Transformations of the compressible turbulent boundary layer with heat exchange

Abstract

A mathematical transformation is presented which converts the integral turbulent boundary-layer equations at high speed into one at low speed. The transformation is inspired by that recently introduced by Coles for the constant-pressure case. Here it is developed for the general case when pressure gradients, as well as heat exchange, are present. It is shown that in this case two transformations can be defined: an £ transformation, in which the lowspeed fluid is incompressible, and an I transformation, in which the low-speed fluid is a gas. The conditions under which the transformations operate correctly, not only on the integral equations but also on the whole system of partial differential equations, are discussed.