zbMATH — the first resource for mathematics

Stability of stratified shear flows. (English) Zbl 0575.76106
For a steady plane parallel flow of an inviscid, incompressible fluid of variable density under gravity, it is shown that the complex wave velocity for any unstable mode lies in a semiellipse-type region whose major axis coincides with the diameter of Howard’s semicircle, while its minor axis depends on the stratification. If \(kc_ i\) denotes the complex part of wave frequency and \(J_ 0\) the minimum of the local Richardson number over the flow domain, it is further established that \(kc_ i\to 0+\) as \(J_ 0\to 1/4-\). The case of free upper surface and conditional reduction dependent on the curvature of the basic velocity of the unstable region is also studied.

76V05 Reaction effects in flows
76E05 Parallel shear flows in hydrodynamic stability
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76F10 Shear flows and turbulence
Full Text: DOI
[1] Banerjee, M.B; Jain, R.K, Math. student, 40, 111-119, (1972)
[2] Banerjee, M.B; Gupta, J; Gupta, S.K, J. math. phys. sci., 8, 475-484, (1974)
[3] Banerjee, M.B; Shandil, R.G; Gupta, J, J. math. phys. sci., 12, 1-18, (1978)
[4] Howard, L.N, J. fluid mech., 10, 509-512, (1961)
[5] Kochar, G.T; Jain, R.K, J. fluid mech., 91, 489-491, (1979)
[6] Kochar, G.T; Jain, R.K, J. phys. soc. Japan, 47, 654-658, (1979)
[7] Miles, J.W, J. fluid mech., 10, 496-508, (1961)
[8] Schultz, M.H, Spline analysis, (1973), Prentice-Hall Englewood Diffs, N. J · Zbl 0333.41009
[9] Synge, J.L, Trans. roy. soc. Canada, 27, 1-18, (1933)
[10] Yih, C.S, (), 857-861
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.