Banerjee, Mihir B.; Shandil, R. G.; Prakash, Jyoti; Bandral, Balraj Singh; Lal, Prem; Kanwar, Vinay On Howard’s conjecture in heterogeneous shear flows instability of modified \(s\)-waves. (English) Zbl 0891.76030 Indian J. Pure Appl. Math. 28, No. 6, 825-834 (1997). Summary: We examine the conjecture of L. N. Howard [J. Fluid Mech. 10, 509-512 (1961; Zbl 0104.20704)] that in the linear instability problem for inviscid heterogeneous parallel shear flow the growth rate of an arbitrary unstable wave tends to zero as the wave length tends to zero. A rigorous mathematical proof of this assertion is presented here for Garcia flows, where the basic velocity distribution has an inflexion point in the flow domain while the vertical gradient of the basic density distribution vanishes at this oint. Cited in 3 Documents MSC: 76E05 Parallel shear flows in hydrodynamic stability Keywords:inflexion point; Garcia flows; linear instability problem; inviscid heterogeneous parallel shear flow Citations:Zbl 0104.20704 PDFBibTeX XMLCite \textit{M. B. Banerjee} et al., Indian J. Pure Appl. Math. 28, No. 6, 825--834 (1997; Zbl 0891.76030)