On the short-wave instability of natural convection boundary layers

Abstract

This paper considers the stability of the one-dimensional boundary layer generated by sudden heating of an infinite vertical wall. A quasi-steady approximation is used to obtain the asymptotic form of the growth rate and phase speed of disturbances whose wavelength is comparable with the boundary-layer width. Results for the inviscid modes governed by Rayleigh's equation are obtained for several values of the Prandtl number and are compared with solutions of the full stability equations. As the wavelength increases,the phase speed of disturbances approaches the maximum flow speed of the boundary layer and a five-tier structure extends across and outside the boundary layer. This intermediate regime,where viscous effects are important within a critical layer centred on the position of maximum flow speed,provides a link with an earlier long-wave analysis of the problem.