Bounds on the phase speed and growth rate of the extended Taylor-Goldstein problem

In this paper we consider the extended Taylor-Goldstein problem of hydrodynamic stability dealing with the stability of stratified shear flows in sea straits of arbitrary cross section. For this problem we have obtained the upper and lower bounds on the phase velocity of neutral modes and estimates for the growth rate of unstable modes. Furthermore, we have found a semielliptical instability region depending on the minimum Richardson number and parabolic instability regions which intersect the semielliptical instability region for a class of basic flows.