On the Nonlinear Stability of Inviscid Homogeneous Shear Flows in Sea Straits of Arbitrary Cross Sections

  • V Ramakrishnareddy Department of Mathematics, Pondicherry University, Pondicherry-605014, India
  • M Subbiah Department of Mathematics, Pondicherry University, Pondicherry-605014, India
Keywords: Nonlinear stability, inviscid shear flows, variable bottom, sea straits.


V I Arnol’d, On an a priori estimate in the theory of hydrodynamical stability, Amer. Math. Soc. Trans. Ser. 2, vol. 79, pp. 267-269, 1969.

J Deng, L Pratt, L Howard and C Jones, On stratified shear flows in sea Straits of arbitrary cross section, Studies in Appl. Math., vol. 111, pp. 409-434, 2003.

L J Pratt, H E Deese, S P Murray and W Johns, Continuous dynamical Modes in straits having arbitrary cross sections with applications to the Bab al Mandab, J. Phys. Oceanogr., vol. 30, pp. 2515-2534, 2000.

P G Drazin and W H Reid, Hydrodynamic Stability, Cambridge University Press, Cambridge, UK, 1981.

M Subbiah and V Ganesh, On the stability of homogeneous shear flows in sea straits of arbitrary cross section, Indian J. Pur Appl. Math., vol. 38, pp. 43-50, 2007.

M Subbiah and V Ganesh, On short wave stability and sufficient conditions for stability in the extended Rayleigh problem of hydrodynamic stability, Proc. Indian Acad. Sci. (Math Sci), vol. 120, pp. 387-394, 2010.

M Subbiah and V Ramakrishnareddy, On the role of topography in the stability analysis of homogeneous shear flows, Journal of Analysis (to appear).

D D Joseph, Stability of fluid motions I, II, Springer, 1976.

V I Arnol’d, Conditions for nonlinear stability of stationary plane curvilinear flows of an ideal fluid, Sov. Math. Dokl., vol. 6, pp. 773-776, 1965.

V I Arnol’d and B Khesin, Topological Methods in Hydrodynamics, Applied Mathematical Sciences, vol. 125, Springer, 1998.

C Marchioro and M Pulvirenti, Mathematical theory of incompressible non-viscous fluids, Applied Mathematical Sciences, vol. 95, Springer, 1995.

D D Holm, J E Marsden and T Ratiu, Nonlinear stability of the Kelvin-Stuart cat’s eyes flow, Lect. in Appl. Mathematics, AMS, vol. 23, pp. 171-186, 1986.

M E McIntyre and T G Shepherd, An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows with remark on Hamiltonian structure and on Arnol’d’s stability theorems, J. Fluid Mech., vol. 181, pp. 527-565, 1987.

M Subbiah and M Padmini, Note on the nonlinear stability of equivalent barotropic flows, Indian. J. Pure Appl. Math., vol. 30, pp. 1261-1272, 1999.

M Subbiah and V Ganesh, Bounds on the phase speed and growth rate of the extended Taylor-Goldstein problem, Fluid Dynamics Research, vol. 40, pp. 364-377, 2008.

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