NONLINEAR GRAVITY AND CAPILLARY-GRAVITY WAVES

TLDR

This review surveys the bifurcation, stability, and evolution of gravity and capillary‑gravity waves, including recent findings on two‑dimensional solitary waves at the minimum of the dispersion curve and short‑crested waves. The authors aim to survey mechanisms explaining frequency downshift and to examine the influence of surface tension on steep waves. They review recent mechanisms for frequency downshift and analyze surface‑tension effects on steep waves. Recent results highlight horseshoe patterns—three‑dimensional structures observed on the sea surface under wind or in wave‑tank experiments.

Abstract

▪ Abstract This review deals primarily with the bifurcation, stability, and evolution of gravity and capillary-gravity waves. Recent results on the bifurcation of various types of capillary-gravity waves, including two-dimensional solitary waves at the minimum of the dispersion curve, are reviewed. A survey of various mechanisms (including the most recent ones) to explain the frequency downshift phenomenon is provided. Recent significant results are given on “horseshoe” patterns, which are three-dimensional structures observable on the sea surface under the action of wind or in wave tank experiments. The so-called short-crested waves are then discussed. Finally, the importance of surface tension effects on steep waves is studied.