The influence of a third diffusing component upon the onset of convection

Journal of Fluid Mechanics - Tập 92 Số 4 - Trang 659-670 - 1979
Ross W. Griffiths1
1Research School of Earth Sciences, The Australian National University, P.O. Box 4, Canberra 2600

Tóm tắt

The small amplitude stability analysis for the onset of double-diffusive convection when the density gradient is gravitationally stable is extended to include a third diffusing component. Special attention is given to systems with κ1 [Gt ] κ2, κ3 and Pr [Gt ] κ/κ1, where κi is the molecular diffusivity of the ith component and Pr is the Prandtl number based on the largest of the Ki. It is found that the boundary for the onset of overstability is approximated by two straight lines in a Rayleigh number plane. Small concentrations of a third property with a smaller diffusivity can have a significant effect upon the nature of diffusive instabilities, the magnitude of this effect being proportional to κ1/Ki. Oscillatory and direct ‘salt-finger’ modes are found to be simultaneously unstable under a wide range of conditions when the density gradients due to the components with the greatest and smallest diffusivities are of the same sign.

Từ khóa


Tài liệu tham khảo

Mcintyre, M. E. 1970 Diffusive destabilization of the baroclinic circular vortex.Geophys. Fluid Dynamics. 1,19–57.

Veronis, G. 1965 On finite amplitude instability in thermohaline convection.J. Mar. Res. 23,1–18.

Baines, P. G. & Gill, A. E. 1969 On the thermohaline convection with linear gradients.J. Fluid Mech. 37,289–306.

Walin, G. 1964 Note on the stability of water stratified by both salt and heat.Tellus 16,389–393.

Turner, J. S. 1974 Double-diffusive phenomena.Am. Rev. Fluid Mech. 6,37–56.

Nield, D. A. 1967 The thermohaline Rayleigh-Jeffreys problem.J. Fluid Mech. 19,545–58.

Lambert, R. B. 1974 Small-scale dissolved oxygen variations and the dynamics of Gulf Stream eddies.Deep-Sea Res. 21,529–46.

Huppert, H. E. 1976 Transitions in double-diffusive convection.Nature 263,20–22.

Turner, J. S. , Shirtcliffe, T. G. L. & Brewer, P. G. 1970 Elementary variations of transport coefficients across density interfaces in multiple-diffusive systems.Nature 228,1083–1084.

Degens, E. T. , Von Herzen, R. P. , Wong, H. K. , Deuser, W. G. & Jannasch, H. W. 1973 Lake Kivu: structure, chemistry and biology of an East African rift lake.Geol. Rundschau 62,245–277.

Huppert, H. E. & Moore, D. A. 1976 Nonlinear double-diffusive convection.J. Fluid Mech. 78,821–854.

Stern, M. E. 1960 The ‘salt-fountain’ and thermohaline convection.Tellus 12,172–175.

Jakeman, E. & Hurle, D. T. J. 1972 Thermal oscillations and their effect on solidification processes.Rev. Phys. Tech. 3,3–30.

Veronis, G. 1968 Effect of a stabilizing gradient of solute on thermal convection.J. Fluid Mech. 34,315–336.

Straus, J. M. 1972 Finite amplitude doubly diffusive convection.J. Fluid Mech. 56,353–74.

Thông tin
Thông tin xuất bản

Journal of Fluid Mechanics

Tập 92 Số 4

659-670

Thông tin tác giả