Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON THE IMPROVED INSTABILITY REGION FOR THE CIRCULAR RAYLEIGH PROBLEM OF HYDRODYNAMIC STABILITY

  • G., CHANDRASHEKHAR (Department of Mathematics, Osmania University) ;
  • A., VENKATALAXMI (Department of Mathematics, Osmania University)
  • Received : 2022.03.27
  • Accepted : 2022.09.02
  • Published : 2023.01.30
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Abstract

We consider circular Rayleigh problem of hydrodynamic stability which deals with linear stability of axial flows of an incompressible iniviscid homogeneous fluid to axisymmetric disturbances. For this problem, we obtained two parabolic instability regions which intersect with Batchelor and Gill semi-circle under some condition. This has been illustrated with examples. Also, we derived upper bound for the amplification factor.

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Acknowledgement

The authors thankful to the reviewers for valuable suggestion to improve the manuscript.

References

  1. M.B. Banerjee and J.R. Gupta and M. Subbiah, On reducing Howard's semi circle for homogeneous shear flows, J. Math Anal. Appl. 130 (1988), 398-402. https://doi.org/10.1016/0022-247x(88)90315-0
  2. G.K. Batchelor and A.E. Gill, Analysis of the stability of axisymetric jets, J. Fluid Mech. 14 (1962), 529-551. https://doi.org/10.1017/S0022112062001421
  3. S. Chandrasekhar, Hydrodynamic and hydromagnetic instability, Clarendon Oxford, 1961.
  4. P.G. Drazin and W.H. Reid, Hydrodynamic stability, Cambridge University Press, Cambridge, 1981.
  5. J.R. Gupta, R.G. Shandil and S.D. Rana, On hydrodynamic and hydromagnetic stability of inviscid flows between coaxial cylinders, Inter. J. Fluid Mech. Res. 144 (1989), 367-376.
  6. M.S.A. Ipye, and M. Subbiah, On hydrodynamic and hydromagnetic stability of inviscid flows between coaxial cylinders, Inter. J. Fluid Mech. Res. 37(2) (2010), 1-15. https://doi.org/10.1615/InterJFluidMechRes.v37.i1.10
  7. P. Pavithra and M. Subbiah, On sufficient conditions for stability in the circular Rayleigh problem of hydrodynamics stability, The Journal of Analysis 27 (2019), 781-795. https://doi.org/10.1007/s41478-018-0128-z
  8. P. Pavithra and M. Subbiah, Note on instability regions in the circular Rayleigh problem of hydrodynamic Stability, Proc. Natl. Aca. Sci. 91 (2021), 49-54.
  9. K. Reena Priya and V. Ganesh, On the instability region for the extended Rayleigh problem of hydrodynamic stability, Applied Mathematical Science 9 (2015), 2245-2253. https://doi.org/10.12988/ams.2015.53205
  10. K. Reena Priya and V. Ganesh, An improved instability region for the extended Rayleigh problem of hydrodynamic stability, Computational and Applied Mathematical Sciences 38 (2019), 1-11. https://doi.org/10.1007/s40314-019-0767-y
  11. A.G. Walton, Stability of circular Poiseuille-Couette flow to axisymmetric disturbances, J. Fluid Mech. 500 (2004), 169-210.  https://doi.org/10.1017/S0022112003007158