On the consequences of nonlinearity and gravity-capillary waves on wind-wave interaction

In this paper we would like to revisit the problem of the interaction of wind and waves with emphasis on strong winds. For these extreme events it is assumed that nonlinearity is so large that the slope of the wind waves has reached a limiting steepness. This limitation has been implemented in the the WAM model version at ECMWF (called ecWAM, ECMWF 2020) and has resulted in a reduced increase of the drag coefficient with wind speed in the range of large wind speed.

However, observations suggest that the drag may even decrease with increasing wind speed and here it is pointed out that in the original approach (Janssen, 1989) the assumption was made that the dimensionless background roughness gz_b/u²_∗ associated with the growth of gravity-capillary waves is a constant. Using the VIERS model an explicit calculation of the background roughness length can be made and for relatively mild winds and fairly old windsea this assumption is valid, but for young, steep windsea it is shown that the background roughness length almost vanishes. As a consequence, for strong winds having young windseas, the drag over wind waves is much reduced.

In addition, there is a strong interaction between the wind and waves. The slowing down of the wind is a nonlinear process, because it depends on the wave spectrum itself. Therefore, the growthrate of the waves by wind depends on the wave spectrum, and following work by Miles (1965) it is straightforward to obtain the sea state dependence of the growthrate. For strong winds it is found that, since the waves are typically steep, this nonlinear effect gives a further reduction of the wind input. As a consequence, in  these extreme circumstances the drag coefficient may decrease with increasing wind.