Laminar Boundary Layer Based on a Minimum Theorem

Abstract

TH E classical t rea tment by Blasius which develops the velocity profile and thickness of the laminar boundary layer on an open air-washed surface under constant pressure, although rigorous as developed, rests upon the ra ther severe assumption of similitude of velocity profiles. In recent years, both theoretical and experimental evidence has arisen which makes the validity of this assumption open to question. Aside from the fact t ha t direct laboratory measurements of the velocity profiles do not show strict similitude and t ha t careful indirect studies based on the heat which is carried away by the boundary layer of a hot surface indicate profiles more nearly parabolic than Blasian near the beginning of the layer, the chief difficulties with the Blasian profile are t ha t it is out of balance with respect to energy, and t ha t it fails to give any indication of flow transition from the laminar to the turbulent phase. These objections to the Blasius t reatment , which virtually exhausts the possibilities of the NavierStokes' equation as a basis for analysis, together with a growing need for new help in handling not only laminar layers under constant pressure, bu t laminar and turbulent layers under gradients of pressure as well, led the author about four years ago to examine the possibility of approaching these problems from the standpoint of certain minimum theorems. The present paper is a progress report on only tha t par t of these exploratory studies which has to do with laminar boundary layer under constant pressure and over surfaces of zero curvature.