Vortex Layer on the β-Plane in the Miles – Ribner Formulation. Pole on the Real Axis

V. V. Zhmur1, 2, 3, V. S. Travkin1, ✉, T. V. Belonenko1, D. A. Arutyunyan3

1 St. Petersburg State University, Saint Petersburg, Russian Federation

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

3 Moscow Institute of Physics and Technology, Moscow, Russian Federation

✉ e-mail: vtravkin99@gmail.com

Abstract

Purpose. The process of a mesoscale vortex stretching is called elongation so that its longitudinal scale becomes larger than the transverse one. The work is aimed at studying the energy transformation of a vortex that changes its shape by stretching during evolution, and also at verifying the theory by comparing the results with the estimates obtained from the field data.

Methods and Results. It is revealed theoretically that a vortex stretching is accompanied by a decrease in its kinetic and potential energy. It is shown that when a vortex is deformed by a barotropic flow, the vertical semi-axis, the product of the horizontal semi-axes, and, agreeably, the effective radius does not change. The vortex which initially had a round shape in the horizontal plane, in the process of its evolution on April 4–24, 2012 was noted to be stretched in such a way that by the end of the deformation period, its longitudinal scale became 4 times longer than the transverse one. At that, the effective radius changes insignificantly, and its values at the beginning and at the end of the vortex life cycle are close in magnitude. An increase in the vortex compression parameter is found to be related to an increase in the Väisälä-Brunt frequency. The change in the vortex energy during its transformation is analyzed depending both on the parameters characterizing the vortex shape, and on the Väisälä-Brunt frequency. The theoretical conclusions were verified using the mesoscale vortex located in the Lofoten basin (the Norwegian Sea) on April 4–24, 2012. The kinetic and potential energy was analyzed using the data of oceanic reanalysis GLORYS12V1.

Conclusions. It is shown that, in general, the vortex potential energy exceeds its kinetic one by 1.5 times. When the vortex is elongated, its kinetic energy decreases by 3 times, and its potential energy – on average by 1.7 times. The vortex’s total energy has decreased by 2.3 times. The coefficient estimates of relative attenuation of different types of vortex energy inferred from GLORYS12V1, qualitatively confirm the theoretical conclusions. Some discrepancies in the quantitative estimates can be conditioned by inaccuracy in practical determining the vortex scales derived from the in-situ data.

Keywords

mesoscale vortex, kinetic and potential energy, kinetic energy, potential energy, vortex, Lofoten vortex, vortex elongation, oblateness parameter, GLORYS12V1, Lofoten basin

Acknowledgements

The work was carried out with financial support of the Russian Science Foundation, grant No. 22-27-00004, and within the framework of the state assignment of IO RAS on theme No. 0128-2021-0002.

Original russian text

Original Russian Text © The Authors, 2022, published in MORSKOY GIDROFIZICHESKIY ZHURNAL, Vol. 38, Iss. 5, pp. 466–480 (2022)

For citation

Zhmur, V.V., Travkin, V.S., Belonenko, T.V. and Arutyunyan, D.A., 2022. Transformation of Kinetic and Potential Energy during Elongation of a Mesoscale Vortex. Physical Oceanography, 29(5), pp. 449-462. doi:10.22449/1573-160X-2022-5-449-462

DOI

10.22449/1573-160X-2022-5-449-462

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