Propagation and modulational instability of Rossby waves in stratified fluids

doi:10.1088/1674-1056/ac4e0a

中国物理B ›› 2022, Vol. 31 ›› Issue (7): 70202-070202.doi: 10.1088/1674-1056/ac4e0a

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

收稿日期:2021-12-07 修回日期:2022-01-18 接受日期:2022-01-24 出版日期:2022-06-09 发布日期:2022-06-13
通讯作者: Ning Zhang E-mail:zhangningsdust@126.com
基金资助:
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).

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

Received:2021-12-07 Revised:2022-01-18 Accepted:2022-01-24 Online:2022-06-09 Published:2022-06-13
Contact: Ning Zhang E-mail:zhangningsdust@126.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: Rossby waves, Hirota bilinear method, modulational instability, stratified fluids

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.

Key words: Rossby waves, Hirota bilinear method, modulational instability, stratified fluids

中图分类号: (Partial differential equations)

02.30.Jr

03.65.Ge (Solutions of wave equations: bound states)

Xiao-Qian Yang(杨晓倩), En-Gui Fan(范恩贵), and Ning Zhang(张宁). Propagation and modulational instability of Rossby waves in stratified fluids[J]. 中国物理B, 2022, 31(7): 70202-070202.

Xiao-Qian Yang(杨晓倩), En-Gui Fan(范恩贵), and Ning Zhang(张宁). Propagation and modulational instability of Rossby waves in stratified fluids[J]. Chin. Phys. B, 2022, 31(7): 70202-070202.

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Propagation and modulational instability of Rossby waves in stratified fluids

Propagation and modulational instability of Rossby waves in stratified fluids

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