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Canuto, V.M., 1998: Turbulence in stars. II. Shear, stable stratification, and radiative losses. Astrophys. J., 508, 767-779, doi:10.1086/306427.
For many years shear-driven turbulence was thought to provide sufficient turbulent mixing in stably stratified regions to explain stellar structure data. It has recently been argued that the mixing is too weak and that alternative mixing mechanisms are required. The conclusion is predicated, among others, on the key assumption that turbulence exists only for Ri < Ricr = 1/4. This result follows from linear stability anlysis and contradicts a variety of data. We suggest a new definition of Ricr: it is the value of Ri at which the turbulent kinetic energy vanishes. We find that for Pe > 1 (no radiative losses) Ricr ~ 1, while for Pe < 1 (important radiative losses) Ricr ~ Pe-1 ≥ 1. Thus, we find more mixing. We present an internally consistent treatment of all the physical variables, individually and collectively, and show that turbulence is alive and well above the Ri > 1/4 limit. However, without a specific application of the model to a stellar case, we cannot claim that the new model will provide the mixing required by stellar data.
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