A Consideration for the Relation between Turbulent Transition and Viscous Dissipation of Mean Velocity Distribution.

Abstract

The purpose of this study is to consider a necessary condition on which turbulent transition can occur. The attention was paid to the viscous dissipation rate of turbulent and laminar velocity distribution. For the fully developed internal flow, the laminar parabolic distribution gives the minimum dissipation rate. Hence the dissipation of the average turbulent velocity distribution should be greater than that of the laminar flow. From this vewpoint, the limit Reynolds number Reo below which there can not exist the turbulent flow was estimated by assuming the wall law for the distribution. The calculated Reo's roughly agreed with those of experimental critical Reynolds numbers for pipe flow, channel flow, plane Couette flow and boundary layer on plate. The physical meaning was briefly discussed for the necessary condition in this study.