The Effects of Sea-Spray and Foam on Aerodynamic Resistance of Water Surface in Strong Winds

One of key problems of the air-sea coupling in extreme winds is the sea-surface drag saturation (and even reduction) at the wind speeds exceeding 30 m/s. This effect was observed in a number of field and lab experiments but remained insufficiently understood and poorly modeled. We explain it by the combined effect of the two phenomena inherent to strong winds: the spume droplets turn-off off the crest of waves, and the foam at water surface.

Experimental data for this study were obtained in two lab experiments. First, we used high-speed video filming of the near-water air flow to reveal that dominant mechanism of generation of spume droplets in very strong winds is the bag breakup fragmentation of the air-water interface. In view of this knowledge, we derive a new fetch-dependent spray-generation function (SGF), valid in both lab and field conditions. Then we quantify contributions from the bag-breakup mechanism to the air-sea momentum flux due to:

• resistance of "bags" just as obstacles (before their fragmentation),
• acceleration by wind of the droplets resulted from bag-fragmentation,
• stable stratification in the near-surface air flow caused by levitating droplets.

In the second experiment, we investigated the impact of foam on the short-wave part of surface waves and, further, on the momentum exchange at the air-sea interface.

Analyses of data reveal that the surface-drag coefficient essentially correlates with the foam coverage fraction and the mean square slope (m.s.s.) of surface waves. Indeed, at a certain wind speed, its further increase causes increasing foam coverage, thus suppressing short waves, their m.s.s. and, hence, aerodynamic roughness of the sea surface. Basing on these findings, we derive and validate empirically new physically grounded models of

• eddy-viscosity in airflow over water surface, accounting for the levitating droplets, and
• aerodynamic roughness of the sea surface accounting for suppression of waves by foam.

The models yield realistic non-monotonous dependence of the surface drag coefficient on the 10-m wind speed. This seemingly paradoxical dependence results from the interplay of the following effects of increasing wind:

• decreasing surface form-drag due to suppressing of waves by foam,
• increasing number of droplets and bags,
• decreasing sizes of droplets and bags.

We expect use of these results in modelling and forecasting hurricanes.

Acknowledgements: This work has been supported by RFBR (16-05-00839, 16-55-52025); experiments and equipment was also supported by RSF (14-17-00667, 15-17-20009); travel was partially supported by FP7 Collaborative Project No. 612610. SZ acknowledges support from the Academy of Finland projects ABBA No. 280700 (2014-2017) and ClimEco No. 314 798/799 (2018-2020)