Primary instability of a Taylor-Couette flow with a radial stratificationand radial buoyancy

We consider the primary instability onset of a Taylor-Couette flow with a radial stratification and radial volumic force. Our system corresponds to a simplified geophysical model that takes into account the effect of the buoyancy opposed to the centrifugal force. Three parameters of the physical problem, which correspond to the buoyancy, the diffusivity, and the rotational velocity, are considered to describe the onset of the primary instability. Using an efficient numerical method, we compute the threshold value of the Taylor number, which depends on the Froude and Schmidt numbers, and describe the most unstable mode provided by the linear analysis.