Experimental observation of azimuthal shock waves on nonlinear acoustical vortices

Thomas Brunet,Jean-Louis Thomas,Régis Marchiano,François Coulouvrat

doi:10.1088/1367-2630/11/1/013002

Abstract

Thanks to a new focused array of piezoelectric transducers, experimental results are reported here to evidence helical acoustical shock waves resulting from the nonlinear propagation of acoustical vortices (AVs). These shock waves have a three-dimensional spiral shape, from which both the longitudinal and azimuthal components are studied. The inverse filter technique used to synthesize AVs allows various parameters to be varied, especially the topological charge which is the key parameter describing screw dislocations. Firstly, an analysis of the longitudinal modes in the frequency domain reveals a wide cascade of harmonics (up to the 60th order) leading to the formation of the shock waves. Then, an original measurement in the transverse plane exhibits azimuthal behaviour which has never been observed until now for acoustical shock waves. Finally, these new experimental results suggest interesting potential applications of nonlinear effects in terms of acoustics spanners in order to manipulate small objects.

Highlights

The magnitude is limited by the resolution of our scan, which tends to smooth the azimuthal shock wave and, tends to reduce the associated pressure gradient, this experimental result provides a qualitative picture in terms of acoustical spanning by means of nonlinear fields
The highlight of this paper is the experimental observation of azimuthal shock waves on nonlinear acoustical vortices (AVs) of different topological charge (l = 1 and l = 3)
After recovering the conservation law between the topological charge and the harmonic order on fully developed shock waves, we investigated the helical structure of the azimuthal shock waves that proves stable during propagation

Summary

Methods

As previously done [7], we use the linear inverse filter technique [11] to synthesize AVs. Once the propagation operator has been experimentally recorded, an appropriate numerical treatment is applied to compute the signals that the transducers have to emit to synthesize the desired field at the control points. We choose to use the Gauss–Laguerre (GL) beams as the ‘target’ pattern in the control plane to synthesize AV. These beams are known to carry screw dislocations [12]. They have a limited spatial extension and, are of finite energy. GL beams are exact solutions of the linear paraxial wave equation

Results

Discussion

Conclusion