On upper bounds for the growth rate in the extended Taylor-Goldstein problem of hydrodynamic stability

Abstract

For the extended Taylor-Goldstein problem of hydrodynamic stability governing the stability of shear flows of an inviscid, incompressible but density stratified fluid in sea straits of arbitrary cross-section a new estimate for the growth rate of an arbitrary unstable normal mode is given for a class of basic flows. Furthermore the Howard's conjecture, namely, the growth rate kci → 0 as the wave number k →∞ is proved for two classes of basic flows.