The influence of atmospheric stratification on the growth of water waves

The atmospheric surface layer over sea has a density stratification which varies with moisture content and air/sea temperature difference. This influences the growth of water waves. To study the effect quantitatively, the Reynolds equations are solved numerically. For given wind speed and surface roughness, wave growth is found to be more rapid in unstably stratified conditions than in stable conditions. This is due to an increase in turbulence, primarily caused by an increase of mixing length. Under the assumption of a Charnock relation between surface roughness and friction velocity, it is found that for large inverse wave age (u sub(*)/c > 0.07), the effect of stratification on wave growth is well described by Monin-Obukhov scaling of the friction velocity. For smaller values of u sub(*)/c, Monin-Obukhov scaling overpredicts. The effect on duration-limited wave growth is studied with the third-generation WAM surface wave model driven by 10 m winds. Effects of stratification on the significant wave height are found to be of the order of 10%. The results are comparable to those of a recent reanalysis of field measurements, although the measured stratification effect is somewhat stronger. Implementation of a stratification-dependent growth in wave models is recommended, as it can lead to small but significant improvements in wave forecasts when accurate air and sea temperatures are available.