Wave Motion 42 (2005) 211–225 Reflection of caustics and focused sonic booms Pablo Luis Rend´ on ∗ , Franc ¸ois Coulouvrat Laboratoire de Mod´ elisation en M´ ecanique, UMR CNRS 7607, Universit´ e Pierre et Marie Curie, case 162, 4 Place Jussieu, 75252 Paris Cedex 05, France Received 23 November 2004; received in revised form 2 February 2005; accepted 8 February 2005 Available online 5 March 2005 Abstract 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. © 2005 Elsevier B.V. All rights reserved. Keywords: Nonlinear acoustics; Sonic boom; Focusing; Caustics; Ground effects; Impedance Introduction Sonic boom is a community acceptance problem that remains to be overcome for a supersonic overland flight, a key point for the future development of any profitable and green civil high speed aircraft. The most intense sonic boom, the so-called superboom due to sound focusing occuring during the aircraft transsonic acceleration from Mach 1 to cruise speed, cannot be avoided by realistic maneuvers. For present aircraft configurations, it leads to an amplification of ground pressures up to two to three times the unfocused boom shock strength. To comply with a future international regulation on sonic boom, an accurate prediction of the level of focused booms is required. A new algorithm has been recently designed [1,2] that is numerically solving the nonlinear Tricomi [3,4] ∗ Corresponding author. Present address: Centro de Ciencia Aplicada y Desarrollo Tecnol´ ogico, Universidad Nacional Aut´ onoma de M´ exico, Ciudad Universitaria, M´ exico, D.F. 04510, Mexico. Tel.: +5255 56228627x1218; fax: +5255 56228675. E-mail addresses: rendon@aleph.cinstrum.unam.mx (P.L. Rend´ on), coulouvr@ccr.jussieu.fr (F. Coulouvrat). 0165-2125/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.wavemoti.2005.02.002