Group velocity and dispersion of Buchwald and Adams shelf waves. A new analytical approach
https://doi.org/10.59887/2073-6673.2023.16(2)-1
Abstract
In this paper, a new analysis of the known topographic models of Rossby waves for piecewise exponential topography profiles is performed. A mathematical method is proposed that allows us to find analytically the group velocity and variance. A numerical comparison is made of the relations presented in the study of Buchwald and Adams and the dependencies obtained within the framework of a new analytical approach. Numerical comparative analysis showed that the discrepancy for the phase velocities lies in the range of five percent. For group speeds, the discrepancy reaches nineteen percent for the first mode and decreases for higher mode numbers. We also consider long-wave asymptotics of eigenfunctions. It is established that the long-wave limit for Rossby shelf waves has specifics: the longitudinal wave number tends to zero, and the transverse wave number reaches a certain finite positive constant, which is the greater the higher the mode number. It is shown that in the long-wave limit, Rossby shelf waves transform into shelf topographic currents, while there is a certain self-similarity for the phase and group velocities of shelf currents depending on the value of the topography gradient.
Keywords
Rossby waves,
topographic waves,
shelf waves,
exponential profile,
group velocity,
dispersion,
self-similarity,
mesoscale eddies
Supporting agencies: This work was financially supported by the RNF grant No. 22-27-00004, financial support of the SPbSU grant No. 94033410 and under the state assignment No. 0128-2021-0003.
About the Authors
V. G. Gnevyshev
Shirshov Institute of Oceanology RAS
Russian Federation
Russian Federation
117997, Nahimovsky Pr., 36, Moscow
V. S. Travkin
St. Petersburg State University; N.N.Zubov’s State Oceanographic Institute, Roshydromet
Russian Federation
Russian Federation
199034, 7–9, Universitetskaya Nab., St. Petersburg
119034, 6, Kropotkinskiy Lane, Moscow
T. V. Belonenko
St. Petersburg State University
Russian Federation
Russian Federation
199034, 7–9, Universitetskaya Nab., St. Petersburg
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For citations:
Gnevyshev V.G., Travkin V.S., Belonenko T.V. Group velocity and dispersion of Buchwald and Adams shelf waves. A new analytical approach. Fundamental and Applied Hydrophysics. 2023;16(2):8-20. (In Russ.) https://doi.org/10.59887/2073-6673.2023.16(2)-1
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