A comprehensive theoretical-laboratory-numerical study is proposed to advance our knowledge about nonlinear dynamics of rotating stratified spin-up flows with particular emphasis on (i) the late-time flow evolution characterized by the non-axisymmetric flow behavior, and (ii) the effects of bottom topography on the boundary flows, global circulation and flow stability. Many flows generated by rotation in axisymmetric enclosures break into non-axisymmetric patterns when the governing parameters exceed some threshold values. Axisymmetry-breaking instabilities are of major importance in many applications. A large number of engineering, environmental and geo/astrophysical applied problems where the flow stability depends on interplay between shear and stratification effects provides for the need of deeper understanding of physical mechanisms governing the flow dynamics.