Anomalous Behavior of the Vertical Structure of Rossby Waves on Non-Zonal Shear Flow in the Vicinity of the Focus

V. G. Gnevyshev1, T. V. Belonenko2, ✉

1 P. P. Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, Russian Federation

2 St Petersburg University, St Petersburg, Russian Federation

✉ e-mail: btvlisab@yandex.ru

Abstract

Purpose. The work aims to study the behavior of vertical barotropic-baroclinic modes of Rossby waves on a non-zonal shear flow in the vicinity of the focus.

Methods and Results. Inferred from the reference equation, we consider some variants of the behavior of eigenfunctions in the vicinity of the focus. It is shown that the number of possible variants for non-zonal flows increases compared with the zonal case. This means that qualitatively new additional scenarios appear in the case of a non-zonal flow compared with the problem for internal waves when the behavior of Rossby waves in the vicinity of the localization level qualitatively coincides with the behavior for the zonal case, herewith the coefficient of a passage through the focus is always exponentially small. The solution becomes extremely sensitive to the initial parameters of the wave incident on the non-zonal focus. Another important point is that the second, additional anomalous focus appears on the non-zonal flow. When a wave falls on this focus on one side, it behaves like a classic focus with a classic wave adhering. And when falling from the opposite side, the Rossby wave does not notice the focus and passes it without a short-wave transformation. In the problem, abnormal scenarios appear with the passage of the focus without difficulty with a coefficient of passage equal to one in addition to the scenario with an infinitely long time adhering to the focus and an exponentially small coefficient of passage.

Conclusions. The anomalous behavior of Rossby waves in the horizontal plane on non-zonal flows is accompanied by anomalous behavior of the vertical mode, in contrast to the strictly zonal case of flow with different kinematics. The eigenvalues of the Sturm-Liouville problem change abruptly during the transition from the non-zonal to the zonal case. As a consequence, there is no limit transition from a weakly non-zonal case to a strictly zonal one. Such an extremely ambiguous analytical behavior of Rossby waves in the vicinity of the focus on baroclinic non-zonal flows rather indicates the absence of analytical prediction and the need for a deeper and more detailed analysis using numerical methods.

Keywords

Rossby waves, non-zonal flow, focus, Sturm-Liouville problem

Acknowledgements

The study was carried out with the support of the RSF grant No. 22-27-00004 and within the framework of the state assignment on theme 0128-2021-0003.

Original russian text

Original Russian Text © V. G. Gnevyshev, T. V. Belonenko, 2022, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 38, Iss. 6, pp. 585-604 (2022)

For citation

Gnevyshev, V.G. and Belonenko, T.V., 2022. Anomalous Behavior of the Vertical Structure Rossby Waves on Non-Zonal Shear Flow in the Vicinity of the Focus. Physical Oceanography, 29(6), pp. 567-586. doi:10.22449/1573-160X-2022-6-567-586

DOI

10.22449/1573-160X-2022-6-567-586

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