Analytical Solution of the Ray Equations of Hamilton for Rossby Waves on Stationary Shear Flows
https://doi.org/10.59887/fpg/4eh4-83zr-r1fm
Abstract
The asymptotic behavior of Rossby waves in the ocean interacting with a shear stationary flow is considered. It is shown that there is a qualitative difference between the problems for the zonal and non-zonal background flow. Whereas only one critical layer arises for a zonal flow, then several critical layers can exist for a non-zonal flow. It is established that the integrated ray equations of Hamilton are equivalent to the asymptotic behavior of the Cauchy problem solution. Explicit analytical solutions are obtained for the tracks of Rossby waves as a function of time and initial parameters of the wave disturbance, as well as the magnitude of the shear and angle of inclination of the flow to the zonal direction. The ray equations of Hamilton are analytically integrated for Rossby waves on a shear flow. The obtained explicit expressions make it possible to calculate in real-time the Rossby wave tracks for any initial wave direction and any shear current inclination angle. It is shown qualitatively that these tracks for a non-zonal flow are strongly anisotropic.
Keywords
Rossby waves,
shear flow,
zonal,
non-zonal,
Hermitian operators,
Non-Hermitian operators,
ray equations of Hamilton
Supporting agencies: The publication was funded by the Russian Science Foundation, project No 22-27-00004. The work of V.G.G. was carried out within the State Task for the Shirshov Institute of Oceanology RAS, project No 0128-2021-0003.
About the Authors
V. G. Gnevyshev
Shirshov Institute of Oceanology, Russian Academy of Sciences
Russian Federation
Russian Federation
117997, Nahimovsky Pr., 36, Moscow
T. V. Belonenko
St. Petersburg State University
Russian Federation
Russian Federation
199034, 7–9, Universitetskaya Emb., St. Petersburg
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Review
For citations:
Gnevyshev V.G., Belonenko T.V. Analytical Solution of the Ray Equations of Hamilton for Rossby Waves on Stationary Shear Flows. Fundamental and Applied Hydrophysics. 2022;15(2):8-18. https://doi.org/10.59887/fpg/4eh4-83zr-r1fm
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