The development of horizontal boundary layers in stratified flow. Part 1. Non-diffusive flow

Abstract

The development of the boundary layer on the upper surface of a horizontal flat plate in a non-diffusive, stratified flow is described. It is shown that the flow can be characterized by two basic parameters, the Reynolds (RL) and Russell (RuL) numbers, and that, depending on the relative magnitude of these two parameters, three different régimes of flow can be defined. The delineation of these régimes and the description of the flow in each of them is obtained by deriving a uniformly valid first approximation to the Boussinesq equations of motion for a flow contained in the two-dimensional parameter spaceRuL> 0,RL> 1. The critical stratification for the self-blocking of a horizontal boundary layer is shown to be given by the conditionRuL=O(RL½).