On regularizing the strongly nonlinear model for two-dimensional internal waves

Ricardo Barros, Wooyoung Choi

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

To study the evolution of two-dimensional large amplitude internal waves in a two-layer system with variable bottom topography, a new asymptotic model is derived. The model can be obtained from the original Euler equations for weakly rotational flows under the long-wave approximation, without making any smallness assumption on the wave amplitude, and it is asymptotically equivalent to the strongly nonlinear model proposed by Choi and Camassa (1999) [3]. This new set of equations extends the regularized model for one-dimensional waves proposed by Choi et al. (2009) [30], known to be free from shear instability for a wide range of physical parameters. The two-dimensional generalization exhibits new terms in the equations, related to rotational effects of the flow, and possesses a conservation law for the vertical vorticity. Furthermore, it is proved that if this vorticity is initially zero everywhere in space, then it will remain so for all time. This property-in clear contrast with the original strongly nonlinear model formulated in terms of depth-averaged velocity fields-allows us to simplify the model by focusing on the case when the velocity fields involved by large amplitude waves are irrotational. Weakly two-dimensional and weakly nonlinear limits are then discussed. Finally, after investigating the shear stability of the regularized model for flat bottom, the effect of slowly-varying bottom topography is included in the model.

Original languageEnglish (US)
Pages (from-to)27-34
Number of pages8
JournalPhysica D: Nonlinear Phenomena
Volume264
DOIs
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Keywords

  • Internal waves
  • Regularization
  • Strongly nonlinear model

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