Journal of Fluid Mechanics



A direct stability analysis of a radiation-induced natural convection boundary layer in a shallow wedge


CHENGWANG LEI a1 and JOHN C. PATTERSON a1
a1 School of Engineering, James Cook University, Townsville, Queensland 4811, Australia

Abstract

This study considers the convective instability of a water-filled shallow wedge with an absorptive bottom subject to solar radiation. Previous studies have revealed that a thermal boundary layer develops along the sloping bottom due to the absorption of penetrative radiation there, and this boundary layer is potentially unstable to the Rayleigh–Bénard instability. The stability properties of the thermal boundary layer are determined in the present study by perturbing the three-dimensional numerical solution. The result of the direct stability analysis has confirmed previous scaling with respect to the convective instability. Additional features of the thermal layer instability have also been revealed from the direct stability analysis.

(Received May 7 2002)
(Revised October 29 2002)



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