Abstract |
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