ON MAGNETOHYDRODYNAMIC VERONIS’S THERMOHALINE CONVECTION

Abstract

In this paper, the mathematically correct solution to more general physical situation such as magnetohydrodynamic Veronis’s [17] thermohaline convection problem for the case of dynamically free, thermally insulating and electrically perfectly conducting boundaries is obtained. Some important results pertaining to the validity of principle of exchange of stabilities has been derived and discussed in detail

Keywords

• Convection, magnetohydrodynamic, principle of exchange of stability, viscosity

References

1. [1] M.B. Banerjee, J.R. Gupta, R.G. Shandil, S.K. Sood, B. Banerjee, K. Banerjee, On the principle of exchange of stabilities in magnetohydrodynamic simple Bénard problem, J. Math. Anal. Applns. 108 (1985) 216-222.
2. [2] M.B. Banerjee, J.R. Gupta, S.P. Katyal, A characterization theorem for magnetotherohaline convection, J. Math. Anal. Applns. 144 (1989) 141-146.
3. [3] M.B. Banerjee, J.R. Gupta, R.G. Shandil, H.S. Jamwal, K. Banerjee, J.K. Bhattacharjee, Settlement of long standing controversy in magnetothermoconvection in favour of S. Chandrasekhar, J. Math. Anal. Applns. 144 (1989) 356-366.
4. [4] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford University Press, London, 1961.
5. [5] C.F. Chen, D.H. Johnson, Double-diffusive convection; Areport on engineering foundation conference, J. Fluid Mech.138 (1984) 405-416.
6. [6] J.R. Gupta, S.K. Sood, R.G. Shandil, M.B. Banerjee, K. Banerjee, Bound for the growth rate of a perturbation in double-diffusive convection problems, J. Aus. Math. Soc. Ser. B 25 (1983) 276-285.
7. 7. J.R. Gupta, S.K. Sood, U.D. Bhardwaj, On Rayleigh- Bénard convection with rotation and magnetic field, ZAMP. 35 (1984) 252-256.
8. [8] J.R. Gupta, S.K. Sood, U.D. Bhardwaj, On the characterization of non-oscillatory motions in rotatory hydromagnetic thermohaline convection, Ind. J. Pure and Appl. Math. 17 (1986) 100-107.

9. [9] B. Linhert, N.C. Little, Experiments on the effect of inhomogeneity and obliquity of magnetic field in inhibiting convection, Tellus. 9 (1957) 97-103.
10. [10] H. Mohan, On modified thermohaline magnetoconvection: A characterization theorem, J. Appl. Sciences. 12 (2012) 186-190.
11. [11] C. Normand, Y. Pomeau, M. Velarde, Convective instability: A physicists approach, Rev. Mod. Phys. 49 (1977) 581-624.
12. [12] A. Pellew, R.V. Southwell, On the maintained convective motion in a fluid heated from below, Proc. Roy. Soc. London, Ser A. 176 (1940) 312-343.
13. [13] N. Rudraiah, I. S. Shivkumara, Double-diffusive convection with an imposed magnetic field, Int. J. Heat Transf. 27 (1984) 1825-1836.
14. [14] T.G.L. Shirtcliffe, Thermosolutal convection: Observation of an overstable mode, Nature (Lon.), 213, (1967), 489-490.
15. [15] W.B. Thompson, Thermal convection in a magnetic field, Philos. Meg. Ser. 7, 42 (1951) 1417- 1432.
16. [16] J.S. Turner, Double-diffusive phenomena, Ann. Rev. Fluid Mech. 6 (1974) 37-56.
17. [17] G. Veronis, On finite amplitude instability in thermohaline convection, J. Mar. Res. 23 (1965) 1- 17.
18. [18] G. Veronis, Effects of a stabilizing gradient of solute on thermal convection, J. Fluid Mech. 34 (1968) 315-336.