Leading Edge of a Shock‐Induced Boundary Layer

Abstract

The boundary layer which is formed as a shock wave propagates down a shock tube causes both shock attenuation and shock curvature. Hartunian studied the curvature effect; however, as he points out, because of the singularities at the leading edge of the boundary layer his solution is not valid where the shock wave touches the tube wall. A detailed study is now made of the flow near the leading edge of this shock‐induced boundary layer for a weak shock wave. The leading‐edge flow can be divided into a shear layer near the wall, and into a free stream or shock region. By expanding the Navier—Stokes equations in the small parameter M1* — 1 and stretching the coordinates, simplified equations for the shear layer and shock region are obtained. The shear layer and shock region flows interact and it is found that the shock region must be a zone of non‐Hugoniot flow where the shock structure is two dimensional. An approximate solution of the shock shape is obtained by replacing the shock region by an oblique shock which is approximately matched to the shear layer.