Non-linear effects in steady supersonic dissipative gasdynamics Part 1. Two-dimensional flow

Abstract

Steady supersonic two-dimensional flows governed by the Navier–Stokes equations are considered. For flows past a thin body, the Oseen theory is shown to fail at large distances. An investigation of the equations bridging the linear and non-linear zones is made. From this, it follows that the resulting equations are a system of Burgers and diffusion equations. The Whitham theory is shown to result under the inviscid limit of our analysis. Various other limits are also obtained.An explicit expression for flows past a thin airfoil is given, and the flow past a double wedge is exhibited in terms of known functions.