Chin. Phys. B, 2016, Vol. 25(4): 044302    DOI: 10.1088/1674-1056/25/4/044302
Special Issue: Virtual Special Topic — Acoustics
 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next

# Analytical solution based on the wavenumber integration method for the acoustic field in a Pekeris waveguide

Wen-Yu Luo(骆文于)1, Xiao-Lin Yu(于晓林)1,2, Xue-Feng Yang(杨雪峰)2,3, Ren-He Zhang(张仁和)1
1 State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China;
2 University of Chinese Academy of Sciences, Beijing 100049, China;
3 Shanghai Acoustic Laboratory, Chinese Academy of Sciences, Shanghai 200032, China
Abstract  An exact solution based on the wavenumber integration method is proposed and implemented in a numerical model for the acoustic field in a Pekeris waveguide excited by either a point source in cylindrical geometry or a line source in plane geometry. Besides, an unconditionally stable numerical solution is also presented, which entirely resolves the stability problem in previous methods. Generally the branch line integral contributes to the total field only at short ranges, and hence is usually ignored in traditional normal mode models. However, for the special case where a mode lies near the branch cut, the branch line integral can contribute to the total field significantly at all ranges. The wavenumber integration method is well-suited for such problems. Numerical results are also provided, which show that the present model can serve as a benchmark for sound propagation in a Pekeris waveguide.
Keywords:  wavenumber integration technique      Pekeris waveguide      analytical solution      branch line integral
Received:  22 September 2015      Revised:  19 October 2015      Accepted manuscript online:
 PACS: 43.30.Bp (Normal mode propagation of sound in water) 43.20.Bi (Mathematical theory of wave propagation)
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11125420), the Knowledge Innovation Program of the Chinese Academy of Sciences, the China Postdoctoral Science Foundation (Grant No. 2014M561882), and the Doctoral Fund of Shandong Province, China (Grant No. BS2012HZ015).
Corresponding Authors:  Wen-Yu Luo     E-mail:  lwy@mail.ioa.ac.cn