Abstract
Acoustic particle velocities can provide additional energy flow information of the sound field; thus, the vector acoustic model is attracting increasing attention. In the current study, a vector wavenumber integration (VWI) model was established to provide benchmark solutions of ocean acoustic propagation. The depth-separated wave equation was solved using finite difference (FD) methods with second- and fourth-order accuracy, and the sound source singularity in this equation was treated using the matched interface and boundary method. Moreover, the particle velocity was calculated using the wavenumber integration method, consistent with the calculation of the sound pressure. Furthermore, the VWI model was verified using acoustic test cases of the free acoustic field, the ideal fluid waveguide, the Bucker waveguide, and the Munk waveguide by comparing the solutions of the VWI model, the analytical formula, and the image method. In the free acoustic field case, the errors of the second- and fourth-order FD schemes for solving the depth-separated equation were calculated, and the actual orders of accuracy of the FD schemes were tested. Moreover, the time-averaged sound intensity (TASI) was calculated using the pressure and particle velocity, and the TASI streamlines were traced to visualize the time-independent energy flow in the acoustic field and better understand the distribution of the acoustic transmission loss.
Highlights
Underwater acoustic wave propagation excited by a time harmonic source can be described by the Helmholtz equation in the frequency domain, which can be solved using the wavenumber integration technique [2,3], the fast field program (FFP) [4,5,6], normal modes [7], ray theory [8], the parabolic equation [9], the finite difference method (FDM) [10], and the spectral method [11]
The present range-independent vector wavenumber integration (VWI) model can serve as a benchmark vector model for other acoustic models, such as FDM models and spectral method models
By applying the particle velocity, the time-averaged sound intensity (TASI) streamlines can be computed and displayed, thereby bettering our understanding of the transmission loss (TL) distribution, and these TASI streamlines can be applied to other vector acoustic models
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Underwater acoustic wave propagation excited by a time harmonic source can be described by the Helmholtz equation in the frequency domain, which can be solved using the wavenumber integration technique [2,3], the fast field program (FFP) [4,5,6], normal modes [7], ray theory [8], the parabolic equation [9], the finite difference method (FDM) [10], and the spectral method [11] As these models for predicting the scalar sound level have reached a high level of development, our interest is in developing a vector model to accurately predict the particle velocity. TASI streamlines in the test cases show that the regions through which the energy flow is concentrated form zones of sound convergence
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