A nonlinear geometrical theory of diffraction for predicting sonic boom in the shadow zone

Abstract

Inside the geometrical shadow zone, it is well-known that the sound field emanates from rays diffracted by creeping waves propagating along the ground. A nonlinear, time-domain formulation of the geometrical theory of diffraction is proposed. Nonlinear effects are shown to be small, except for small sound speed gradients. In the linear case, the matching with geometrical acoustics leads to an analytical expression for the pressure field in the shadow zone, that takes into account all creeping waves and finite ground impedance. Numerical simulations indicate the ground impedance influences the sonic boom amplitude and rise time mostly close to the carpet edge. Comparisons with Concorde sonic boom measurements are favorable. In the nonlinear case, a generalized Burgers equation is proposed for modeling the sound field in the shadow zone over a rigid ground. The classical viscous term is replaced by a ‘‘diffraction operator’’ that describes the way sound diffracts along the ground. This operator takes into account the sound absorption and dispersion associated to all creeping waves. [Work supported by Aérospatiale Aéronautique, Toulouse, France.]