Non-self-adjoint model statement of boundary problem of acoustics. Part 1
https://doi.org/10.59887/2073-6673.2023.16(2)-8
Abstract
Based on the mathematical definition of a non-self-adjoint operator and the physical meaning of a specific boundary value problem, a non-self-adjoint model statement of boundary value problems in acoustics is formulated. As an example, boundary value problems for the reflection of a plane wave and a spherical wave at the interface between two liquid media are considered. A new definition of the reflection coefficient of a spherical wave is introduced. In the region of subcritical angles of incidence, the new definition takes into account the appearance in the total sound field of converging recoil waves corresponding to the eigenfunctions of the adjoint operator. In the region of supercritical angles of incidence, the participation of the eigenfunctions of two conjugate operators in the total sound field forms a nonzero power flux through the interface and its transformation into the vortex component of the intensity vector at the total internal reflection horizon. The definition of the total internal reflection horizon is given. Experimental data are presented that confirm the new definition of the reflection coefficient and the physical correctness of the non-self-adjoint model statement.
Keywords
non-self-adjoint model setting,
converging recoil waves,
transformation horizon,
vortex component of the intensity vector
Supporting agencies: The work was carried out in IPMT FEB RAS within the framework of the state assignment on the theme № 121030400088-1, and also in FEFU, within the framework of the state assignment of the Ministry of Education and Science of Russia in the sphere of scientific activity under the project № FZNS-2023-0008
About the Authors
B. A. Kasatkin
Institute of Marine Technology Problems, Far Eastern Branch of the Russian Academy of Sciences
Russian Federation
Russian Federation
5a Sukhanova St., Vladivostok, Primorsky Krai, 690091
N. V. Zlobina
Institute of Marine Technology Problems, Far Eastern Branch of the Russian Academy of Sciences
Russian Federation
Russian Federation
5a Sukhanova St., Vladivostok, Primorsky Krai, 690091
L. G. Statsenko
Far Eastern Federal University
Russian Federation
Russian Federation
p. Ajaks, 10, Russkiy Isl., Vladivostok, Primorsky Krai, 690922
S. B. Kasatkin
Institute of Marine Technology Problems, Far Eastern Branch of the Russian Academy of Sciences
Russian Federation
Russian Federation
5a Sukhanova St., Vladivostok, Primorsky Krai, 690091
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Review
For citations:
Kasatkin B.A., Zlobina N.V., Statsenko L.G., Kasatkin S.B. Non-self-adjoint model statement of boundary problem of acoustics. Part 1. Fundamental and Applied Hydrophysics. 2023;16(2):111-125. (In Russ.) https://doi.org/10.59887/2073-6673.2023.16(2)-8
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