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J-Baptiste SAULNIER Ecole Centrale de Nantes, LHEEA (France) Ile de Berder – 05/07/2013

Partitionnement de spectres et statistiques sur l’acuité (  ) des systèmes de vagues observés sur le site d’expérimentation EMR SEM-REV. J-Baptiste SAULNIER Ecole Centrale de Nantes, LHEEA (France) Ile de Berder – 05/07/2013 (Comm. OMAE2013-11470). Introduction.

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J-Baptiste SAULNIER Ecole Centrale de Nantes, LHEEA (France) Ile de Berder – 05/07/2013

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  1. Partitionnement de spectres et statistiques sur l’acuité () des systèmes de vagues observés sur le site d’expérimentation EMR SEM-REV J-Baptiste SAULNIER Ecole Centrale de Nantes, LHEEA (France) Ile de Berder – 05/07/2013 (Comm. OMAE2013-11470)

  2. Introduction • Marine Renewable Energy needs fine characterisation of environmental parameters, and sea state ones in particular (design, survivability, commissioning/decommissioning…) Wave spectra from in situ measurements (wave buoys, ADCPs…) • Statistics of Hs, Tp… and spectral peakedness (bandwidth/narrowness) required in particular for simulating extreme sea states (fatigue and survivability) using e.g. JONSWAP spectra  effect of wave groups • A sea state is the combination of several independent wave systems (swell(s) and wind-sea) Sea state partitioning for considering wave systems individually and the peakedness characterising each system

  3. - I - WAVE SYSTEM IDENTIFICATION AND MODELLING

  4. Goal Complex sea state Hm0 Tp, T02… θp, θm… γ (shape)...??? …  Not relevant if more than 1 peak in the spectrum Individual components ‘i’ (swells, wind-sea)  i, Hm0,i Tp,i, T02,i… θp,i, θm,i… γi … • More relevant physically(simulations, design…) Simple methodology

  5. STEP 1 SWELL Partitioning of the discrete spectral matrix Ŝ(fi,θj) (source: dir. wave buoy, ADCP, array of sensors… or numerical models) Simplified watershed technique [Hanson et Phillips, 2001] WIND-SEA Ŝ(f,θ) Watershed partitioning algorithm = path of steepest ascent technique (e.g. Hanson & Phillips, 2001) Bimodal directional spectrum estimated from buoy measurements (with smoothing)

  6. STEP 2 fs = separation frequency Partitions grouping: • Partitions withfp > fs PARTITION 1 = WIND-SEA • Partitions withfp <= fs & Hm0 >= Hmin PARTITION = SWELL j • Partitions withfp<= fs& Hm0<Hmin GROUPED WITH SWELL WITH CLOSEST fp Fitting of analyticalshapes (least-squares minimisation) • JONSWAP for Sj(f) (∫partition_j(f,θ) dθ) [Hasselmann et al., 1973] • Cos^2s for Dj (θ) (∫partition_j(f,θ) df) [e.g. Mitsuyasu et al., 1975]  P partitions identified (1 wind-sea + (P-1) swells) STEP 3 JONSWAP Set of parameters for each identified wave system Cos^2s

  7. Frequency fitting shapes… JONSWAP spectra (gamma = 1, 3.3, 7) Cos^2s function (s = 2, 10, 50) … Directional fitting shapes (not crucial here)

  8. STEP 4 Correction of mutual influences [Kerbiriou et al., 2007]  Correction of Hm0,j so as to minimise the area difference of the total reconstructed density S(f) with target Ŝ(f) e ~ 25% Goodness-of-fit estimator:

  9. - II - SEM-REV WAVE DATA

  10. SEM-REV location Nantes (50km) Loire estuary

  11. SEM-REV location BMTO2 E WAVE BUOY W WAVE BUOY ADCP

  12. Datawelldirectionalbuoy and spectral processing: • Measurements of {x,y,z} motions (continuous) • 1.28Hz sampling rate • HF radio transmission + onboardstorage • 1h-based signals for cross-spectral analysis • 36 non-overlapping 100s periodograms (72 dof) • Cos^2s directional reconstruction (based on 1st- and 2nd-order dir. Fourier coefficients) • Δf= 0.01Hz, Δθ = 10° • Spectral smoothing (3x3 cellmovingaverage)  8748 hourly directional spectra in 2011 (easternmost buoy) over 8760 expected (99.9% success rate)

  13. - III - RESULTS AND DISCUSSION

  14. Processing of SEM-REV 2011 hourlydir. spectra • Separationfrequencyswell/wind-sea: Interpolated (1h) ECMWF ERA-Interim10m-height wind speed for location (4.75°N, 3.0°W) close to SEM-REV In practice here: fs = min(g/2πβU10 , 0.20Hz) • Min. threshold for swell partition grouping : Hmin = 0.20m

  15. Time evolution of wave system parameters (~18600 systems extracted, ~2.1 syst./s.s.) No time tracking Correlation to ECMWF wind data (ERA-Interim) ECMWF wind data Algorithm performance emean= 17,7% (95% | e ≤ 30%)

  16. Sea states type in SEM-REV (2011) for different Hm0 thresholds (i.e., wave systems with Hm0 lower than this value are disregarded in the counting) /8748 Sea states may be considered as unimodal only 25% to 64% of time! (according to threshold)

  17. Peakedness statistics (γ < 10, -3%) f [0.04;0.08Hz[ [0.08;0.12Hz[ [0.12;0.15Hz[ [0.15;0.20Hz[ [0.20;0.50Hz[ Hm0,i > 0,5m Hm0,i > 1m no data no data Hm0,i > 3m ? SWELLS WIND-SEAS

  18. Again, statisticsvaryaccording to Hm0threshold • Meanpeakedness values foundwithin [1;2] (except HF)Values range from 1 to 5 mostly, even for swells • In ]0.04; 0.12Hz] (swells) γ decreaseswithfp on average • consistent withtheory of swellevolution[e.g. Gjeviket al., 1988] • Above 0.15Hz γ (wind-seas) increaseswithfp on average •  consistent with JONSWAP observations as peakednessdecreasesduringseagrowth[Hasselmannet al., 1973] • [5% bias to bedeductedfromγhereapprox. due to samplingvariability in the spectral estimation with 72 dof(seepaperOMAE2013-10004, sameauthor)]

  19. Peakedness in severe sea states  fatigue, survivability, certifications… Severe sea state: Hm0 > 3m (> 8m Joachim storm in December 2011) Regression line: γ (biased) against Hm0 for Hm0 > 3m (100% sea states are unimodal)  More data required Storms with low fp within ]0.04Hz;0.12Hz]

  20. - IV - CONCLUSIONS & FURTHER WORKS

  21. On average, JONSWAP peakednessγdecreases and increaseswithpeakfrequencywithin [1;2] – fromswell to wind-seafrequency range (most values within [~1;5] for both) • Partitioningalgorithmsuccessful: In SEM-REV in 2011, sea states couldbeconsidered as unimodal64% of time at best partitioningrequired for metocean and engineering studies • Furtherwork 1:JONSWAPsadapted to the spectral modelling of swells?... (preliminaryresultsavailablenow) • Furtherwork 2: dynamictracking of wavesystems for better system type identification

  22. Merci de votre attention Contact: jbsaulni@ec-nantes.fr (< août 2013) toupaixil@yahoo.fr (ensuite)

  23. SEM-REV location Le Croisic town Cable route SEM-REV Salt evaporation ponds of Guérande

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