Three-Wave Resonance in a Two-Dimensional Stationary Problem of Gas Dynamics

Abstract

The isentropic motion of a perfect ideal gas on a constant homogeneous supersonic background is considered. A two-dimensional stationary potential problem of gas dynamics is solved to study the interaction of three traveling waves whose amplitudes and phases are slowly varying in the direction of the background flow in the case when the sum of “harmonic” phases is exactly equal to zero. The equations of amplitude and phase variation are derived and their solutions are analyzed analytically. The question of what boundary conditions should be satisfied is discussed.