City Research Online

Abstract

The theoretical basis for modeling sound propagation in marine waveguides essentially leads to analysis of the boundary value problem of the Helmholtz equation, and the ocean bottom is generally assumed to be an uneven interface composed of different media. This article presents an analytical solution to the classical acoustic problem of sound propagation by a point source in a waveguide, which comprises a cylindrical seamount or a cavity. The velocity potential is constructed for each part of the waveguide as a series of normal modes. Conditions of continuity of the acoustic field have led to an infinite system of linear algebraic equations in terms of the unknown coefficients of normal modes. It is shown for the first time that the derived infinite system is quasi-regular and has a unique bounded solution. Asymptotic behavior of unknowns in the system is established with the help of the law of singularity of particle velocity at the edge of the waveguide. The derived asymptotic solution of the unknowns permits the use of the method of improved reduction for the determination of the coefficients of normal modes. Examples of numerical implementation of the proposed theory are presented by varying significant parameters of geophysical waveguides.

Publication Type:	Article
Additional Information:	© 2026 ASME. This is the accepted manuscript of an article published by American Society of Mechanical Engineers. Please refer to the publisher’s terms and conditions for information on re-use.
Publisher Keywords:	acoustic geophysical waveguides, uneven bottom, Helmholtz equation, normal modes, analytical solution, infinite system of linear equations, regularity of infinite system, asymptotic behavior, acoustic emission, flow-induced noise and vibration, modal analysis, propagation and radiation, structural acoustics
Subjects:	Q Science > QC Physics T Technology > TA Engineering (General). Civil engineering (General)
Departments:	School of Science & Technology
SWORD Depositor:	Symplectic Administrator

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