On transition via transient growth in Couette flow

A possible explanation for the transition phenomenon in Couette flow is the mechanism of transient growth. In this work we consider the instability of a two dimensional base-flow, consisting of Couette flow and pair of streamwise independent counter-rotating vortices (CVPs). We show analytically that the inclusion of nonlinear interactions between the base-flow and the CVPs is required in order to obtain eigenvalues that correspond to transition scenarios obtained using a direct numerical simulation (DNS). The relative dominance of the inflection points in the wall-normal and spanwise directions is studied using linear and nonlinear analysis.