Summary
We present and discuss some numerical experiments in double-diffusive convection where a layer of fluid, stably stratified by concentration, is subject to heating. By considering first the case where the fluid is heated from below we justify the need of highly accurate numerical approximations, like spectral methods. The spectral Chebyshev method for solving the equations governing the motion of a double-diffusive fluid is then briefly described. Finally, the case where the fluid is laterally heated is discussed in more details. In particular, the formation of convective layers followed by the merging of some of them is discussed from the numerical results.
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References
J.S. Turner, “Double-diffusive phenomena”, Ann. Rev. Fluid Mech., 6, 37–56 (1974).
J.S. Turner, “Multicomponent convection”, Ann. Rev. Fluid Mech., 17, 11–44 (1985).
J.S. Turner, “The behaviour of a stable salinity gradient heated from below”, J. Fluid Mech., 33, 168–200 (1968).
T.G.L. Shirtcliffe, “An experimental investigation of thermosolutal convection at marginal stability”, J. Fluid Mech., 35, 677–688 (1969).
H.E. Huppert and P.F. Linden, “On heating a stable salinity gradient from below”, J. Fluid Mech., 95, 431–464 (1979).
G. Veronis, “Effect of a stabilizing gradient of solute on thermal convection”, J. Fluid Mech., 34, 314–336 (1968).
E.K. Knobloch, D.R. Moore, J. Toomre and N.O. Weiss, “Transition to chaos in two-dimensional double-diffusive convection”, J. Fluid Mech., 166, 409–448 (1986).
E.K. Knobloch, M.R.E. Proctor and N.O. Weiss, “Heteroclinic bifurcations in a simple model of double-diffusive convection”, J. Fluid Mech., 239, 273–292 (1992).
H.E. Huppert and D.R. Moore, “Nonlinear double-diffusive convection”, J. Fluid Mech., 78, 851–854 (1976).
S.M. Chang, S.A. Korpela and Y. Lee, “Double-diffusive convection in the diffusive regime”, Appl. Sei. Res., 39, 301–319 (1982).
U. Ehrenstein and R. Peyret, “A Chebyshev collocation method for the Navier-Stokes equations with application to double-diffusive convection”, Int. J. Numer. Methods Fluids, 9, 427–452 (1989).
B. Roux (ed), “Numerical Simulation of Oscillatory Convection in Lower-Pr Fluids”, Proc. GAMM Workshop, Marseille ( 1988 ), Vieweg, Braunschweig, 1990.
P. Le Quéré, “Transition to unsteady natural convection in a tall water-filled cavity”, Phys. Fluids, A2, 503–515 (1990).
J. Ouazzani, R. Peyret and A. Zakaria, “Stability of collocation-Chebyshev schemes with application to the Navier-Stokes equations”, in D.Rues and W. Kordulla (eds), Proc. Sixth GAMM Conf. on Numerical Methods in Fluid Mechanics, Vieweg, Braunschweig, 1986, pp. 287–294.
J. Fröhlich, T. Gerhold, J.M. Lacroix and R. Peyret, “Fully implicit spectral methods for convection”, in M. Durand and F. El Dabaghi (eds), High Performance Computing II, North-Holland, Amsterdam, 1991, pp. 585–596.
J.M. Vanel, R. Peyret and P. Bontoux, “A pseudo-spectral solution of vorticitystream function equations using the influence matrix technique”, in K.W. Morton and M.J. Baines (eds), Numerical Methods for Fluid Dynamics II, Clarendon Press, Oxford, 1986, pp. 463–475.
D.B. Haidvogel and T. Zang, “The accurate solution of Poisson’s equation by expansion in Chebyshev polynomials”, J. Comput. Phys., 30, 167–180 (1979).
U. Ehrenstein, “Méthodes spectrales de résolution des équations de Stokes et de Navier-Stokes. Application à des écoulements de convection double-diffusive”, Thèse Doctorat, Mathématiques Appliquées, Université de Nice, 1986.
R. Bwemba and R. Pasquetti, “About the influence matrix used in the spectral solution of the 2D incompressible Navier-Stokes equations (vorticity-stream function formulation)”, to appear.
S.A. Thorpe, P.K. Hütt ans R. Soulsby, “The effect of horizontal gradients on thermohaline convection”, J. Fluid Mech., 38, 375–400 (1969).
R. A. Wirtz, D.G. Briggs and C.F.Chen, “Physical and numerical experiments on layered convection in a density stratified fluid”, Geophys. Fluid Dyn., 3, 265–288 (1972).
V.N. Nekrasov, V.A. Popov and Yu.D. Chashechkin, “Formation of periodic convective-flow structure on lateral heating of a stratified liquid”, Izv. Atmosph. Ocean. Phys., 12, 1191–1200 (1976), English transi, pp.733–739.
Y. Suzukawa and U. Narusawa, “Structure of growing double-diffusive convection cells”, J.Heat Transfer, 104, 248–254 (1982).
J. Tanny and A.B. Tsinober, “The dynamics and structure of double-diffusive layers in sidewall-heating experiments”, J. Fluid Mech., 196, 135–156 (1988).
J. Tanny and A.B. Tsinober, “On the behavior of a system of double diffusive layers during its evolution”, Phys. Fluids, Al, 606–609 (1989).
J.E. Hart, “On sideways diffusive instability”, J. Fluid Mech., 49, 279–288 (1971).
J.E. Hart, “Finite amplitude sideways diffusive convection”, J. Fluid Mech., 59, 47–64 (1973).
O. Kerr, “Heating a salinity gradient from a vertical sidewall: linear theory”, J. Fluid Mech., 207, 323–352 (1989).
O. Kerr, “Heating a salinity gradient from a vertical sidewall: nonlinear Theory”, J. Fluid Mech., 217, 529–546 (1990).
C.F. Chen, “Onset of cellular convection in a salinity gradient due to a lateral temperature gradient”, J. Fluid. Mech., 63, 563–576 (1974).
S. Thangam, A. Zebib and C. F. Chen, “Double-diffusive convection in an inclined fluid layer”, J. Fluid Mech., 116, 363–378 (1982).
R. A. Wirtz and L. H. Liu, “Numerical experiments on the onset of layered convection in a narrow slot containing a stably stratified fluid”, Int. J. Heat Mass Transfer, 18, 1299–1305 (1975).
C.S. Reddy, “Cell merging and its effect on heat transfer in thermosolutal convection”, J. Heat Transfer, 102, 172–174 (1980).
Y. Demay, J.M. Lacroix, R. Peyret and J.M. Vanel, “Numerical experiments on stratified fluids subject to heating”, Proc. Third Inter. Symp. on Stratified Flows, Pasadena, 1987, E.J. List and G.H. Jirka (eds), American Society of Civil Engineers, New York, 1990, pp. 588–597.
H.C. Ku, R.S Hirsh and T.D. Taylor, “A numerical simulation of the effect of salinity on a thermally driven flow”, in M. Deville (ed), Proc. Seventh GAMM Conf. on Numerical Methods in Fluid Mechanics, Vieweg, Braunschweig, 1988, pp. 151–158.
C.E. Mendenhall and M. Mason, “The stratified subsistence of fine particles”, Proc. Nat. Acad. Sci. USA, 9, 199–207 (1923).
C. Sabbah, “Etude numérique de la formation et l’évolution de cellules convectives dans un fluide stratifié chauffé latéralement”, Projet de stage de DEA “Turbulence et Systèmes Dynamiques”, Université de Nice-Sophia Antipolis, 1994.
J.P. Pulicani, “A spectral multi-domain method for the solution of 1-D Helmholtz and Stokes-type equations”, Computers and Fluids, 16, 207–215 (1988).
R. Peyret, “The Chebyshev multidomain approach to stiff problem in Fluid Mechanics”, Comp. Meth. Appl. Mech. Eng., 80, 129–145 (1990).
H. Guillard and R. Peyret, “ On the use of spectral methods for the numerical solution of stiff problems”, Comp. Meth. App. Mech. Eng., 66, 17–43 (1988).
J.M. Lacroix, R. Peyret and J.P. Pulicani, “A pseudospectral multidomain method for the Navier-Stokes equations with application to double-diffusive convection”, in M. Deville (ed), Proc. Seventh GAMM Conf. on Numerical Methods in Fluid Mechanics, Vieweg, Braunschweig, 1988, pp. 167–174.
A. Mofid, “Application des méthodes spectrales à l’étude de l’effet d’une source de chaleur dans un fluide stratifié”, Thèse de Doctorat, Sciences de l’ingénieur, Université de Nice-Sophia Antipolis, 1992.
J. P. Pulicani, “Modélisation isotherme d’une interface diffusive en convection de double-diffusion”, Int. J. Heat Mass Transfer (to appear).
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© 1995 Springer-Verlag Berlin Heidelberg
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Peyret, R., Vanel, J.M. (1995). Numerical Experiments in Double-Diffusive Convection. In: Leutloff, D., Srivastava, R.C. (eds) Computational Fluid Dynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79440-7_3
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DOI: https://doi.org/10.1007/978-3-642-79440-7_3
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