Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media |
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Authors: | M V Aver’yanov V A Khokhlova O A Sapozhnikov Ph Blanc-Benon R O Cleveland |
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Institution: | (1) Moscow State University, Vorob’evy gory, Moscow, 119992, Russia;(2) LMFA, UMR CNRS 5509, Ecole Centrale de Lyon, 69134 Ecully Cedex, France;(3) Department of Aerospace and Mechanical Engineering, Boston University, 110 Cummington Street, Boston, Massachusetts 02115, USA |
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Abstract: | A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The
equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial
inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case.
A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with
random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation
direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of
vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present,
the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong
shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity
is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear
wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption.
Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 6, pp. 725–735.
This article was translated by the authors. |
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