On the modulation instability of the shallow wake flows via a higher-order extended Ginzburg–Landau model

Na Liu, Chaoyue Qu, Quansheng Liu and Ruigang Zhang

Chaos, Solitons & Fractals, 2026, vol. 208, issue P4

Abstract: This paper focuses on the modulation instability and nonlinear evolution of shallow wake flows. Under the f-plane approximation, starting from the two-dimensional viscous shallow water equations, a higher-order extended Ginzburg–Landau equation is derived using the multi-scale expansion method. This equation retains the effects of weak viscosity, bottom friction, and higher-order nonlinear coupling on the evolution of the wake flow envelope, thereby providing a theoretical basis for revealing the formation mechanism and evolution process of the fluid structure behind obstacles in real oceans or lakes. Subsequently, the equation is solved using the finite difference method combined with a semi-implicit time stepping. Further, based on the continuous wave background, the dispersion relation and gain spectrum of the modulation instability are obtained. The results show that the system exhibits a typical symmetric double-peak gain structure, where the stability parameter S serves as a key role for the gain peak and unstable bandwidth. Additionally, the evolution of the stream function is mainly governed by the stability parameter S and the velocity ratio R. As the stability parameter increases, the flow field structure gradually evolves from weak stripe-like wave trains to localized wave packets near the wake center, thereby promoting the formation of vortex pairs.

Keywords: Shallow wake flows; Ginzburg–Landau equation; Modulation instability; Stability parameter (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077926005291
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:208:y:2026:i:p4:s0960077926005291

DOI: 10.1016/j.chaos.2026.118388

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().