THE OVERSTABILITY MODE OF ROTATING CONVECTION IN THE PRESENCE OF MAGNETIC FIELD
Keywords:
Chandrasekhar Number , Convection, Rotating Convection, Magnetic Field, Rayleigh Number , Over-Stability convection, Taylor Number , Prandtl number , Prandtl magnetic numberAbstract
The fact of convection is one of the most remarkable problems in fluid dynamics. In this paper we shall study the case of over-stability mode of linear stability of rotating electrically conducting viscous layer heated from below lying in a uniform magnetic field based on the Boussinesq approximation. We shall follow the same analysis used in previous paper when we analyses the case of stationary convection of linear stability at the onset of rotating convection in the presence of magnetic field, so we restrict our study to the case when the direction of magnetic field and rotation are parallel; the discussion is focused on the case of large Taylor number and Chandrasekhar number . Generally, we have seen early in a rotating and magnetic convection that thermal stability sets mostly as over stability [11], when we combine rotation and magnetic field the manner of the instability behaves in a complicated way depending on four dimensionless numbers , , and [11]. We shall study the over-stability case seeking the nature of the dependence of these dimensionless numbers.
References
Chandrasekhar. S., (1961). Hydrodynamic and hydromagnetic stability, Oxford, Clarendon Press.
Choudhuri. A. R., (1998). The physics of uids and plasmas : an introduction for astrophysicists, Cambridge University Press.
Cramer. f. n., (2001). The Physic of Alfven Waves, Germany, federal republic of Germany.
Davidson. P. A., (2001). An Introduction to Magnetohydrodynamics, Cambridge University Press.
Davies. G.M., (2011). Mantle convection for geologists, New York, Cambridge University Press.
Davies. J.C., (2009). Thermal core-mantle interactions: convection, magnetic field generation, and observational constraints (University of Leeds PhD. Thesis).
Drazin.P.G., (2002). Introduction to Hydrodynamic Stability, Cambridge, Cambridge University Press.
Holton. R., (2004). An Introduction to dynamic meteorology, Elsevier Academic Press.
King. M. E.; Stellmach. S., Noir. J., Hansen. U., Aurnou. J. M., (2009), Boundary layer control of rotating convection systems, Journal of Nature. Vol.457, No. 07647 (Jan.15, 2009).
Kundu. P. K., Cohen. M. I. & Dowling. R. D., (2004). Fluid Mechanics, 3th edition, Oxford, Academic Press.
Laqab. M. I; Alogab. M. F, (2018). Linear stability at the onset of rotating convection in the presence of magnetic field, Journal of Humanities and Applied Science (JHAS), No. 31, December (2018) pp. 40-58.
Lord. R., (1916a). On convection currents in a horizontal layer of fluid, when the higher temperature is on one side, Phil. Mag. (6) 32, pp. 529-534.
Maple 18. (Maple soft).
Pedlosky.J. (1987). Geophysical fluid dynamics, New York, Springer.w-Hill, 1964, pp. 15–64.
Rebhi, R.; Mamou, M.; Hadidi, N, (2021). Onset of Linear and Nonlinear Thermosolutal Convection with Soret and Dufour Effects in a Porous Collector under a Uniform Magnetic Field. Fluids, 6,243.
Wakif. A., Boulahia. Z. Sehaqui. R, (2017). Numerical analysis of the onset of longitudinal convective rolls in a porous medium saturated by an electrically conducting nanofluid in the presence of an external magnetic field, Results in Physics. Vol 7, pp 2134-2152.
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