Summary
A theoretical study is made of the onset of steady double-diffusive convection in a circular cylinder of small to moderate aspect ratio. An eigenfunction expansion method is used to derive systems of amplitude equations for weakly nonlinear evolution of critical disturbances. It is shown that the nature of the convective solution near criticality depends strongly on the cylinder's aspect ratio; this is particularly the case at or near aspect ratios where two modes become unstable at the same Rayleigh number. There is also a strong dependence on Prandtl number, which is discussed.
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Stern, M. E.: The “salt-fountain” and thermohaline convection. Tellus12, 172 (1960).
Veronis, G.: On finite amplitude instability in thermohaline convection. J. Mar. Res.23, 1 (1965).
Veronis, G.: Effect of a stabilizing gradient of solute on thermal convection. J. Fluid Mech.34, 315 (1968).
Huppert, H. E., Moore, D. R.: Nonlinear double-diffusive convection. J. Fluid Mech.78, 821 (1976).
Huppert, H. E., Linden, P. F.: On heating a stable salinity gradient from below. J. Fluid Mech.95, 431 (1979).
Huppert, H. E., Turner, J. S.: Double-diffusive convection. J. Fluid Mech.106, 299 (1981).
Proctor, M. R. E.: Steady subcritical thermohaline convection. J. Fluid Mech.105, 507 (1981).
Knobloch, E., Proctor, M. R. E.: Nonlinear periodic convection in double-diffusive systems. J. Fluid Mech.108, 291 (1981).
Zangrando, F., Bertram, L.: The effect of variable stratification on linear doubly diffusive stability. J. Fluid Mech.151, 55 (1985).
Olson, J. M., Rosenberger, F.: Convective instabilities in a closed vertical cylinder heated from below. J. Fluid Mech.92, 631 (1979).
Abernathay, J. R., Rosenberger, F.: Soret diffusion and convective stability in a closed vertical cylinder. Phys. Fluids24, 377 (1981).
Rosenblat, S.: Thermal convection in a vertical circular cylinder. J. Fluid Mech.122, 395 (1982).
Doedel, E.: AUTO: A program for the automatic bifurcation analysis of autonomous systems. Cong. Num.30, 265 (1981).
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Georgopoulos, E., Horwitz, J.A. & Rosenblat, S. Double-diffusive convection in a circular cylinder. Acta Mechanica 70, 177–192 (1987). https://doi.org/10.1007/BF01174654
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DOI: https://doi.org/10.1007/BF01174654