A Parameter Study for Baroclinic Vortex Amplification

Recent studies have shown that baroclinic vortex amplification is strongly dependent on certain factors, namely, the global entropy gradient, the efficiency of thermal diffusion and/or relaxation as well as numerical resolution. We conduct a comprehensive study of a broad range and combination of various entropy gradients, thermal diffusion and thermal relaxation time-scales via local shearing sheet simulations covering the parameter space relevant for protoplanetary disks. We measure the Reynolds stresses as a function of our control parameters and see that there is angular momentum transport even for entropy gradients as low as $\beta=-{d\ln s}/{d\ln r}={1}/{2}$, which corresponds to values observed in protoplanetary accretion disks. The amplification-rate of the perturbations, $\Gamma$, appears to be proportional to $\beta^2$ and thus proportional to the square of the \BV ($\Gamma \propto \beta^2 \propto N^2$). The saturation level of Reynolds stresses on the other hand seems to be proportional to $\beta^{1/2}$. This highlights the importance of baroclinic effects even for the low entropy gradients expected in protoplanetary disks.
Comment: 13 pages, 11 figures, 1 table, accepted by ApJ