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Wind-wave growth in the laboratory studies

Wind-wave growth in the laboratory studies. S. I. Badulin (1) and G. Caulliez ( 2 ) (1) P.P. Shirshov Institute of Oceanology, Moscow, Russia (2) Institut de Recherche sur les Phénomènes Hors Equilibre, Marseille, France. carriage. laser sheet. laser slope gauge. HR or fast-speed

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Wind-wave growth in the laboratory studies

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  1. Wind-wave growth in the laboratory studies S. I. Badulin(1) and G. Caulliez (2) (1) P.P. Shirshov Institute of Oceanology, Moscow, Russia (2)Institut de Recherche sur les Phénomènes Hors Equilibre, Marseille, France

  2. carriage laser sheet laser slope gauge HR or fast-speed video cameras X wavemaker The large IRPHE-Luminy wind-wave tank water tank: L= 40 m, l = 2.6 m, d = 0.9 m air tunnel: L= 40 m, l = 3.2 m, h = 1.5 m U10  2.5 to 17 m/s • Experimental conditions • various fetches ranging from 2 to 26.5 m: X = 2, 4, 6, 9, 13, 18, 26 m • various wind speeds Uref ranging from 2.5 m/s to 13 m/s: U10 2.5 to 17 m/s

  3. A crazy question • Can we reproduce wind-sea growth in the wind-wave tank?

  4. A regular answer • NO

  5. The tiny IRPHE-Luminy wind-wave tank • Problems • Scales • Capillarity • Drift currents • Air flow • etc Length = O(102) wavelengths Width = O(10) wavelengths Height = O(10) wavelengths Depth = O(10) wavelengths

  6. A. We certainly cannot model growth of wind-driven seas in wind-wave channels

  7. WhyWave growth in wave tanks is consistent both qualitatively and quantitatively with wave growth in open sea? Ex.: The Toba 3/2 law (Toba, 1972, 1973) Hs=B(gu*)1/2Ts3/2 B=0.061 May be it is just happy chance when formally invalid tool works well

  8. Try to answer within the statistical approach(formally invalid) The kinetic equation for wind-driven seas (the Hasselmann equation) • Nonlinear transfer is described from `the first principles’ • External forcing is parameterized by empirical formulas

  9. Try to answer within the weakly turbulent self-similar wave growth law (Badulin et al., 2007) The split balance of wind-driven seas Hyp.Nonlinear transfer dominates over wind input and dissipation • Conservative Hasselmann equation assures universality (self-similarity) of nonlinear transfer • External forcing (spectral fluxes) controls evolution as total quantities. Details of the forcing are of no importance

  10. Self-similar solutions dictates Kolmogorov-like wave-growth law Badulin, Babanin, Resio & Zakharov, JFM, 2007 e - Total energy wp - peak frequency ass - self-similarity parameter • Integral net wave input is rigidly linked to instantaneous wave parameters: characteristic wave energy and wave frequency; • Dependencies of sea wave growth of field experiments are consistent with the law

  11. Measurements were carried out in the Large IRPHE-Luminy wind-wave channel in 2006with no reference to the problem of growth of wind-driven seas • Experimental conditions • various fetches ranging from 2 to 26.5 m: • X = 2, 4, 6, 9, 13, 18, 26 m • various wind speeds Uref ranging from • 2.5 m/s to 13 m/s: U10 2.5 to 17 m/s Tools: wave capacity probes, laser slope gauge

  12. Our data cover wider range of conditions (cf. Toba, 1972`Traditional’ wave speed scaling gives high dispersion(good in logaritmic axes only) Blue stars – data by Toba (1972) New approach – new knowledge ?

  13. Weakly turbulent scaling (energy-to-flux)Not so bad if locally measured frequency is used(perfect! Axes are linear!) Ewp4/g2=Steepness2 ass=0.5

  14. Problems of the new presentation: derivatives and instantaneous quantities (wave heights and frequencies) total mean square slope dominant wavelength X = 6 m: ld 30 cm X = 13 m: ld 45 cm X = 26 m: ld 80 cm E* w4/g2 = mssd DE/DX w2/2g = D(A.AK)/2DX Capillary and drift effects are included , i.e taken into account in mssd Below ld 30 cm, gravity-capillary and capillary- gravity waves: action of T/r and shear drift effects

  15. Better than perfect ! ass=0.5 <ak>2=Steepness2 Rate of energy=(d(a2k2)/dt/(2wp))1/3

  16. We are the best ! Concl.:We showed consistency of the wind-channel data and the weakly turbulent law (Badulin et al., 2007) The talk is over (?) No, it is just the very begining

  17. Try to estimate net wave input and scale it in physically consistent wayThe weakly turbulent Kolmogorov-like law gives us a chance

  18. Very preliminary results: Wave input vs u* or vs Cp (Air flow vs wave dynamics) <de/dt> ~ e3w9 !!! Different symbols are used for different wind speeds Scaling in wave phase speed looks more attractive

  19. The well-known Toba’s law as a particular case of weakly turbulent wind-wave growth Let One can estimate energy production from instantaneous Hs, Ts

  20. Very preliminary results Wave input normalized by the Toba input vs Cp The scaling is relevant to constant in time production of wave energy

  21. The less-known Hasselmann, Ross, Muller & Sell, 1976(“Special solutions” for a parametric wave model) - total wave momentum Let See also Resio, Long, Vincent, JGR 2004 Get

  22. Very preliminary results Wave input for scaling Resio et al. 2004 Relevant to constant in time production of wave momentum

  23. Summary • Wind-wave tank data (Toba 1973, Caulliez 2006) are consistent with weakly turbulent scaling – Kolmogorov’s energy-to-flux rigid link • The weakly turbulent approach and the new data allow one • to identifyqualitatively different physical regimesof wave growth; • to describe quantitatively wind-wave interaction

  24. Summary Wind-wave tanks can give us real physics at unreal conditions Marseille, 07/01/2009

  25. Welcome to Marseille !

  26. Motivation • “Witha wider perspective and in the long term, we need the wild horse that comes out with unconventional ideas…” L. Cavaleri et al. / Progress in oceanography,75 (2007) 603–674

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