Secondary instability and tertiary states in rotating plane Couette flow

Abstract

Recent experimental studies have shown rich transition behaviour in rotating plane Couette

ow (RPCF). In this paper we study the transition in supercritical RPCF theoretically by determination of equilibrium and periodic orbit tertiary states via Floquet analysis on secondary Taylor vortex solutions. Two new tertiary states are discovered which we name oscillatory wavy vortex ow (oWVF) and skewed vortex ow (SVF). We present the bifurcation routes and stability properties of these new tertiary states, and in addition, we describe a bifurcation procedure whereby a set of defected wavy twist vortices are approached. Further to this, transition scenarios at ow parameters relevant to experimental works are investigated by computation of the set of stable attractors which exist on a large domain. The physically observed ow states are shown to share features with states in our set of attractors.