Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 112
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Li, You-Rong Zhang, Huan Zhang, Li and Wu, Chun-Mei 2016. Three-dimensional numerical simulation of double-diffusive Rayleigh–Bénard convection in a cylindrical enclosure of aspect ratio 2. International Journal of Heat and Mass Transfer, Vol. 98, p. 472.

    Beaume, Cédric Kao, Hsien-Ching Knobloch, Edgar and Bergeon, Alain 2013. Localized rotating convection with no-slip boundary conditions. Physics of Fluids, Vol. 25, Issue. 12, p. 124105.

    Deal, M. Deheuvels, S. Vauclair, G. Vauclair, S. and Wachlin, F. C. 2013. Accretion from debris disks onto white dwarfs. Astronomy & Astrophysics, Vol. 557, p. L12.

    Beaume, Cédric Bergeon, Alain and Knobloch, Edgar 2011. Homoclinic snaking of localized states in doubly diffusive convection. Physics of Fluids, Vol. 23, Issue. 9, p. 094102.

    El-Sebaii, A.A. Ramadan, M.R.I. Aboul-Enein, S. and Khallaf, A.M. 2011. History of the solar ponds: A review study. Renewable and Sustainable Energy Reviews, Vol. 15, Issue. 6, p. 3319.

    Alloui, I. Benmoussa, H. and Vasseur, P. 2010. Soret and thermosolutal effects on natural convection in a shallow cavity filled with a binary mixture. International Journal of Heat and Fluid Flow, Vol. 31, Issue. 2, p. 191.

    Muthsam, Herbert J. Kupka, Friedrich Mundprecht, Eva Zaussinger, Florian Grimm-Strele, Hannes and Happenhofer, Natalie 2010. Simulations of stellar convection, pulsation and semiconvection. Proceedings of the International Astronomical Union, Vol. 6, Issue. S271, p. 179.

    Papanicolaou, E. and Belessiotis, V. 2008. Patterns of Double-Diffusive Natural Convection With Opposing Buoyancy Forces: Comparative Study in Asymmetric Trapezoidal and Equivalent Rectangular Enclosures. Journal of Heat Transfer, Vol. 130, Issue. 9, p. 092501.

    YU, YOUMIN CHAN, CHO LIK and CHEN, C. F. 2007. Effect of gravity modulation on the stability of a horizontal double-diffusive layer. Journal of Fluid Mechanics, Vol. 589,

    Mahidjiba, A. Bennacer, R. and Vasseur, P. 2006. Flows in a fluid layer induced by the combined action of a shear stress and the Soret effect. International Journal of Heat and Mass Transfer, Vol. 49, Issue. 7-8, p. 1403.

    Kozitskiy, S. B. 2005. Fine structure generation in a double-diffusive system. Physical Review E, Vol. 72, Issue. 5,

    Millour, E. Labrosse, G. and Tric, E. 2003. Sensitivity of binary liquid thermal convection to confinement. Physics of Fluids, Vol. 15, Issue. 10, p. 2791.

    Sibgatullin, I. N. Gertsenstein, S. Ja. and Sibgatullin, N. R. 2003. Some properties of two-dimensional stochastic regimes of double-diffusive convection in plane layer. Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 13, Issue. 4, p. 1231.

    Shukla, KN 2001. Hydrodynamics of diffusive processes. Applied Mechanics Reviews, Vol. 54, Issue. 5, p. 391.

    Tuckerman, Laurette S. 2001. Thermosolutal and binary fluid convection as a 2×2 matrix problem. Physica D: Nonlinear Phenomena, Vol. 156, Issue. 3-4, p. 325.

    Hadji, L and Sharif, M.A.R 2000. Penetrative convection in a horizontal layer of seawater near its freezing point. Applied Mathematical Modelling, Vol. 24, Issue. 10, p. 733.

    Yin, Hongbin and Koster, Jean N 2000. Double-diffusive convective flow and interface morphology during transient Ga–5% In alloy melting. Journal of Crystal Growth, Vol. 217, Issue. 1-2, p. 170.

    Balmforth, N. J. Casti, A. R. R. and Julien, K. A. 1998. Thermohaline convection with nonlinear salt profiles. Physics of Fluids, Vol. 10, Issue. 4, p. 819.

    Balmforth, Neil and Casti, Alexander 1998. Convection in a slowly diffusing, weakly stratified salt field. Physics Letters A, Vol. 238, Issue. 1, p. 35.

    Becerril, R. and Swift, J. B. 1997. Amplitude equations for isothermal double diffusive convection. Physical Review E, Vol. 55, Issue. 5, p. 6270.


Nonlinear double-diffusive convection

  • Herbert E. Huppert (a1) and Daniel R. Moore (a1)
  • DOI:
  • Published online: 01 April 2006

The two-dimensional motion of a fluid confined between two long horizontal planes, heated and salted from below, is examined. By a combination of perturbation analysis and direct numerical solution of the governing equations, the possible forms of large-amplitude motion are traced out as a function of the four non-dimensional parameters which specify the problem: the thermal Rayleigh number RT, the saline Rayleigh number ES, the Prandtl number σ and the ratio of the diffusivities τ. A branch of time-dependent asymptotic solutions is found which bifurcates from the linear oscillatory instability point. In general, for fixed σ, τ and RS, as RT increases three further abrupt transitions in the form of motion are found to take place independent of the initial conditions. At the first transition, a rather simple oscillatory motion changes into a more complicated one with different structure, at the second, the motion becomes aperiodic and, at the third, the only asymptotic solutions are time independent. Disordered motions are thus suppressed by increasing RT. The time-independent solutions exist on a branch which, it is conjectured, bifurcates from the time-independent linear instability point. They can occur for values of RT less than that at which the third transition point occurs. Hence for some parameter ranges two different solutions exist and a hysteresis effect occurs if solutions obtained by increasing RT and then decreasing RT are followed. The minimum value of RT for which time-independent motion can occur is calculated for fourteen different values of σ, τ and RS. This minimum value is generally much less than the critical value of time-independent linear theory and for the larger values of σ and RS and the smaller values of τ, is less than the critical value of time-dependent linear theory.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *