Natural convection boundary layers on evenly heated plates

Abstract

A scaling analysis is used to obtain a description of the basic structure of the boundary layer ow adjacent to a vertical semi-infinite evenly heated plate in the presence of a stably stratified ambient fluid. The scaling analysis provides relations between such quantities as the development time and boundary layer thickness and the fluid properties and control parameters. In particular the scaling analysis predicts a large y one-dimensional ow region that provides a suitable base flow for the examination of the stability properties of the boundary layer via direct numerical simulation. The numerical simulations show that above an initial critical Reynolds number the one-dimensional boundary layer is unstable with respect to two-dimensional travelling waves, while above a second, higher, Reynolds number, the boundary layer is unstable to three-dimensional waves.