Reflection of caustics and focused sonic booms

Sonic boom, a community acceptance problem for the future development of civil high speed aircraft, is most intense (the so-called “superboom”) when focussed during the aircraft transsonic acceleration from Mach 1 to cruise speed. The ground reflection of superboom is studied. It is shown that the incident and the reflected fields are solutions of two uncoupled nonlinear Tricomi equations. The coupling between the two fields is expressed straightforwardly only through a linear ground impedance condition. For waves reflected off the ground or off rough sea surface, the effects of ground impedance may be noticeable, especially in the case of a soft ground. Amplitude reduction is also enhanced in the weakly nonlinear case, where the peaks are sharper. That behaviour is similar for reflection off a sea rough surface. However, in all investigated cases, the amplitude reduction of the reflected field remains limited. Hence, from a perception point of view, no significant mitigation of superboom is likely to be expected from passive absorption.