Chin. Phys. B, 2022, Vol. 31(7): 070202    DOI: 10.1088/1674-1056/ac4e0a
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# Propagation and modulational instability of Rossby waves in stratified fluids

Xiao-Qian Yang(杨晓倩)1, En-Gui Fan(范恩贵)3, and Ning Zhang(张宁)1,2,†
1 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;
2 Department of Fundamental Course, Shandong University of Science and Technology, Tai'an 271019, China;
3 School of Mathematical Sciences, Fudan University, Shanghai 200433, China
Abstract  Perturbation analysis and scale expansion are used to derive the (2+1)-dimensional coupled nonlinear Schrödinger (CNLS) equations that can describe interactions of two Rossby waves propagating in stratified fluids. The (2+1)-dimensional equations can reflect and describe the wave propagation more intuitively and accurately. The properties of the two waves in the process of propagation can be analyzed by the solution obtained from the equations using the Hirota bilinear method, and the influence factors of modulational instability are analyzed. The results suggest that, when two Rossby waves with slightly different wave numbers propagate in the stratified fluids, the intensity of bright soliton decreases with the increases of dark soliton coefficients. In addition, the size of modulational instable area is related to the amplitude and wave number in y direction.
Keywords:  Rossby waves      Hirota bilinear method      modulational instability      stratified fluids
Received:  07 December 2021      Revised:  18 January 2022      Accepted manuscript online:  24 January 2022
 PACS: 02.30.Jr (Partial differential equations) 03.65.Ge (Solutions of wave equations: bound states)
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11805114) and the Shandong University of Science and Technology Research Fund (Grant No. 2018TDJH101).
Corresponding Authors:  Ning Zhang     E-mail:  zhangningsdust@126.com