Interaction between convective and elliptical instabilities in rotating fluids

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Turbulent convection is a ubiquitous fluid dynamical process in nature, occurring in industrial applications as well as in the interiors of many stars and planets. Elliptical fluid streamlines are unstable to a generic fluid dynamical instability referred as the elliptical instability, which can drive inertial waves to become unstable and potentially lead to turbulence. The interaction of these two instabilities in rotating fluids has not been studied in detail previously, and yet both are believed to occur together in several applications, including in tidally-deformed planets. This project will study the fundamental interaction between elliptical instabilities and convection, using both analytical and numerical approaches. In particular, the nonlinear outcome of the two instabilities will be simulated numerically with the goal to determine how the turbulent transport and resulting flows due to each instability are affected by the presence of the other. This study will benefit our understand of the general interaction of two distinct fluid dynamical instabilities and the resulting turbulence, but it also has specific applications to tidally-deformed planets in astrophysics.