Research output: Contribution to journal › Article › peer-review
АНАЛИТИЧЕСКОЕ РЕШЕНИЕ ЛУЧЕВЫХ УРАВНЕНИЙ ГАМИЛЬТОНА ДЛЯ ВОЛН РОССБИ НА СТАЦИОНАРНЫХ СДВИГОВЫХ ПОТОКАХ. / Gnevyshev, V. G.; Belonenko, T. V.
In: Fundamental and Applied Hydrophysics, Vol. 15, No. 2, 2022, p. 8-18.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - АНАЛИТИЧЕСКОЕ РЕШЕНИЕ ЛУЧЕВЫХ УРАВНЕНИЙ ГАМИЛЬТОНА ДЛЯ ВОЛН РОССБИ НА СТАЦИОНАРНЫХ СДВИГОВЫХ ПОТОКАХ
AU - Gnevyshev, V. G.
AU - Belonenko, T. V.
N1 - Funding Information: 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. Publisher Copyright: © 2022 Russian Academy of Sciences,Department of the Earth Sciences. All rights reserved.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Hermitian operators
KW - Non-Hermitian operators
KW - non-zonal
KW - ray equations of Hamilton
KW - Rossby waves
KW - shear flow
KW - zonal
KW - Hermitian operators
KW - Non-Hermitian operators
KW - Rossby waves
KW - non-zonal
KW - ray equations of Hamilton
KW - shear flow
KW - zonal
UR - http://www.scopus.com/inward/record.url?scp=85133687165&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/e4fa7275-5db3-31bf-b2dd-b2b4c7700b17/
U2 - 10.48612/fpg/4eh4-83zr-r1fm
DO - 10.48612/fpg/4eh4-83zr-r1fm
M3 - статья
AN - SCOPUS:85133687165
VL - 15
SP - 8
EP - 18
JO - ФУНДАМЕНТАЛЬНАЯ И ПРИКЛАДНАЯ ГИДРОФИЗИКА
JF - ФУНДАМЕНТАЛЬНАЯ И ПРИКЛАДНАЯ ГИДРОФИЗИКА
SN - 2073-6673
IS - 2
ER -
ID: 97594113