety of astrophysical binaries. For example, this type of dissipationdetermines the rate of orbital circularization in a binary with a post-mainsequence star that is evolving toward a common envelope phase. Viscousdissipation can also influence binaries with solar-type stars, or stars with aclose-in giant planet. In general, the effective viscosity in a convectivestellar envelope depends on the tidal forcing frequency $\omega_{\rm tide}$;when $\omega_{\rm tide}$ is larger than the turnover frequency of convectiveeddies, the viscosity is reduced. Previous work has focused on binaries innearly circular orbits. However, for eccentric orbits, the tidal potential hasmany forcing frequencies. In this paper, we develop a formalism for computingtidal dissipation that captures the effect of frequency-dependent turbulentviscosity and is valid for arbitrary binary eccentricities. We also present analternative simpler formulation that is suitable for very high eccentricities.We apply our formalisms to a giant branch (GB) star model and a solar-type starmodel. We find that a range of pseudosynchronous rotation rates are possiblefor both stellar models, and the pseudosynchronous rate can differ from theprediction of the commonly-used weak tidal friction theory by up to a factor ofa few. We also find that tidal decay and circularization due to turbulentviscosity can be a few orders of magnitude faster than predicted by weak tidalfriction in GB stars on eccentric, small pericentre orbits, but is suppressedby a few orders of magnitude in solar-type stars due to viscosity reduction.

Tidal Evolution of Eccentric Binaries Driven by Convective Turbulent Viscosity