Atmospheric and Oceanic Sciences Departmental Seminar Series
Instabilities in rotating shear flows: role in driving large scale vortices
a talk by
Applied Mathematics, UC Santa Cruz
We study the effects of global rotation on the growth and saturation of the fingering (double- diffusive) instability and estimate the compositional transport rates as a function of the relevant non-dimensional parameters (Rossby number and density ratio) at low Prandtl numbers through direct numerical simulations (DNSs). Rather surprisingly, within our explored range of parameters, we find rotation to have very little eff on vertical transport apart for an exceptional case where a cyclonic large scale vortex (LSV) is observed at low density ratio and fairly high Taylor number. The LSV leads to significant enhancement in the fingering transport rates by concentrating high composition fluid at its core which moves downward. The formation of such LSVs is of particular interest for solving the missing mixing problem in the astrophysical context of RGB stars though the parameter regime in which we observe the emergence of this LSV seems to be quite far from the astrophysical expectation. Nevertheless, we attempt to explain the origin of such vortical flows from two separate points of view within the framework of the classical inverse cascade ideas as well from linear theory of an idealized columnar shear flow through a rectangular domain in a rotating frame as well as idealized DNSs to predict the eff of increasing rotation on various modes of instabilities, and discuss their role in imparting angular momentum to the shear flow.