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Rogue waves in baroclinic flows

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Abstract

We investigate an AB system, which can be used to describe marginally unstable baroclinic wave packets in a geophysical fluid. Using the generalized Darboux transformation, we obtain higher-order rogue wave solutions and analyze rogue wave propagation and interaction. We obtain bright rogue waves with one and two peaks. For the wave packet amplitude and the mean-flow correction resulting from the self-rectification of the nonlinear wave, the positions and values of the wave crests and troughs are expressed in terms of a parameter describing the state of the basic flow, in terms of a parameter responsible for the interaction of the wave packet and the mean flow, and in terms of the group velocity. We show that the interaction of the wave packet and mean flow and also the group velocity affect the propagation and interaction of the amplitude of the wave packet and the self-rectification of the nonlinear wave.

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Authors and Affiliations

  1. Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing, China

    Da-Wei Zuo, Yi-Tian Gao, Yu-Jie Feng, Long Xue & Yu-Hao Sun

  2. Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, China

    Da-Wei Zuo

Authors
  1. Da-Wei Zuo
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  2. Yi-Tian Gao
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  3. Yu-Jie Feng
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  4. Long Xue
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  5. Yu-Hao Sun
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Correspondence to Da-Wei Zuo.

Additional information

This research was supported by the National Natural Science Foundation of China (Grant No. 11272023), the Open Fund of State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications (Grant No. IPOC2013B008), and the Foundation of Hebei Education Department of China (Grant No. QN2015051).

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 191, No. 2, pp. 291–303, May, 2017.

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Zuo, DW., Gao, YT., Feng, YJ. et al. Rogue waves in baroclinic flows. Theor Math Phys 191, 725–737 (2017). https://doi.org/10.1134/S0040577917050129

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  • DOI: https://doi.org/10.1134/S0040577917050129

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