Interaction of Plane Nonlinear Waves in a Compressible Fluid and Two-Dimensional Shock Turbulence

Abstract

Interaction of two intersecting plane nonlinear waves in a compressible fluid such as shocks, expansion waves, slip flows and contact surfaces are investigated using the reductive perturbation method. It is shown that intersections of waves belonging to different families of characteristics do not alter the nature of the waves but change their amplitudes, phase-velocities and paths, whereas intersections of waves belonging to the same family of characteristics make them either coalesce or absorb each other. It is inferred from these results that the statistical properties of two-dimensional shock turbulence is identical to those of the Burgers turbulence.