An Attempt on the Analysis of the Vortex Streets Developed in a Free-Convection Boundary Layer

Abstract

Preliminarily it was pointed out, for the case of free convection phenomena, that the transition point from laminar flow to vortex streets flow would not be given by the critical Reynolds number. Then we divided the laminar boundary layer by an imaginary wave length along the flow direction, made the ratio of the momentum energy of the imaginarily divided part in the case that the part would move en bloc independently to the increase of the momentum energy of the same part in the case that the part would move still one more wave length, maintaining the laminar state continuously, and supposed that the transition would happen when the ratio reaches a critical number. The critical Grashoff number was given from that ratio, and also the wave length and the frequency of the vortex streets were calculated with the same ratio, under the assumption of the continuity of the vorticity flow before and behind the transition. Nearly good coincidence was observed between the theoretical relations and the experimental data measured by the author with water and ethylene-glycol and Eckert-Soehngen with air.