ANALYTIC STUDY OF THERMOHALINE CONVECTIVE STABILITY IN A COUPLE-STRESS FLUID
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Abstract
This work investigates nonlinear analysis for thermohaline convective stability in a steady, viscous, incompressible couple-stress fluid by performing a generalized energy method. It is observed that the linear and nonlinear threshold that reflects the physics of the onset of convection is the same. The couple stress and solute gradient are seen to have a stabilizing impact on the system.
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References
Chandrasekhar S. (1981) Hydrodynamic and Hydromagnetic Stability, New York, Dover.
Choudhary S. & Sunil (2019) Global stability for double-diffusive convection in a couple-stress-fluid saturating a porous medium, Studia Geotechnica et Mechanica 41(1):13. DOI: https://doi.org/10.2478/sgem-2018-0044
Galdi G. P. (1985) Nonlinear stability of the magnetic Bénard problem via a generalized energy Method, Archive of Rational Mechanics and Analysis87:167-186. DOI: https://doi.org/10.1007/BF00280699.
Galdi G. P.& Straughan B. (1985) A nonlinear analysis of the stabilizing effect of rotation in the Bénard problem, Proceedings of the Royal Society of London A. 402:257-283. DOI:10.1098/rspa.1985.0118
Galdi G. P. & Padula M. (1990) A new approach to energy theory in the stability of fluid Motion, Archive of Rational Mechanics and Analysis 110:187-286. DOI: https://doi.org/10.1007/BF00375129
Joseph D. D. (1965) On the stability of the Boussinesq equations, Archive of Rational Mechanics and Analysis20:59- 71. DOI: https://doi.org/10.1007/BF00250190.
Joseph D. D. (1966) Nonlinear stability of the Boussinesq equations by the method of energy,Archive of Rational Mechanics and Analysis 22: 163-184.DOI: https://doi.org/10.1007/BF00266474.
Joseph D. D. (1976) Stability of Fluid Motions, Springer Verlag, New York.Rionero S. (1968) Metodivariazionali per la stabilitfiasintotica in media in magnetoidrodinamica, Annali di Matematica Pura ed Applicata78:339-364. DOI: https://doi.org/10.1007/BF02415121.
Orr W. McF. (1907) Stability or instability of the steady motions of a perfect liquid, Proceedings of the Royal Irish Academy A. 27:9-68:69-138.
Reynolds O. (1895) On the dynamical theory of incompressible viscous fluids and the determination of the criterion, Philosophical Transactions Royal Society of London A. 186:123-164. DOI: http://dx.doi.org/10.1098/rsta.1895.0004
Rionero S. &Mulone G. (1988) A non-linear stability analysis of the magnetic Bénard problem through the Lyapunov direct method, Archive for Rational Mechanics and Analysis 103:347-368. DOI: DOI:10.1007/BF00251445
Mulone G. & Rionero S. (1989) On the nonlinear stability of the rotating Bénard problem via the Lyapunov direct method, Journal of Mathematical Analysis and Applications 144:109-127. DOI:10.1016/0022-247X (89)90362-4
Serrin J. (1959) On the stability of viscous fluid motions, Archive Rational Mechanics and Analysis3:1-13. DOI: https://doi.org/10.1007/BF00284160.
Stokes V. K. (1966) Couple stresses in fluids,Physics of Fluids9:1709.
Stokes V. K. (1984) Theories of Fluids with Microstructure, Springer, New York.
Straughan B. (2004) The Energy Method, Stability, and Nonlinear Convection, Springer Verlag, New York.
Sunil, Choudhary S. & Bharti P. K. (2013) Global stability for thermal convection in a couple-stress fluid with temperature and pressure dependent viscosity, Studia Geotechnica et Mechanica 35(3): 85-102. DOI:10.2478/sgem-2013-0032
Sunil, Choudhary S. & Mahajan A. (2014) Conditional stability for thermal convection in a rotating couple-stress fluid saturating a porous medium, Special Topics & Reviews in Porous Media 5(2):119-132. DOI: 10.1615/SpecialTopicsRevPorousMedia.v5.i2.30
Sunil, Choudhary S.& Mahajan A. (2019) Stability analysis of a couple-stress fluid saturating a porous medium with temperature and pressure dependent viscosity using a thermal non-equilibrium model,Applied Mathematics and Computation 340(1):15-30. DOI: https://doi.org/10.1016/j.amc.2018.08.025
Sunil, Devi R. & Mahajan A. (2011) Global stability for thermal convection in a couple stress fluid, International Communications in Heat and Mass Transfer 38: 938–942. DOI: https://doi.org/10.1016/j.icheatmasstransfer.2011.03.030