Study on Weak Nonlinear Waves in Two-Dimensional Supersonic Flow by the Reductive Perturbation Method

Abstract

The second order approximation in the reductive perturbation method has been investigated for weak nonlinear waves in two-dimensional supersonic flow with viscosity and heat-conductivity. As a result it is found that the second order equation is reduced to the linearized Burgers equation with inhomogeneous terms. The renormalization of secular term included in inhomogeneous terms is carried out for the case of a weak oblique shock by making use of the method of Kodama & Taniuti. It is shown that the corrected inclination of the shock front to the uniform flow coincides with the expression obtained from the Rankine-Hugoniot relation under the weak shock approximation. The solution up to the second order is obtained analytically and it has the form, for special case, like Becker’s solution under the same approximation.