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

• Published in: Chinese physics B 2016-04, Vol.25 (4), p.194-205
• Main Author: 骆文于 于晓林 杨雪峰 张仁和
• Format: Article
• Language: English
• Subjects: Benchmarking; Exact solutions; Integrals; Mathematical analysis; Mathematical models; Stability; Waveguides; Wavenumber; 声场; 数值模型; 无条件稳定; 波导; 波数; 积分方法; 稳定性问题; 解析解
• ISSN: 1674-1056; 2058-3834; 1741-4199
• DOI: 10.1088/1674-1056/25/4/044302

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.