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Ray Method Expansions for Surface and Internal Waves in Inhomogeneous Oceans of Variable Depth
Author(s) -
Hector D.,
Cohen J.,
Bleistein N.
Publication year - 1972
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1972512121
Subject(s) - ordinary differential equation , mathematical analysis , dispersion relation , internal wave , amplitude , mathematics , differential equation , eigenvalues and eigenvectors , variable (mathematics) , wave propagation , dispersion (optics) , physics , mechanics , optics , quantum mechanics
A ray method formalism is developed for the analysis of surface and internal waves in an inhomogeneous ocean of variable depth. In this method, we deduce from the governing system of equations a system of first order ordinary differential equations, for the group lines (rays of the ray method) and the propagation of phase and amplitude on them. The dispersion relation for these waves arises as an eigen‐condition on an eigen‐value problem involving an ordinary differential equation in the depth variable. The deduced equation for amplitude propagation has the interpretation of a statement of conservation of action.