Interactions between Wind and Water Waves near Circular Flows

2025/08/01 by Changfeng Gui, Gui, Changfeng, Liu, Sicheng
Earth and Planetary Sciences · Mathematics · #35Q35 #76E07 #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.2508.00444

openalex publication_date 2025/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This manuscript concerns the dynamical interactions between wind and water waves, which are characterized through two-phase free interface problems for the Euler equations. We provide a comprehensive derivation on the linearized problems of general two-phase flows. Then, we study the instability issues of perturbing waves around circular steady solutions, and we demonstrate a semi-circle result on the possible locations of unstable modes. We also present necessary conditions and sufficient ones for the instability of wind-perturbing water waves near Taylor-Couette flows.

Citations

• Local Well-posedness of the Incompressible Current-Vortex Sheet Problems
• On the spectra of the gravity water waves linearized at monotone shear flows
• Instability and spectrum of the linearized two-phase fluids interface problem at shear flows
• Capillary gravity water waves linearized at monotone shear flows: eigenvalues and inviscid damping
• Stability of Vortices in Ideal Fluids : the Legacy of Kelvin and\n Rayleigh
• On circular flows: linear stability and damping
• Unstable surface waves in running water

Related

• Steady water waves in the presence of wind
• Mathematics for 2d Interfaces
• Two-phase flow simulations of surface waves in wind-forced conditions
• A non-equilibrium system in a steady state: wind waves in the open ocean
• Mechanistic, empirical and numerical perspectives on wind-waves\n interaction