kzk equation
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2020 ◽  
Author(s):  
Michael Muhlestein ◽  
Carl Hart

Nonlinear propagation of shock waves through periodic structures have the potential to exhibit interesting phenomena. Frequency content of the shock that lies within a bandgap of the periodic structure is strongly attenuated, but nonlinear frequency-frequency interactions pumps energy back into those bands. To investigate the relative importance of these propagation phenomena, numerical experiments using the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation are carried out. Two-dimensional propagation through a periodic array of rectangular waveguides is per-formed by iteratively using the output of one waveguide as the input for the next waveguide. Comparison of the evolution of the initial shock wave for both the linear and nonlinear cases is presented.


2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Haisen Li ◽  
Jingxin Ma ◽  
Jianjun Zhu ◽  
Baowei Chen

The Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation has been widely used in the simulation and calculation of nonlinear sound fields. However, the accuracy of KZK equation reduced due to the deflection of the direction of the sound beam when the sound beam is inclined incidence. In this paper, an equivalent sound source model is proposed to make the calculation direction of KZK calculation model consistent with the sound propagation direction after acoustic refraction, so as to improve the accuracy of sound field calculation under the inclined incident conditions. The theoretical research and pool experiment verify the feasibility and effectiveness of the proposed method.


2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Ke Qu ◽  
Binbin Zou ◽  
Jingjing Chen ◽  
Yingge Guo ◽  
Runtian Wang

Broadband parametric acoustic arrays appear to offer advantages for shallow water sub-bottom profiling. In this paper, the performance of a broadband parametric acoustic array system was experimentally evaluated. In tank experiments using the nonlinear parabolic wave (KZK) equation, the directivity, source level, parametric acoustic array length, and penetration depth were evaluated. Based on Berktay’s far-field solution, the system’s emission signal was designed. According to sea trials of the broadband parametric acoustic array system as designed, a clear sub-bottom profile was obtained. Moreover, buried pipelines in the seabed were effectively detected, verifying the system’s effectiveness.


Author(s):  
Junpei Takeno ◽  
Takashi Misaka ◽  
Koji Shimoyama ◽  
Shigeru Obayashi
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