Momentum Flux at High Wind Speeds

1. Momentum Flux at High Wind Speeds Tetsu Hara, Isaac Ginis, Il-ju Moon, Tobias Kukulka Graduate School of Oceanography University of Rhode Island Stephen E. Belcher Department of Meteorology University of Reading, UK CBLAST-Hurricane Science Meeting April 4, 2005

2. Introduction • Present parameterizations of the wind stress (or drag coefficient) over the ocean is far from satisfactory. • Operational atmospheric (hurricane) models use a simple bulk parameterization (constant Charnock coefficient) :equivalent roughness length • One of the main uncertainties is the effect of ocean surface wave field (in particular, growing seas, confused seas). OBJECTIVE: Physics based parameterization of air-sea momentum flux (including surface wave effect)

3. Outline of the talk THIS TALK (Hara) • A new model of wave boundary layer • Drag coefficient over growing seas • Breaking wave effects NEXT TALK (Moon) • Drag coefficient over complex (hurricane) seas • Coupled hurricane-wave-ocean model

4. (1) A new model of wave boundary layer (no breaking effects)(Hara and Belcher, JPO, 2004) • We have developed a new model of the wave boundary layer based on momentum conservation and energy conservation, which obviates the need to use an eddy viscosity model. • We have obtained analytical expressions of the mean wind profile and the Charnock coefficient over mature seas, and examine the results in terms of key nondimensional parameters.

5. Conservation of momentum in the wave boundary layer Total stress = constant Turbulent stress Wave boundary layer Air-sea interface Wave stress

6. Conservation of energy in the wave boundary layer Viscous dissipation rate is parameterized in terms of the turbulent stress : (turbulence closure) Eddy viscosity is not needed

7. (2) Effect of Surface Waves on Air-Sea Momentum Flux over Growing Seas • Previous observations show that the drag coefficient strongly depends on the wave age . Here, is the phase speed of dominant waves (waves at the spectral peak.) • The dependence of the drag coefficient on the wave age is still controversial. • Recent observations show that the drag coefficient is much lower than the bulk estimate at very high winds under tropical cyclones (e.g., Powell et al. 2003). The reason is still unclear. • We extend our theoretical model to study the drag coefficient over growing and complex (hurricane) seas

8. Coupled wave-wind model -drag coefficient over growing and complex seas (Moon et al., JAS, 2004a) • Spectrum near the peak is simulated using the WAVEWATCH III model. • Unresolved high frequency part of the spectrum is estimated using the equilibrium spectrum model of Hara and Belcher (JFM 2002). • Wind profile and drag coefficient are calculated based on the wave boundary layer model of Hara and Belcher (JPO 2004). No breaking wave effects are included.

9. Growing Seas Wind speed Low wind Young seas Higher drag Mature seas High wind Young seas Lower drag  older (developed) seas

10. Growing Seas Older sea (WW3) Older sea (present model) Older sea

11. Why do young seas at high winds yield lower drag? Older sea Older sea Saturation Spectrum Wavenumber

12. (3) Breaking wave effect • Basic constraints of momentum conservation and energy conservation in the wave boundary layer are still valid. • Momentum conservation is modified by the breaking wave induced stress and the spatial sheltering due to breaking • Energy conservation is modified by the energy input into breaking waves

13. NEW: Wind-input to breakingwaves (flow separation) Pressure1 Pressure2 Spatial sheltering Pressure drop depends on wind speed!

14. Conservation of momentum in the wave boundary layer--------------- ------- Conservation of energy in the wave boundary layer

15. Progress to date: • We have obtained analytical results with breaking waves only (i.e., zero form drag on nonbreaking waves). • Our previous “no breaking wave” model and the new “breaking only” model can be considered as two extreme conditions. • The true results are likely to be somewhere between the two extreme results.

16. Toba et al., 1990 Data composite from Toba & Ebuchi, 1991 [Charnock coefficient] Data composite from Drennan et al., 2003 Drennan et al., 2003 Data from Donelan et al., 2004 (HIGH WIND) Younger sea Fully developed [Wave age]

17. [Charnock coefficient] No wave breaking Moon et al., 2004 Low wind High wind Younger sea Fully developed [Wave age]

18. Only wave breaking Beaking + nonbreaking? [Charnock coefficient] No wave breaking Moon et al., 2004 Low wind High wind Younger sea Fully developed [Wave age]

19. Conclusion • We have estimated the drag coefficient over mature and growing seas (Moon et al. 2004a) by combining the WAVEWATCH III, the equilibrium wave spectral model (Hara and Belcher, 2002), and the wave boundary layer model (Hara and Belcher, 2004). No breaking wave effects are included. • As the wave field develops (the wave age increases), the Charnock coefficient decreases at lower winds, being consistent with previous observations. But, the Charnock coefficient increases with wave age at higher winds (i.e., lower drag for young seas at high winds). • We have included the breaking wave effects in the model. So far we have obtained the Charnock coefficient with breaking waves only. More work is in progress.