Coupled dynamics of short waves and the airflow over long surface waves

Abstract

A study is presented of modulations induced by a dominant long surface wave (LW) in the coupled airflow–short wind‐generated waves (SW) system. The modulation of SWs in the gravity range results from their interaction with the LW orbital velocity and their interaction with the wind stress modulated by the LW. The modulation of waves in the capillary range is mainly due to the modulation of the rate of generation of parasitic capillaries by steep short gravity waves. The variation of the wind surface stress is described by the dynamics of the turbulent airflow over the LW with the surface roughness varying along its profile. The variation of the surface roughness is caused by the variation of the form drag supported by modulated SWs. In turn, the LW‐induced variation of the surface stress affects the SW modulation. This provides a feedback in the coupled airflow–SW system in the presence of the LW. The model results show that the amplitude of the surface roughness modulation can be large. In terms of the modulation transfer function (MTF), it can reach values of 10–20. The modulation of the form drag, which causes the modulation of the surface roughness, comes mainly from short breaking waves strongly modulated by dominant waves. The modulation of the surface roughness considerably affects the dynamics of the airflow over the LW and thus the LW wind growth rate. Models of the airflow above waves assuming a constant roughness parameter underestimate the growth rate parameter approximately two to three times as compared to the measured values. The present study shows that when the variation in the surface roughness is accounted for, the growth rate parameter increases roughly twice, which to a large extent reduces the discrepancy with measurements.