Vertically Staggered Patterns in Free Convective Flow

Abstract

The theory of cellular convection admits solutions which not only show periodicity in horizontal direction but also describe a vertical echelon of the flow. Such a flow pattern is attributed to the higher eigenvalues (critical Rayleigh numbers) of the corresponding stability problem (for details see S. Chandrasekhar (1961)). The mechanism of such layered cellular patterns was explained in some detail by J. Zierep (1959). So far this type of flow could not be realized experimentally in homogeneous fluids of large horizontal extent. An obvious explanation for this is that, when heating the fluid layer quasi-steadily from below, the mode belonging to the smallest critical Rayleigh number is generated first. If the vertical temperature gradient is increased furtheron, the intensity of the convective flow corresponding to the first mode becomes so large that the amplitudes of the higher modes cannot dominate the pattern of the first mode. A layered cellular convection can be realized by quasi steady heating only if provision is made to sunpress the generation of the M basic mode ¹⁾ or to inhibit the growth rate of the amplitude when increasing the temperature gradient.

The basic mode describes the convective flow, that circulates liquid from the bottom to the top of the layer.