1 Wavelength Scaling of Ocean Surface Friction Coefficient in Wind Sea and Mixed Sea Paul A. Hwang Remote 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 similarity relation of the ocean surface friction coefficient: (wink) (wink) reference wind velocity Comparison with field data Wind sea Mixed sea

3 Schlichting, 1955~68+ [1951] 100 Smooth pipe Rough pipe Hagen-Poiseuille Blasius 1913 Prandtl Nikuradse 1929 Rough plate 1000C f Smooth plate Prandtl/Schlichting 1934 Schultz-Grunow 1940 Law of friction and velocity distribution

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.

Law of friction and velocity distribution 5 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.

A c =  10  2, a c = Wavelength range D  [3.3, 5.7] M  [8.6, 19.0] A  [28.6, 75.8] J [56.4, 101.6] 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 ) Steady wind No swell k p available Q=0.95Q=0.74 Hwang 2004

Hwang 2005

Comparison of calculated C 10 using wavelength scaling similarity with measurements. Once the similarity relation is found, it is easy to compute C 10 for practical application.

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

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

11 (0.142, 0.932) (0.178, 0.800) (0.192, 0.598) (rms, R 2 ) Equivalent momentum weighting 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.

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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

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19 A c =  10  2, a c = Hwang 2006

20 Friction coefficient of the ocean sea surface: dimensionally consistent similarity relation 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: /2011JPO (in press).

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

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

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25 Mature Young

Phillips 1985 Felizardo and Melville 1995 Hanson and Phillips

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