The sensitivity of stratified flow stability to base flow modifications

We present a novel theory that determines the sensitivity of linear stability to changes in the density or velocity of a base flow. The sensitivity is based on global direct and adjoint eigenmodes of the linearized Boussinesq equation, and is inspired by constantdensity sensitivity analysis. The theory can be applied broadly to incompressible flows with small density variations, but it specifically provides new insight into the stability of density-stratified flows. Examples are given for the flows around a transverse thin plate at a Reynolds number of 30, a Prandtl number of 7.19, and Froude numbers of ∞ and 1. In the unstratified flow, the sensitivity is largest in the recirculation bubble; the stratified flow, however, exhibits high sensitivity in regions immediately upstream and downstream of the bluff body.