This article is cited in 4 papers

Rogue waves in baroclinic flows

Da-Wei Zuo^ab, Yi-Tian Gao^a, Yu-Jie Feng^a, Long Xue^a, Yu-Hao Sun<sup>a

a</sup> Ministry of Education, Key Laboratory of Fluid Mechanics, Laboratory of Computational Fluid Mechanics, Beihang University, Beijing, China
^b Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, China

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.

Keywords: baroclinic flow, rogue wave, Darboux transformation.

PACS: 05.45.Yv, 47.35.Fg, 02.30.Jr

Received: 21.03.2016
Revised: 09.05.2016

DOI: 10.4213/tmf9192

 English version: Theoretical and Mathematical Physics, 2017, 191:2, 725–737

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