Weak shock diffraction

The diffraction of a weak shock by a rigid wedge is analyzed theoretically via the theory of weakly nonlinear geometrical acoustics, which is the same as Whitham's nonlinearization technique. First linear weakly nonlinear geometrical acoustics is explained. Then the linear acoustics results for weak shock diffraction by a wedge are presented. Next these results are modified according to the principles of weakly nonlinear geometrical acoustics. The results show that the compressive diffracted wavefronts of linear acoustics are actually shocks, and their positions and strengths are found. The infinite gradients of the linear acoustics rarefaction waves are found to be finite but discontinuous gradients. Finally the results are specialized to a shock hitting a right-angled wedge, a shock coming off a right-angled wedge, and a shock hitting a thin semi-infinite screen.