Reciprocity of scalar and vector sound field at low frequency for directional sound source in shallow seas

Liang ZHANG; Haigang ZHANG; Chunxia MENG

doi:10.11990/jheu.202506020

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Reciprocity of scalar and vector sound field at low frequency for directional sound source in shallow seas

Research Article | 更新时间：2026-03-31

- Reciprocity of scalar and vector sound field at low frequency for directional sound source in shallow seas
- Journal of Harbin Engineering University Vol. 46, Issue 8, Pages: 1516-1521(2025)
- 作者机构：
  
  1.哈尔滨工程大学水声技术全国重点实验室, 黑龙江哈尔滨 150001
  2.海洋信息获取与安全工信部重点实验室(哈尔滨工程大学) 工业和信息化部, 黑龙江哈尔滨 150001
  3.哈尔滨工程大学水声工程学院, 黑龙江哈尔滨 150001
  4.大连测控技术研究所, 辽宁大连 116013
- 作者简介：
- 基金信息：
- DOI：10.11990/jheu.202506020
  CLC： TB566
- Received：09 June 2025，
  
  Online First：23 June 2025，
  
  Published：05 August 2025
- 稿件说明：
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Liang ZHANG, Haigang ZHANG, Chunxia MENG. Reciprocity of scalar and vector sound field at low frequency for directional sound source in shallow seas[J]. Journal of Harbin Engineering University, 2025, 46(8): 1516-1521.
DOI：

Liang ZHANG, Haigang ZHANG, Chunxia MENG. Reciprocity of scalar and vector sound field at low frequency for directional sound source in shallow seas[J]. Journal of Harbin Engineering University, 2025, 46(8): 1516-1521. DOI： 10.11990/jheu.202506020.

摘要

为快速评估船舶水下辐射噪声的标量矢量声场，针对浅海低频指向性声源，本文研究其标量场与矢量场的互易性。通过仿真分析了浅海不同类型声源的低频标量矢量声场沿着垂直方向的分布

建立了指向性声源的标量声场和矢量声场的数学模型，给出了单极子、偶极子等不同类型声源的标量声压场、水平振速声场和垂直振速声场的数学表达式。结果表明：单极子声源和水平偶极子声源的声压场及水平振速声场满足互易原理

但其垂直振速声场不满足互易原理；垂直偶极子声源的垂直振速声场满足互易原理

但其声压场及水平振速声场不满足互易原理。研究结论为水下声源标矢量声场特性的快速评估提供了理论依据，并为利用多种声场信息进行水下实际声源信息挖掘提供了技术支持，具有重要的实用价值。

Abstract

For the rapid evaluation of the scalar and vector sound fields of underwater radiated noise from ships

the reciprocity of the low-frequency scalar and vector fields of directional sound sources in shallow seas were studied. The scalar and vector sound fields of directional sound sources were mathematically modeled

and mathematical expressions of the scalar sound pressure field

horizontal particle velocity field

and vertical particle velocity field for different types of sound sources

such as monopoles and dipoles

were determined. The vertical distribution of the low-frequency scalar and vector sound fields was simulated for different types of sound sources in shallow seas. The sound pressure fields and horizontal particle velocity fields of monopole and horizontal dipole sound sources satisfy the reciprocity principle

unlike the vertical particle velocity fields. The vertical particle velocity field of the vertical dipole sound source satisfies the reciprocity principle

in contrast with the sound pressure field and horizontal particle velocity field. The results provide a theoretical basis for rapid evaluation of the characteristics of the scalar and vector sound fields of underwater sound sources

and offer technical support as an adjunct to mining information for actual underwater sound sources using various sound field information

which is of great practical value.

关键词

Keywords

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Key Laboratory of Underwater Acoustic Environment, Institute of Acoustics, Chinese Academy of Sciences

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