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

Part of: Hydrodynamic stability

Published online by Cambridge University Press:  28 November 2017

S. Sridevi ,
Huashu Dou  and
V. Ganesh
S. Sridevi*
Affiliation:
Research and Development Centre, Bharathiyar University, Coimbatore–641046, India Department of Mathematics, Rajiv Gandhi College of Engineering and Technology, Kirumampakkam, Puducherry-607402, India
Huashu Dou*
Affiliation:
Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China
V. Ganesh
Affiliation:
Department of Mathematics, Rajiv Gandhi College of Engineering and Technology, Kirumampakkam, Puducherry-607402, India
*
*Corresponding author. Email:[email protected] (S. Sridevi), [email protected] (H. S. Dou)
*Corresponding author. Email:[email protected] (S. Sridevi), [email protected] (H. S. Dou)
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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.

Keywords

Hydrodynamic stabilityshear flowsvariable bottomsea straits

MSC classification

Secondary: 76E05: Parallel shear flows
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 6 , December 2017 , pp. 1404 - 1419
Copyright
Copyright © Global-Science Press 2017 

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References

[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. 2515–2534.2.0.CO;2>CrossRefGoogle Scholar
[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. 409–434.CrossRefGoogle Scholar
[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. 364–377.CrossRefGoogle Scholar
[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. 415–427.Google Scholar
[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. 119–135.Google Scholar
[6] Ganesh, V. and Subbiah, M., On an Eigen value problem of hydrodynamic stability, J. Anal., 15 (2007), pp. 43–52.Google Scholar
[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. 1459–1480.CrossRefGoogle Scholar