The stability of stratified, gravity driven exchange flow

Exchange flows are found in a wide variety of scenarios, both industrial and natural, with a wide range of parameter regimes – for instance from low viscosity oceanographic flows to high viscosity oils to the extreme viscosity of lava. The possible arrangements of such flows and their respective stabilities are the subject of much ongoing interest. Here we analyse the stability of stratified, gravity driven exchange flow. We consider developed flow profiles, rather than an initialisation problem, in order to establish what long-time arrangements may be possible.