SINGLE-MODE DYNAMICS OF CONVECTIVE INSTABILITIES IN A HORIZONTAL LIQUID LAYER

A theoretical description of the single-mode dynamics of both the Rayleigh-Bénard instability (RBI) and the Soret-driven instability (SDI) is provided, starting from the general conservation equations and exploiting a technique similar to that used for the laser instability. A system of nonlinear dynamic equations is found to describe self-consistently both the RBI and the SDI. The single-mode steady-state solutions are derived without making use of perturbation expansions. A quantitative theoretical explanation is found to account for such recent experimental results as the saturation of the horizontally averaged concentration gradient at midheight in the SDI, the appearance of relaxation oscillations in RBI and SDI transients, and the dependence of the oscillation period on the temperature difference between the plates. The analogy with the laser suggests the possibility of observing giant pulses in the transient well above threshold, and of measuring pretransitional fluctuations of the mode which goes unstable. Connections with the Lorenz model are also discussed. © 1979 The American Physical Society.