Preprints
https://doi.org/10.5194/os-2022-5
https://doi.org/10.5194/os-2022-5
 
08 Feb 2022
08 Feb 2022
Status: this preprint has been withdrawn by the authors.

Analytical solution of the ray equations of Hamilton for Rossby waves on stationary shear flows

Vladimir Gnevyshev1 and Tatyana Belonenko2 Vladimir Gnevyshev and Tatyana Belonenko
  • 1Shirshov Institute of Oceanology Russian Academy of Science, 117997, Nakhimovskiy pr., 36, Moscow, Russia
  • 2St. Petersburg State University, 199034, Universitetskaya emb., 7-9, St. Petersburg, Russia

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. On the example of Rossby waves on a shear flow, the ray equations of Hamilton are analytically integrated. 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.

This preprint has been withdrawn.

Vladimir Gnevyshev and Tatyana Belonenko

Interactive discussion

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on os-2022-5', Anonymous Referee #1, 03 Mar 2022
    • AC1: 'Reply on RC1', Tatyana Belonenko, 10 Mar 2022
  • RC2: 'Comment on os-2022-5', Anonymous Referee #2, 05 Mar 2022
    • CC1: 'Reply on RC2', Tatyana Belonenko, 10 Mar 2022
    • AC4: 'Reply on RC2', Tatyana Belonenko, 06 Apr 2022
  • RC3: 'Comment on os-2022-5', Anonymous Referee #3, 12 Mar 2022
    • AC2: 'Reply on RC3', Tatyana Belonenko, 12 Mar 2022
      • RC4: 'Reply on AC2', Anonymous Referee #3, 12 Mar 2022
        • AC3: 'Reply on RC4', Tatyana Belonenko, 14 Mar 2022

Interactive discussion

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on os-2022-5', Anonymous Referee #1, 03 Mar 2022
    • AC1: 'Reply on RC1', Tatyana Belonenko, 10 Mar 2022
  • RC2: 'Comment on os-2022-5', Anonymous Referee #2, 05 Mar 2022
    • CC1: 'Reply on RC2', Tatyana Belonenko, 10 Mar 2022
    • AC4: 'Reply on RC2', Tatyana Belonenko, 06 Apr 2022
  • RC3: 'Comment on os-2022-5', Anonymous Referee #3, 12 Mar 2022
    • AC2: 'Reply on RC3', Tatyana Belonenko, 12 Mar 2022
      • RC4: 'Reply on AC2', Anonymous Referee #3, 12 Mar 2022
        • AC3: 'Reply on RC4', Tatyana Belonenko, 14 Mar 2022

Vladimir Gnevyshev and Tatyana Belonenko

Vladimir Gnevyshev and Tatyana Belonenko

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This preprint has been withdrawn.

Short summary
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. If only one critical layer arises for a zonal flow, then several critical layers can exist for a non-zonal.