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 specific...

For flow at a fixed gap ratio and Froude number, two distinctly different wake states are observed with the flow passing over the cylinder tending to switch from a state of attachment to the free surface, to one of separation from it, and then back again in a pseudo periodic fashion. The two dimensional numerically predicted behaviour is found to compare favourably with the experimental observa...

A condition is derived for the hydraulic criticality of a 2-layer flow with transverse variations in both layer velocities and thicknesses. The condition can be expressed in terms of a generalized composite Froude number. The derivation can be extended in order to obtain a critical condition for an N-layer system. The results apply to inviscid flows subject to the usual hydraulic approximation ...