Eur. Phys. J. B 35, 531-549 (2003)
https://doi.org/10.1140/epjb/e2003-00307-0

Nonlinear effects and shock formation in the focusing of a spherical acoustic wave

Numerical simulations and experiments in liquid helium

¹ Laboratoire de Physique Statistique de l'ENS, associé au CNRS et aux Universités Paris 6 et 7, 24 rue Lhomond, 75231 Paris Cedex 05, France
² Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur, UPR CNRS 3251, B.P. 133, 91403 Orsay Cedex, France

Corresponding author: ^a appert@lps.ens.fr

Received: 27 November 2002
Revised: 11 July 2003
Published online: 24 October 2003

Abstract

The focusing of acoustic waves is used to study nucleation phenomena in liquids. At large amplitude, nonlinear effects are important so that the magnitude of pressure or density oscillations is difficult to predict. We present a calculation of these oscillations in a spherical geometry. We show that the main source of nonlinearities is the shape of the equation of state of the liquid, enhanced by the spherical geometry. We also show that the formation of shocks cannot be ignored beyond a certain oscillation amplitude. The shock length is estimated by an analytic calculation based on the characteristics method. In our numerical simulations, we have treated the shocks with a WENO scheme. We obtain a very good agreement with experimental measurements which were recently performed in liquid helium. In addition, the comparison between numerical and experimental results allows us to calibrate the vibration of the ceramic used to produce the wave, as a function of the applied voltage.