Wavelength Scaling of Ocean Surface Friction Coefficient in Wind Sea and Mixed Sea

1. Wavelength Scaling of Ocean Surface Friction Coefficient in Wind Sea and Mixed Sea Paul A. HwangRemote Sensing Division, Naval Research Laboratory Héctor García-Nava and Francisco J. Ocampo-Torres Departamento de Oceanografía Física, Centro de Investigación, Científica y de Educación Superior de Ensenada, Ensenada, Baja, California, México

2. Dimensionally consistent similarityrelation of the ocean surface friction coefficient: (wink) (wink) reference wind velocity Comparison with field data Wind sea Mixed sea

3. Law of friction and velocity distribution 100 1000Cf Prandtl 1933-35 Prandtl/Schlichting 1934 Hagen-Poiseuille 1839-40 Schultz-Grunow 1940 Blasius 1913 Smooth pipe Smooth plate Nikuradse 1929 Rough pipe Rough plate Schlichting, 1955~68+ [1951]

4. While in almost all branches of fluid mechanics, the drag coefficient is expresses in dimensionally consistent expressed of the flow/fluid properties, in air-sea interaction, the most common expression is a linear function of wind speed. It violates a basic cardinal rule of fluid dynamics: dimensional consistency.

5. Law of friction and velocity distribution Why 10? The main source of the problem may be the arbitrary reference wind speed (10 m), what’s needed is the free-stream velocity.

6. Ac = 1.220102, ac = 0.704 Wavelength range D  [3.3, 5.7] M  [8.6, 19.0] A  [28.6, 75.8] J  [56.4, 101.6] Steady wind No swell kpavailable Q=0.95 Q=0.74 Hwang 2004 The range of wavelengths/water depth: D: Donelan (1979) [3.3, 5.7]/12m (Lake Ontario) M: Merzi and Graf (1985) [8.6, 19.0]/3m (Lake Geneva) A: Anctil and Donelan (1996) [28.6, 75.8]/2/4/8/12m (Lake Ontario) J: Janssen (1997) [56.4, 101.6]/18m (HEXOS, North Sea MPN Dutch coast )

7. Hwang 2005

8. Comparison of calculated C10 using wavelength scaling similarity with measurements. Once the similarity relation is found, it is easy to compute C10 for practical application.

9. Geernaert et al. 1987 Dobson et al. 1994 Banner et al. 1999 Hwang 2005

10. Mixed sea: IntOA Experiment (García-Nava et al. 2009) Hwang, García-Nava, and Ocampo-Torres 2011 (JPO, in press)

11. Equivalent momentum weighting (rms, R2) (0.142, 0.932) (0.192, 0.598) (0.178, 0.800) 3 apparent choices of reference frequencies. Weighting by equivalent momentum consideration.

12. Works very well for mixed seas also.

13. Swell also contributes, a swell index is suggested.

15. The similarity relation of drag coefficient as a function of dimensionless frequency and swell index.

16. Now the similarity relation of drag coefficient can be applied to both wind sea and mixed sea.

17. Hwang 2006

19. Ac = 1.220102, ac = 0.704 Hwang 2006

20. Friction coefficient of the ocean sea surface: dimensionally consistent similarityrelation referenced to free stream reference wind velocity Wind sea Mixed sea U/2 is U Hwang, P. A., H. García-Nava, and F. J. Ocampo-Torres, 2011: Dimensionally consistent similarity relation of ocean surface friction coefficient in mixed seas. J. Phys. Oceanogr., doi: 10.1175/2011JPO4566.1 (in press).

21. Wave age dependence of the dynamic roughness (Charnock coefficient). Field data are from Toba et al. (1990). Solid curves is wavelength scaling. Both original and corrected versions of the Bass Strait data are shown. Hwang 2005

23. Burling 1959; Hasselmann et al. 1973; Donelan et al. 1985; Dobson et al. 1989; Babanin and Soloviev 1998 Hwang & Wang 2004 23

25. Mature Young

26. Phillips 1985 Felizardo and Melville 1995 Hanson and Phillips 1999