The air-sea interface under tropical cyclone conditions

In this paper, we further develop the hypothesis formulated by Soloviev and Lukas (2010) that the change of the air-sea interaction regime in hurricane conditions is associated with the mechanism of direct disruption of the air-sea interface by pressure fluctuations working against surface tension forces. This can be achieved through the Kelvin-Helmholtz (KH) instability of the interface. In addition, the Tollmien-Schlichting (TS) instability of viscous sublayers from the air and/or water side is potentially another important process taking place at the air-sea interface under hurricane conditions. Similar processes take place at the atomization of liquid fuels in cryogenic and diesel engines (Yecko et al., 2002). Under hurricane conditions, such instabilities initiate the tearing of short wavelet crests, ejection of spume, and smoothing of the sea surface, which reduces the drag coefficient at the air-sea interface, an effect observed in the field and laboratory experiments (Powell et al., 2003; Donelan et al., 2004; Black et al., 2007; Troitskaya et al., 2010).

     Observations of the air-sea interface in hurricane conditions are difficult and data are very limited (Powell et al., 2003; Black et al., 2007). In order to investigate the mechanism of the breakup of the air-sea interface and dynamics of the two-phase transition layer, we have conducted a series of numerical experiments using the volume of fluid multiphase computational fluid dynamics model, which allowed us to simulate the air-sea interface including surface tension at the water surface. The large eddy simulation Wall-Adapting Local Eddy-Viscosity turbulence model (Nicoud and Ducros, 1999) was used for all numerical experiments.

     For the case shown in Figure 1, the wind stress is 4 N m^-2. The wind stress was applied at the upper boundary of the air layer. The disruption of the air-water interface resembles an ‘explosive' type of instability. The formation of a two-phase environment, as a result of the interface disruption, was observed before any significant waves could be generated by wind.

Figure 1. The numerical experiment with an initially flat interface illustrates the possibility of the direct disruption of the air-water interface and formation of the two-phase environment under hurricane force wind.

     The numerical experiments with imposed short wavelets demonstrated the tearing of wave crests, ejection of spume into the air and smoothing of the water surface in the direction of the air flow (Figure 2).

Figure 2. Numerical experiment with imposed short waves demonstrates the tearing of wave crests, formation of water sheets and spume ejection into the air.

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Figure 3 shows a different view on the surface (from the bottom), which reveals intermittent streamwise structures with periodicity in the transverse direction on the top of wavelets, presumably a result of the TS instability. According to McNaughton and Brunet (2002), the nonlinear stage of the TS instability results in streamwise streaks followed by fluid ejections.  This mechanism can contribute to the generation of spume in the form of streaks. Foam streaks are an observable feature on photographic images of the ocean surface under hurricane conditions (see, e.g., Black et al., 2006).

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Figure 3. View on the air-water surface to demonstrate quasi-periodic structures in the transverse direction on the top of wave crests.

Based on the results of numerical simulations, we have provided an improved estimate of the lower limit on the drag coefficient under hurricane conditions. This limit is associated with the presence of two-phase transition layer and is appreciably lower than the wave resistance law; though, it was gradually increasing with wind speed (Soloviev et al., 2011). This study can help in developing a framework for combining the effects of the two-phase environment with the contribution to the drag from waves.

Acknowledgements

The authors are grateful to Roger Lukas (UH), Isaac Ginis and Tetsu Hara (URI), Shuyi Chen, Brian Haus, and Mark Donelan (UM RSMAS), and Vladimir Kudryavtsev (NERSC) for important discussions of the problem. We thank Mikhail Gilman (NCSU) for help with numerical modeling. We acknowledge support from the NSUOC project “Hydrodynamics and remote sensing of far wakes of ships” and the NOPP project “Advanced coupled atmosphere-wave-ocean modeling for improving tropical cyclone prediction models” (PIs: Isaac Ginis and Shuyi Chen) via NSUOC subcontract to URI.