Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON HOMOGENEOUS SHEAR FLOWS WITH BOTTOM CROSS SECTION

  • S. LAVANYA (Research Scholar,Department of Mathematics, Koneru Lakshmaiah Education Foundation) ;
  • V. GANESH (Engineering Department, University of Technology and Applied Sciences) ;
  • G. VENKATA RAMANA REDDY (Department of Mathematics, Koneru Lakshmaiah Education Foundation)
  • Received : 2023.01.19
  • Accepted : 2023.06.12
  • Published : 2023.09.30
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Abstract

We consider inviscid, incompressible homogeneous shear flows of variable cross section known as extended Rayleigh problem. For this extended Rayleigh problem, we derived instability region which intersect with semi-circle instability region under some condition. Also we derived condition for stability, upper bound for amplification factor and growth rate of an unstable mode.

Keywords

Acknowledgement

The authors are thankful to reviewer for valuable suggestion to improve the manuscript.

References

  1. M.B. Banerjee, R.G. Shandil, K.S. Shirkot, and Daleep Sharma, Importance of Tollmien's counted example, Stud. Appl. Math. 105 (2000), 191-202. https://doi.org/10.1111/1467-9590.00148
  2. J. Deng, L. Pratt, L. Howard, and C. Jones, On stratified shear flow in sea straits of arbitrary cross section, Stud. in Appl. Math. 111 (2003), 409-434. https://doi.org/10.1111/1467-9590.t01-1-00040
  3. H.S. Dou, V. Ganesh, Short wave stability of homogeneous shear flows with variable topography, Appl. Math. Mech. 35 (2014), 541-548. https://doi.org/10.1007/s10483-014-1811-7
  4. L.J. Pratt, H.E. Deese, S.P. Murray, and W. Johns, Continuous dynamical modes in straits having arbitrary cross section with application to the Babal Mandab, Journal of Physical Oceanography 30 (2000), 2515-2534.
  5. K. Reena Priya, V. Ganesh, On the instability region for the extended Rayleigh problem of hydrodynamic stability, Applied Mathematical Sciences 9 (2015), 2265-2272. https://doi.org/10.12988/ams.2015.53207
  6. K. Reena Priya, V. Ganesh, An improved instability region for the extended Rayleigh problem of hydrodynamic stability, Computational and Applied Mathematics 38 (2019), 1-11. https://doi.org/10.1007/s40314-019-0767-y
  7. M. Subbiah, V. Ganesh, On the stability of homogeneous shear flows in sea straits of arbitrary cross section, Indian J. Pure Appl. Math. 38 (2007), 43-50.
  8. M. Subbiah, 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.) 120 (2010), 387-394. https://doi.org/10.1007/s12044-010-0030-3
  9. M. Subbiah, V. Ramakrishna Reddy, On the role of topography in the stability analysis of homogeneous shear flows, J. Analysis 19 (2011), 71-86,