Focusing of Finite-Amplitude Waves at Fold Caustics

R.Marchiano, F.Coulouvrat (Laboratoire de Modelisation en Mecanique, Universite Pierre et Marie Curie, CNRS, Paris, France); J.L.Thomas (Laboratoire Ondes et Acoustique, CNRS, Paris, France)

e-mail: marchi@lmm.jussieu.fr

The focusing of acoustic waves at a fold caustic is studied experimentally for different amplitudes  of the incident signals. This focusing occurs, for instance, for the sonic boom in case of aicraft  manoeuvres. The following experiment has been built to scale this phenomenon at 1:100 000 in  a water tank. The first stage consists in determining the signals to be emitted by an array  of piezoelectric antennae in order to obtain the field associated with the caustic to be  synthesized, i.e. the Airy function. This stage is achieved in the linear regime with the inverse  filtering method. In the second stage, the amplitude of the transmitted signals is increased,  which entails nonlinear propagation and induces a deformation (steepening) of the temporal  profile of the incident signals. In the vicinity of the caustic, the transient acoustic field is  measured and compared with a numerical simulation. This simulation solves the nonlinear  Tricomi equation modelling the field near a fold caustic in the nonlinear regime. The algorithm  is a modification of the pseudospectral code used for solving the KZ equation. [work supported by the European Commission, contract G4RD-CT-2000-00398].


Section : 6