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On Howard’s conjecture in heterogeneous shear flows instability of modified \(s\)-waves. (English) Zbl 0891.76030

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.

MSC:

76E05 Parallel shear flows in hydrodynamic stability

Citations:

Zbl 0104.20704
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