Chin. Phys. B, 2022, Vol. 31(9): 094301    DOI: 10.1088/1674-1056/ac6940
 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next

# Wave mode computing method using the step-split Padé parabolic equation

Chuan-Xiu Xu(徐传秀)1,† and Guang-Ying Zheng(郑广赢)1,2
1 Hangzhou Applied Acoustics Research Institute, Hangzhou 310023, China;
2 Science and Technology on Sonar Laboratory, Hangzhou 310023, China
Abstract  Models based on a parabolic equation (PE) can accurately predict sound propagation problems in range-dependent ocean waveguides. Consequently, this method has developed rapidly in recent years. Compared with normal mode theory, PE focuses on numerical calculation, which is difficult to use in the mode domain analysis of sound propagation, such as the calculation of mode phase velocity and group velocity. To broaden the capability of PE models in analyzing the underwater sound field, a wave mode calculation method based on PE is proposed in this study. Step-split Padé PE recursive matrix equations are combined to obtain a propagation matrix. Then, the eigenvalue decomposition technique is applied to the matrix to extract sound mode eigenvalues and eigenfunctions. Numerical experiments on some typical waveguides are performed to test the accuracy and flexibility of the new method. Discussions on different orders of Padé approximant demonstrate angle limitations in PE and the missing root problem is also discussed to prove the advantage of the new method. The PE mode method can be expanded in the future to solve smooth wave modes in ocean waveguides, including fluctuating boundaries and sound speed profiles.
Keywords:  parabolic equation      propagation matrix      eigenvalue decomposition
Received:  29 January 2022      Revised:  22 March 2022      Accepted manuscript online:  22 April 2022
 PACS: 43.30.-k (Underwater sound) 43.30.Bp (Normal mode propagation of sound in water)
Fund: Project supported by Young Elite Scientist Sponsorship Program by CAST (Grant No. YESS20200330).
Corresponding Authors:  Chuan-Xiu Xu     E-mail:  xuchuanxiu715@163.com