Chitkara University Publications

Bounds For The Complex Part of Phase Velocity

Abstract:

We study incompressible, inviscid, density stratified fluid with variable cross section in this present paper. For this problem, we have obtained a bound for the complex part of phase velocity. Furthermore, we have obtained an instability region which depends on number of parameters.

Author(s):

  • S Sridevi, Department of Mathematics, Rajiv Gandhi College of Engineering and Technology, Kirumampakkam, Puducherry, 607 402, India
  • V Ganesh, Department of Mathematics, Higher College of Technology, Muscat, Sultanate of Oman
  • R Thenmozhy, Department of Mathematics, Periyar Govt. Arts College, Cuddalore, Tamilnadu, 607 001, India

DOI: 

Keywords: 

Hydrodynamics, Phase, velocity, Instability, region

References:

Deng, J., Pratt, L., Howard, L., Jones, C. (2008). ”On stratified shear flow in sea straits of arbitrary cross section”, Stud. Appl. Math., 111, 409–434. (https://doi.org/10.1111/1467-9590.t01-1-00040)

Ganesh, V. (2010). New Upper Bound for the growth rate and a modified instability region for the extended Taylor-Goldstein problem of hydrodynamic stability, Ind. J. Maths, 52, 415–427. (www.amsallahabad.org /pdf/ijm522.pdf )

Ganesh, V., Subbiah, M. (2009). “On upper bounds for the growth rate in the extended Taylor-Goldstein problem of hydrodynamic stability”, Proc. Indian Acad. Sci., 119, 119–135. (https://doi.org/10.1007/s12044-009-0012-5)

Pratt, L., Deese, H. E., Murray, S. P. (2000). Johns. W.,“Continuous dynamical modes in sea straits having arbitrary cross section with applications to the Bobal Mandab”, J. Phys. Oceanogo., 30, 2515–2534. ( h t t p s : / / d o i . o r g / 1 0 . 1 1 7 5 / 1 5 2 0 -0485(2000)030<2515:CDMISH>2.0.CO;2)

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Reenapriya, K., Ganesh, V. (2015). On the instability region for the extended taylor-Goldstein problem of hydrodynamic stability, Appl. Maths. Sci., 9, 2265–2272. (https://doi.org/10.12988/ams.2015.53207)

Sridevi, S., Ganesh, V. (2015). On the Bounds for the Complex Wave Velocity for Growing Perturbations, Applied Mathematical Sciences, 9, 2245–2253, (https://doi.org/10.12988/ams.2015.53205)

Sridevi. S. and Ganesh, V. (2016). On the stability of shear flows with bottom topography, International Journal of Mathematical Analysis, 10, 651–659. (https://doi.org/10.12988/ijma.2016.6225)

Sridevi, S. and Ganesh, V. (2018). On the Long wave stability of Shear flows in a sea straits of arbitrary cross section, Int. J. Appl. and Comp. Maths. (https://doi.org/10.1007/s40819-017-0439-9)

Sridevi, S. Hua-Shu, D. and Ganesh, V. (2017). A Unified Instability Region for the extended Taylor -Goldstein Problem of Hydrodynamic Stability, Adv. in Appl. Maths and Mech., 9, 1404–1419. (https://doi.org/10.4208/aamm.OA-2016-0022)

Subbiah, M., Ganesh, V. (2008). “Bounds on the phase speed and growth rate of extended Taylor-Goldstein problem”, Fluid Dynamic Research, 40, 364–377. (https://doi.org/10.1016/j.fluiddyn.2007.11.001)

 

 

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