On the limitations of the complex wave velocity in the instability problem of heterogeneous shear flows

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

“…It may be noted that the parabolic instability regions intersecting the Howard's semicircle were obtained by Banerjee et al (1988) for the Rayleigh problem of hydrodynamic stability. These results were improved and extended to the Taylor-Goldstein problem by Gupta et al (1989). Our results discussed above are extensions of the results of Gupta et al (1989) to the extended Taylor-Goldstein problem.…”

“…These results were improved and extended to the Taylor-Goldstein problem by Gupta et al (1989). Our results discussed above are extensions of the results of Gupta et al (1989) to the extended Taylor-Goldstein problem. Here it may be remarked that the techniques used in the present paper are similar to those used in Subbiah and Padmini (1999) on the barotropic-baroclinic instability problem.…”

“…Then examples of basic flows satisfying these conditions of intersection are constructed. Since the proofs are very similar to the proofs of the corresponding results for the Taylor-Goldstein problem found in Gupta et al (1989) we shall give below only the statements of the theorems.…”

On the Bounded Region for the Stratified Shear Flows in \(\beta\)-plane

“…Kochar and Jain [5] derived a semi ellipse theorem which depends on Richardson number. Gupta et al [2] derived unbounded instability region depending on condition.…”