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Diffraction of high-intensity field in focal region as dynamics of nonlinear system with low-frequency dispersion

Diffraction of high-intensity field in focal region as dynamics of nonlinear system with... Abstract The stationary profile in the focal region of a focused nonlinear acoustic wave is described. Three models following from the Khokhlov-Zabolotskaya (KZ) equation with three independent variables are used: (i) the simplified one-dimensional Ostrovsky-Vakhnenko equation, (ii) the system of equations for paraxial series expansion of the acoustic field in powers of transverse coordinates, and (iii) the KZ equation reduced to two independent variables. The structure of the last equation is analogous to the Westervelt equation. Linearization through the Legendre transformation and reduction to the well-studied Euler-Tricomi equation is shown. At high intensities the stationary profiles are periodic sequences of arc sections having singularities of derivative in their matching points. The occurrence of arc profiles was pointed out by Makov. These appear in different nonlinear systems with low-frequency dispersion. Profiles containing discontinuities (shock fronts) change their form while passing through the focal region and are non-stationary waves. The numerical estimations of maximum pressure and intensity in the focus agree with computer calculations and experimental measurements. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acoustical Physics Springer Journals

Diffraction of high-intensity field in focal region as dynamics of nonlinear system with low-frequency dispersion

Rudenko, O. V.; Hedberg, C. M.
Acoustical Physics , Volume 61 (1): 9 – Jan 1, 2015
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References (27)

Publisher
Springer Journals
Copyright
2015 Pleiades Publishing, Ltd.
ISSN
1063-7710
eISSN
1562-6865
DOI
10.1134/s1063771015010091
Publisher site
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Abstract

Abstract The stationary profile in the focal region of a focused nonlinear acoustic wave is described. Three models following from the Khokhlov-Zabolotskaya (KZ) equation with three independent variables are used: (i) the simplified one-dimensional Ostrovsky-Vakhnenko equation, (ii) the system of equations for paraxial series expansion of the acoustic field in powers of transverse coordinates, and (iii) the KZ equation reduced to two independent variables. The structure of the last equation is analogous to the Westervelt equation. Linearization through the Legendre transformation and reduction to the well-studied Euler-Tricomi equation is shown. At high intensities the stationary profiles are periodic sequences of arc sections having singularities of derivative in their matching points. The occurrence of arc profiles was pointed out by Makov. These appear in different nonlinear systems with low-frequency dispersion. Profiles containing discontinuities (shock fronts) change their form while passing through the focal region and are non-stationary waves. The numerical estimations of maximum pressure and intensity in the focus agree with computer calculations and experimental measurements.

Journal

Acoustical Physics – Springer Journals

Published: Jan 1, 2015

Keywords: Acoustics

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