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Stratified rotational instabilities at low Péclet number

Creative Commons 'BY' version 4.0 license

Observational evidence points to the need for extra mixing in stars. Zahn (1992) proposed a turbulent mixing model due to shear instabilities and the model has been verified to be valid for non-rotating cases. It is not clear, however, whether Zahn’s model would still be valid in the presence of rotation. We use a triply-periodic Cartesian domain in the equator of a rotating star to examine this issue. We use the Boussinesq approximation, and assume the background temperature gradient to be constant, and the flow to experience a horizontal sinusoidal body force. A linear stability analysis reveals the existence of several regimes that are dominated by shear instabilities or GSF instabilities. Based on linear stability results, we run a set of numerical simulations for different control parameters including the rotation rate. At small rotation rates, we recover the previous results obtained in the non-rotating case. At higher rotation rates, we find regions governed by different dynamics that are not accounted for by Zahn’s model. In each case, we provide quantitative data on the heat and momentum transports induced by turbulence.

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