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Publication Type : Journal Article
Publisher : Proceedings of the Indian Academy of Sciences: Mathematical Sciences
Source : Proceedings of the Indian Academy of Sciences: Mathematical Sciences, Volume 120, Number 3, p.387-394 (2010)
Keywords : Basic flow, Critical wave numbers, Flow domains, Hydrodynamic stability, hydrodynamics, Normal modes, Rayleigh, Sea straits, Shear flow, Short waves, Stability, Stability results, Sufficient conditions, Variable bottom, Vertical coordinates, Wave numbers
Year : 2010
Abstract : We consider the extended Rayleigh problem of hydrodynamic stability dealing with the stability of inviscid homogeneous shear flows in sea straits of arbitrary cross section.We prove a short wave stability result, namely, ifk gt; 0 is the wave number of a normal mode then k gt; k c (for some critical wave number k c) implies the stability of the mode for a class of basic flows. Furthermore, if, where U 0 is the basic velocity, T 0 (a constant) the topography and prime denotes differentiation with respect to vertical coordinate z then we prove that a sufficient condition for the stability of basic flow is 0 lt; K(z), where the flow domain is 0 ≤ z ≤ D. © Indian Academy of Sciences.
Cite this Research Publication : Ma Subbiah and Ganesh, Vb, “On short wave stability and sufficient conditions for stability in the extended Rayleigh problem of hydrodynamic stability”, Proceedings of the Indian Academy of Sciences: Mathematical Sciences, vol. 120, pp. 387-394, 2010.