The linear perturbation problem [D. J. Wollkind and H. L. Frisch, Phys. Fluids 14, 13 (1971)] is extended to include a nonlinear stability analysis of a horizontal layer of dissociating fluid, heated from above or below. This analysis deals with the simplest possible nonlinear problem, namely, a two-dimensional situation in which material property variation with temperature is neglected. The results of this analysis show that there exist finite amplitude equilibrium rolls for both the case of heating from below (at a slight departure from the critical conditions for the Bénard problem) and from above (the chemical instability). This problem having been solved, it can then be conjectured with some confidence what a fuller nonlinear analysis would reveal.
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Wollkind et al. (1971) studied this question.
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