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21 Jan 2022
21 Jan 2022
Status: this preprint is currently under review for the journal NPG.

Effects of Rotation and Topography on Internal Solitary Waves Governed by the Rotating-Gardner Equation

Karl Helfrich1, and Lev Ostrovsky2, Karl Helfrich and Lev Ostrovsky
  • 1Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA USA
  • 2University of Colorado Boulder, Boulder, Colorado, and University of North Carolina at Chapel Hill, Chapel Hill, NC USA
  • The authors contributed equally to this work.

Abstract. Nonlinear oceanic internal solitary waves are considered under the influence of the combined effects of saturating nonlinearity, the earth's rotation, and horizontal depth inhomogeneity. Here the basic model is the extended Korteweg-de Vries equation that includes both quadratic and cubic nonlinearity (the Gardner equation) with additional terms incorporating slowly varying depth and weak rotation. The complicated interplay between these different factors is explored using an approximate adiabatic approach and then through numerical solutions of the governing variable-depth, rotating Gardner model. These results are also compared to analysis in the Korteweg-de Vries limit to highlight the effect of the cubic nonlinearity. The study explores several particular cases considered in the literature that included some of these factors to illustrate limitations. Solutions are made to illustrate the relevance of this extended Gardner model for realistic oceanic conditions.

Karl Helfrich and Lev Ostrovsky

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on npg-2022-3', Anonymous Referee #1, 10 Mar 2022
    • AC1: 'Reply on RC1', Lev Ostrovsky, 05 Apr 2022
    • AC2: 'Reply on RC1', Lev Ostrovsky, 05 Apr 2022
  • RC2: 'Comment on npg-2022-3', Anonymous Referee #2, 21 Mar 2022

Karl Helfrich and Lev Ostrovsky

Karl Helfrich and Lev Ostrovsky


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Short summary
This paper studies internal solitary waves (ISWs) in the ocean under simultaneous action of the main defining factors: nonlinearity (quadratic and cubic), earth rotation, and depth variation. Both analytical (adiabatic) theory and numerical simulation are used in the study. The results show a complex interplay of the factors mentioned above that can result in amplification of the ISW or, on the contrary, its destruction. The calculations are made for realistic oceanic parameters.