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Rossby Waves on Non-zonal Flows: Vertical Focusing and Effect of the Current Stratification

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Abstract

This paper considers the interaction of Rossby waves with large-scale flows. We focus on the case of a non-zonal baroclinic plane-parallel flow with vertical shear. We develop short-wave asymptotics for linear waves in the vicinity of the critical layer. Vertical wave modes (eigenfunctions) of the corresponding boundary problem are presented in terms of Hermite polynomials. In addition to the classical case, when the wave modes are focused on the absolute minimum of the vertical profile of the baroclinic flow velocity, we show that there is another option when a mode is formed with focusing not on the minimum, but the absolute maximum of the vertical profile of the background flow velocity. The new option makes it possible to implement new dynamical regimes that are considered in the paper. We obtain a new criterion that limits the number of vertical modes and, thus, determines regimes of the mode localization in depth or its de-localization. Theoretical criteria of different regimes of Rossby wave dynamics in the non-zonal baroclinic are presented in terms of two dimensionless variables: B associated with "an effective \(\beta\) -parameter" and \(S=N^2/f^2\) (N is the Brunt–Väisälä frequency, and f is the Coriolis parameter). The analysis of experimental data shows the relevance of theoretically predicted effects.

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Funding

The work was funded by Russian Foundation for Basic Research #20-05-00066. Section 2 was supported by Russian Science Foundation Grant #19-72-30028 with the contribution of ITPMK Ltd, Moscow Russia. Section 3 was supported in the framework of the Shirshov Institute of Oceanology RAS state assignment N 0128-2021-0003.

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Author notes

  1. Sergei I. Badulin

    Present address: Center for Advanced Studies, Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, bld. 1, 121205, Moscow, Russia

Authors and Affiliations

  1. Shirshov Institute of Oceanology, Russian Academy of Sciences, 36, Nakhimovsky pr., 117997, Moscow, Russia

    Vladimir G. Gnevyshev & Sergei I. Badulin

  2. Saint Petersburg State University, 7, Universitetskaya Emb., 199034, St. Petersburg, Russia

    Aleksey V. Koldunov & Tatyana V. Belonenko

Authors
  1. Vladimir G. Gnevyshev
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  2. Sergei I. Badulin
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  3. Aleksey V. Koldunov
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  4. Tatyana V. Belonenko
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Contributions

VG presented the idea, performed theoretical analysis, and wrote the paper draft. SB checked the algebra, developed analysis of analytic results, and wrote the text. TB plotted figures and wrote and edited the manuscript. AK collected the data, proposed methods for data processing and treatment, and wrote and edited the text. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Sergei I. Badulin.

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Gnevyshev, V.G., Badulin, S.I., Koldunov, A.V. et al. Rossby Waves on Non-zonal Flows: Vertical Focusing and Effect of the Current Stratification. Pure Appl. Geophys. 178, 3247–3261 (2021). https://doi.org/10.1007/s00024-021-02799-8

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