Convective transitions induced by a varying aspect ratio

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Abstract
The Rayleigh number for convective instability of a horizontal layer of fluid to two-dimensional disturbances depends on the wavelength of the disturbance. In a finite rectangular domain with stress-free boundaries, there are critical lengths at which instability to two different sets of rolls occurs simultaneously. This paper gives a nonlinear analysis of this multiple-bifurcation problem. We present a complete characterization of the transitions which occur for lengths near critical. For small values of the Prandtl number the transition between the two sets of rolls occurs via a new type of solution which is represented by the superposition of the two sets of rolls with comparable amplitude. For higher Prandtl numbers the transition is an abrupt one, and is accompanied by hysteresis.

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