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A Unified Instability Region for the Extended Taylor–Goldstein Problem of Hydrodynamic Stability

  • S. Sridevi (a1) (a2), Huashu Dou (a3) and V. Ganesh (a2)
Abstract

We consider inviscid, incompressible shear flows with variable density and variable cross section. For this problem, we derived a new estimate for the growth rate of an unstable mode and a parabolic instability region which intersects semiellipse instability region under some condition.

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*Corresponding author. Email: jaysridevi@yahoo.co.in (S. Sridevi), huashudou@yahoo.com (H. S. Dou)
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[1] Pratt, L., Deese, H. E., Murray, S. P. and Johns, W., Continuous dynamical modes in sea straits having arbitrary cross section with applications to the Babal Mandab, J. Phys. Oceanogo., 303 (2000), pp. 25152534.
[2] Deng, J., Pratt, L., Howard, L. and Jones, C., On stratified shear flow in sea straits of arbitrary cross section, Stud. Appl. Math., 3 (2003), pp. 409434.
[3] Subbiah, M. and Ganesh, V., Bounds on the phase speed and growth rate of extended Taylor-Goldstein problem, Fluid Dynamic Research, 40(5) (2008), pp. 364377.
[4] Ganesh, V., New upper bounds for the growth rate and a modified instability region for the extended Taylor-Goldstein problem of hydrodynamic stability, Indian J. Math., 52(2) (2010), pp. 415427.
[5] Ganesh, V. and Subbiah, M., On upper bounds for the growth rate in the extended Taylor-Goldstein problem of hydrodynamic stability, Proc. Indian Acad. Sci., 119(1) (2009), pp. 119135.
[6] Ganesh, V. and Subbiah, M., On an Eigen value problem of hydrodynamic stability, J. Anal., 15 (2007), pp. 4352.
[7] Reddy, V. R. and Subbiah, M., Staility of stratified shear flows in channel with variable cross sections, Appl. Math. Mech., 36(11) (2015), pp. 14591480.
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Advances in Applied Mathematics and Mechanics
  • ISSN: 2070-0733
  • EISSN: 2075-1354
  • URL: /core/journals/advances-in-applied-mathematics-and-mechanics
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