Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-11T13:59:26.677Z Has data issue: false hasContentIssue false
  • English
  • Français

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:jaysridevi@yahoo.co.in (S. Sridevi), huashudou@yahoo.com (H. S. Dou)
*Corresponding author. Email:jaysridevi@yahoo.co.in (S. Sridevi), huashudou@yahoo.com (H. S. Dou)
Get access

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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