Intrusions with variable inflow into a linearly stratified ambient

The propagation of an intrusion of volume $q t ^\alpha$ into a linearly stratified ambient along the plane of neutral buoyancy is considered ($t$ is the time and $q, \alpha$ are positive constants). Theoretical results are presented for rectangular and cylindrical axisymmetric (or wedge) geometries, for both inertial-buoyancy and viscous-buoyancy balances. However, a sharp practical criterion for the boundary between the regimes is not available. The flow may undergo change of regime inertial/viscous (or the inverse) after some time of propagation, depending on the value of $\alpha$. The differences with the non-stratified counterpart are discussed.