A Study of Linearized Approximations to the Boundary-Layer Equations

Abstract

The general subject of linearized approximations to the boundary-layer equations is considered in terms of the behavior, both qualitative and quantitative, of the resulting approximate solutions. In this regard, two nonsimilar flow problems are treated by various methods which are based upon the linearized concept. The results are analyzed and compared both with each other and “exact” numerical solutions where available. Linearization in the von Mises plane is considered in some generality and typical results are compared with those obtained by the more conventional physical plane linearization technique. In particular, it is shown that the use of the total pressure rather than the velocity as the dependent variable has important advantages even for constant pressure flow problems when subjected to a linearized treatment in the von Mises plane. Finally, specific recommendations are made as to the approach best applied to a given type of physical problem.