Recent developments in wave modelling with the Two-Scale Approximation implemented in WAVEWATCH-III Will Perrie 1, Bash Toulany 1, Don Resio 2, Chuck Long 3, Jean-Pierre Auclair 4 1. BIO, 2. UNF, 3. USACE, 4. Dalhousie 1 TSA background Outline Original and Modified TSA Fetch-limited growth and TSA characteristics Turning winds e.g. passing fronts, hurricanes Example of hurricane Juan (2003) Summary / Conclusions 2 1
Wave generation and growth a balance equation E( f, ) cg E( f, ) Sk( k, ) t where c g = group velocity S in S ds S nl = wind input = wave dissipation k = nonlinear transfer due to wave-wave interactions 3 S nl full Boltzmann Integral - FBI For the change in spectral action density at N 1 (e.g. at k 1 ) due to wave-wave interactions involving k 2, k 3 and k 4 ) - Hasselmann (1962), Zakharov (1966) TSA Two-Scale Approximation N i = N i [broad-scale] + N i [local-scale] Neglect N 2 [local-scale] and N 4 [local-scale] [Resio and Perrie 2008; Perrie & Resio 2009] 4 2
Multiple spectral peaks E(f) f p1 f s f p2 equilibrium range f Broad-scale term parameterization? F(k) Norm = F(k) k 2.5 / [Resio&Perrie, 1989; Resio et al. 2004 ] Should be ~ 1/ f [F(k) k 2.5 ] equilibrium range But equilibrium range is hard to define when f p1 and f p2 are close 5 New TSA variations 1) Variable equilibrium range Set to upper limit on number of frequency bins above fp,, up to 14 bins, because for grid spacing λ=1.05, then λ 14 =2 2. 2) Double-peak Treat as 2 separate peaks and call broad-scale term for each separately 3) Each broad-scale term requires a cos m ( - p) distribution where m is selected to give the best fit to the 1-d energy. 4) And spreading of the broad-scale terms are determined by p 5) Suppose the broad-scale direction is determined by the wind Or maybe only the higher frequency broad-scale terms is determined by the wind direction? 6 3
We ve implemented TSA in WAVEWATCH-III and we made many fetch-limited growth tests - Simple growing wind-generated waves test - Turning winds tests (fast and slow turning) - Real case test with Hurricane Juan (2003) Now lets look at some results. 7 Fetch-limited wave growth 12 hr DIA FBI TSA 8 4
Fetch-limited wave growth 18 hr DIA FBI TSA 9 Fetch-limited wave growth 24 hr DIA FBI TSA 10 5
Fetch-limited wave growth 30 hr DIA FBI TSA 11 Fetch-limited wave growth 36 hr DIA FBI TSA 12 6
Fetch-limited wave growth 42 hr DIA FBI TSA 13 Sudden turning winds 90 o at 48 hr DIA FBI TSA 14 7
Turning winds + 6 hr DIA FBI TSA 15 Turning winds + 12 hr DIA FBI TSA 16 8
Turning winds + 18 hr DIA FBI TSA 17 Turning winds + 24 hr DIA FBI TSA 18 9
Turning winds + 30 hr DIA FBI TSA 19 Turning winds + 36 hr DIA FBI TSA 20 10
Turning winds + 42 hr DIA FBI TSA 21 WRT - Sudden turning winds 90 o at 48 hr DIA 22 11
WRT - Sudden turning winds 90 o at 48 hr Original TSA 23 WRT - Sudden turning winds 90 o at 48 hr NEW double-peak TSA 24 12
1D Energy Evolution at mid-point of box-oceanocean for tu Sudden rning wind case 25 1D Snl Evolution at mid-point of box-oceanocean for Sudden turning wind case 26 13
Growth curves for Sudden turning wind case 27 Growth curves for Sudden turning wind case 28 14
WRT - Slow turning winds 10 o /3hr up to 90 o DIA 29 WRT- Slow turning winds 10 o /3hr up to 90 o NEW double-peak TSA 30 15
WRT- Slow turning winds 10 o /3hr up to 90 o NEW double-peak TSA + wind-direction direction broad-scale 31 1D Energy Evolution at mid-point of box-oceanocean for Slow turning wind case 32 16
1D Snl Evolution at mid-point of box-oceanocean for Slow turning wind case 33 2D Snl 6 hr 34 17
2D Snl 46 hr 35 Growth curves for Slow turning wind case 36 18
Growth curves for Slow turning wind case 37 Wave Simulation during Hurricane Juan (2003) 38 19
Hurricane Juan 39 01 UTC Sept 29 2003 at buoy 44258 2D Snl 40 20
03 UTC Sept 29 2003 at buoy 44258 2D Snl 41 04 UTC Sept 29 2003 at buoy 44258 2D Snl 42 21
05 UTC Sept 29 2003 at buoy 44258 2D Snl 43 06 UTC Sept 29 2003 at buoy 44258 2D Snl 44 22
03 UTC Sept 29 2003 at buoy 44258 2D Energy 45 04 UTC Sept 29 2003 at buoy 44258 2D Energy 46 23
Wave Height [m] WAM-cycle3 for S in, S ds Juan -wam Buoy 44137 Buoy 44142 Buoy 44258 47 Summary / Conclusions 1. Original TSA works fine for simple growing wind-generated waves 2. Doesn t work so well for multi-peak spectra 3. Can generalize by multiple broad-scale terms 4. Hypothetical and real case tests 5. Tuning? WAMcycle3? Tolman/Chalikov? 6. TSA works better with WAM physics Acknowledgements: NOPP, Canadian Panel on Energy R & D 48 24