On the Long Wave Stability of Shear Flows in Sea Straits of Arbitrary Cross Section

We consider an eigen value problem of hydrodynamic stability which deals with inviscid, incompressible, density stratified shear flows of variable topography. In this paper, we obtained a condition for long wave stability i.e., if the wave number kis less than or equal to critical wave number $$k_{c}$$ kc which is greater than zero then the flow is stable. This result is illustrated with examples. An instability region which depends on various parameters is derived for an unstable mode and an estimate for the growth rate of an unstable mode is also obtained.