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 H m0 T p, T 02 … θ p, θ m … γ (shape)...??? …  Not relevant if more than 1 peak in the spectrum Individual components ‘i’ (swells, wind-sea)  i, H m0,i T p,i, T 02,i … θ p,i, θ m,i … γ i …  More relevant physically (simulations, design…) Simple methodology

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

6. Partitions grouping:  Partitions with f p > f s  PARTITION 1 = WIND-SEA  Partitions with f p = H min  PARTITION = SWELL j  Partitions with f p <= f s & H m0 < H min  GROUPED WITH SWELL WITH CLOSEST f p Fitting of analytical shapes (least-squares minimisation)  JONSWAP for S j (f) (∫partition_j(f,θ) dθ) [Hasselmann et al., 1973]  Cos^2s for D j (θ) (∫partition_j(f,θ) df) [e.g. Mitsuyasu et al., 1975] Set of parameters for each identified wave system JONSWAP Cos^2s STEP 2 STEP 3 fs = separation frequency  P partitions identified (1 wind-sea + (P-1) swells)

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

8. Goodness-of-fit estimator: Correction of mutual influences [Kerbiriou et al., 2007]  Correction of H m0,j so as to minimise the area difference of the total reconstructed density S(f) with target Ŝ(f) STEP 4 e ~ 25%

9. - II - SEM-REV WAVE DATA

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

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

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

14. - III - RESULTS AND DISCUSSION

15. Processing of SEM-REV 2011 hourly dir. spectra  Separation frequency swell/wind-sea: Interpolated (1h) ECMWF ERA-Interim 10m-height wind speed for location (4.75°N, 3.0°W) close to SEM-REV In practice here: f s = min(g/2πβU 10, 0.20Hz)  Min. threshold for swell partition grouping : Hmin = 0.20m

17. 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 e mean = 17,7% (95% | e ≤ 30%) Algorithm performance

18. /8748 Sea states may be considered as unimodal only 25% to 64% of time! (according to threshold) Sea states type in SEM-REV (2011) for different H m0 thresholds (i.e., wave systems with H m0 lower than this value are disregarded in the counting)

19. [0.04;0.08Hz[[0.08;0.12Hz[[0.12;0.15Hz[[0.15;0.20Hz[[0.20;0.50Hz[ f SWELLSWIND-SEAS ? H m0,i > 0,5m H m0,i > 1m H m0,i > 3m Peakedness statistics (γ < 10, -3%) no data

20. Again, statistics vary according to H m0 threshold Mean peakedness values found within [1;2] (except HF) Values range from 1 to 5 mostly, even for swells In ]0.04; 0.12Hz] (swells) γ decreases with fp on average  consistent with theory of swell evolution [e.g. Gjevik et al., 1988] Above 0.15Hz γ (wind-seas) increases with fp on average  consistent with JONSWAP observations as peakedness decreases during sea growth [Hasselmann et al., 1973] [5% bias to be deducted from γ here approx. due to sampling variability in the spectral estimation with 72 dof (see paper OMAE2013-10004, same author)]

21. Peakedness in severe sea states  fatigue, survivability, certifications… Severe sea state: H m0 > 3m (> 8m Joachim storm in December 2011) Regression line: γ (biased) against H m0 for H m0 > 3m (100% sea states are unimodal)  More data required Storms with low f p within ]0.04Hz;0.12Hz]

22. - IV - CONCLUSIONS & FURTHER WORKS

23. On average, JONSWAP peakedness γ decreases and increases with peak frequency within [1;2] – from swell to wind-sea frequency range (most values within [~1;5] for both) Partitioning algorithm successful: In SEM-REV in 2011, sea states could be considered as unimodal 64% of time at best  partitioning required for metocean and engineering studies Further work 1: JONSWAPs adapted to the spectral modelling of swells?... (preliminary results available now) Further work 2: dynamic tracking of wave systems for better system type identification

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

25. IntervalH m0 min 0.2m0.5m1m3m 0.04-0.08Hz9.2%7.0%3.9%0.2% 0.08-0.12Hz29.6%21.6%10.0%0.6% 0.12-0.15Hz10.5%7.1%4.8%<0.1% 0.15-0.20Hz8.5%6.0%9.9%0 0.20-0.30Hz16.5%10.1%1.1%0 0.30-0.50Hz15.4%2.3%00 0.20-0.50Hz31.9%12.4%1.1%0

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