Stability of Stratified Compressible Shear Flow

Dr. ManjuBala

doi:https://doi.org/10.14445/22315373/IJMTT-V46P511

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 46 | Number 2 | Year 2017 | Article Id. IJMTT-V46P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V46P511

Stability of Stratified Compressible Shear Flow

Dr. ManjuBala

Citation :

Dr. ManjuBala, "Stability of Stratified Compressible Shear Flow," International Journal of Mathematics Trends and Technology (IJMTT), vol. 46, no. 2, pp. 53-61, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V46P511

Abstract

In the present chapter we have studied the effect of a magnetic field on linear stability of stratified horizontal flows of an in viscid compressible fluid by the generalized progressing wave expansion method. Here we have discussed the different cases and have established the conditions for the stability. It is found that the magnetic field stabilizes the system.

Keywords

Linear stability, Inviscid compressible fluid shear flows.

References

[1]. Eckhoff, S. Khut and Storesletten, L., J. Fluid Mech. 89, 401, (1978)
[2]. Ellingsen, T. and Palm, E., Phys. Fluids 18, 487, (1975).
[3]. Falsaperla, P. and Mulone, G., Stability in the rotating Bfenard problem with Newton-Robin and fixed heat flux boundary conditions. Mechanics Research Communications, 37(1),122-128, (2010).
[4]. Gans, R.F., J. Fluid Mech. 68, 413, (1975)
[5]. Hamman, C.W., Kelwick, J.C., & Kirby, R.M., On the Lamb vector divergence in Navier-Stokes flows, J. Fluid Mech. 610 261-284. (2008).
[6]. Howard, L. N., Stud. Appl. Math. 52, 39, (1973).
[7]. Howard, L. N. And Gupta, A.S., J. Fluid mech. 14, 463, (1962).
[8]. Landehl, M. T., J. Fluid Mech. 98, 243, (1980).
[9]. Rudraiah, N., Effect of porous lining on reducing the growth rate of Rayleigh-Taylor instability in the inertial fusion energy target. Fusion Sci., and tech. 43, 307-311, (2003).
[10]. Sharma, V. and Rana, G.C., “Thermosolutal Instability of Rivlin-Ericksen Rotating Fluid in the Presence of Magnetic Field and Variable Gravity Field in Porous Medium”, Proc. Nat. Acad. Sci. India, Vol. 73, No. A, (2003), 1.
[11]. Storesletten, L., Quart. J. Mech. Appl. Math. 35, 326, (1982).
[12]. Storesletten, L. and Barletta, A., Linear instability of mixed convection of cold water in a porous layer induced by viscous dissipation. Int. J. of Thermal Sciences, 48, 655-664, (2009).
[13]. Straughan, B., Stability and wave motion in porous media., volume 165 of Ser. In Appl. Math. Sci. Springer, New-York, (2008).
[14]. Sunil and Mahajan, A., A nonlinear stability analysis for rotating magnetized ferrofluid heated from below. Appl. Math. Computation, 204(1), 299-310, (2008a). ISSN 0096-3003.
[15]. Straughan, E., Stability and wave motion in porous media., volume 165 of Ser. In Appl. Math. Sci. Springer, New-York, (2008).
[16]. Straughan, B., The Energy Method, Stability, and Nonlinear Convection, (2nd ed.), volume 91 of Ser. In Appl. Math. Sci. Springer, New-York, (2004).
[17]. Tillack, M.S., & Morley, N.B., Magnetohydrodynamics, 14-th Editionm. (1998).
[18]. Trefethen, L. N., Trefethen, A.E., Reddy, S.C. & Driscoll, T.A., Hydrodynamic stability without eigenvalues. Science 261, 578-584, (1993).
[19]. Warran, F.W., J. Fluid Mech. 68, 403, (1975).