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Spectral wave modelling with TOMAWAC.
Applications at regional and coastal scales
Michel BenoitProfessor at l’Ecole Centrale Marseille and researcher at IRPHE
Institut de Recherche sur les Phénomènes Hors-Equilibre
(UMR 7342, CNRS, Aix-Marseille Université, Ecole Centrale Marseille)
Team SAO (Structures-Atmosphere-Ocean)
Models for sea-states and wind waves
Two main classes of models:
• Deterministic (phase resolving) wave models• Intra-wave resolution
• Able to resolve all details of wave trains (wave phase, shapes, etc.)
• Based on deterministic equations such as Berkhoff (ARTEMIS),
Boussinesq, Green-Naghdi, Euler, Laplace, etc.
• Phase-averaged wave models:• Consider only averaged properties of the wave field.
=> transformation of wave (variance or action) spectrum
• Spectral models: WAM, SWAN, WaveWatch, TOMAWAC
=> transformation of the distribution of wave heights
• Probabilistic models (less frequently used in practice)
Processes OceanContinental
seasCoastal
zonePorts
Shoaling ++ +++ ++
Bathymetric refraction ++ +++ ++
Refraction by currents + ++
Diffraction / reflection + +++
Wind wave generation +++ +++ +
White capping +++ +++ +
Bathymetric breaking + +++
Bottom friction +++ ++
Quadruplet interactions +++ +++ +
Triplet interactions ++ +
Important physical processes
(based on Battjes, 1994)
TOMAWACARTEMIS
The 3rd generation TOMAWAC code
Modelling the change, in time and in the spatial domain, of the variance
density directional spectrum F(f,q,x,y,t) of wind-driven waves
Applications from the oceanic domain to coastal zones
Unsteady forcing (winds) and environmental conditions (currents, sea
level).
q
f
V
F Full discretization of the
spectrum in (frequency,
direction) space.
Advanced models for
the physical processes
(various options are available)
(TELEMAC-based Operational Model Addressing Wave Computation)
TOMAWAC main equations (1)
Compute the evolution of the variance spectrum F(f,q,x,y,t)
Wave propagation
(+ shoaling)
),,,,(.)()()()()(
tfyxQBf
BFf
BF
y
BFy
x
BFx
t
BFr
r
r q
q
q
Frequency changesRefraction
Source and sink terms
s
UkCgdU
t
d
dfr
..
2
1UyCgy qcos.
UxCgx qsin.
n
U
k
k
n
d
dk
q .
1
),,,,(.),,,,( tfyxFBtkkyxN ryx q 22
gCCB The wave action is written as with
Note the code uses the spectrum as a function on relative frequency.
Kinematics terms are obtained from the linear wave theory
TOMAWAC main equations (2)
• The left hand side (LHS) is linear for describing wave propagation +
refraction + shoaling (effects of bathymetry and ambient currents)
• On the RHS there are several sink/source terms
(based on mathematical models or semi-empirical
parameterizations of the complex physics of waves)
trnlbrbfwcin QQQQQQQ
Generation Dissipation Transfers
wind input whitecapping bottom breaking quadruplets triads friction
Wave development under wind action
Shallow water effects
Source terms (input of energy)
• Generation by wind (Janssen, 1991; Snyder et al., 1981 ; Yan, 1987)
Sink terms (dissipation of energy)
• White-capping(Komen et al., 1984 ; van der Westhuisen, 2007 )
• Bottom friction(Hasselmann et al., 1973; Bouws & Komen, 1983)
• Depth-induced breaking (Battjes & Janssen, 1978; Thornton & Guza, 1983;
Roelvink, 1993; Izumiya & Horikawa, 1984)
Transfer terms
• Quadruplet interactions
(DIA Hasselmann et al., 1985 ; MDIA, Tolman, 2004 ;
GQM exact method, 2009)
• Triad interactions
(LTA Eldebrky & Battjes, 1996; SPB Becq, 1998)
Shallow
water
Deep
waterInterm.
depth
Several formulations available
Physics: source and sink terms in TOMAWAC
Discretizations used in TOMAWAC
• Unstructured grid in spatial domain (either Cartesian or spherical coordinates)
Triangular finite element mesh
• Structured grid in spectral domain
frequencies in geometric progression, evenly distributed directions
• Temporal discretization: constant time step
Two forcing options:- Wind fields over the whole domain
(varying in space and time)
- Incident wave conditions at the
boundaries (from a larger scale model)
Réunion Island sea-state database (1/2)
Two nested TOMAWAC models
Coarse model (1019 nodes, 1919 elements):
Resolution: 40 km offshore, 3 km along the coasts
Time step: 240 s
Fine model (2474 nodes, 4687 elements):
Resolution: ~100 m along the coasts
Time step: 60 s
Forcing conditions: wind fields (10 m) and wave
spectra at boundaries both from ERA-Interim
reanalysis (ECMWF):
Time steps of 6 h
Resolution of ~0.7°(wind) and ~1°(wave spectra)
Time length: 20 years, from 01/01/1989 to 31/12/2008
N
Réunion
Island
Saint
Pierre
10 km
Buoy
Réunion Island sea-state database (2/2)
Model calibration and validation
Reference to wave measurements of a buoy
located off Saint Pierre
Not-calibrated model: discrepancy between buoy
data and model results due to an overestimation
of the wave spectra at low significant wave
heights
Calibrated model: correction of the wave spectra
of the ERA Interim reanalysis
2001
0.5
1.5
2.5
3.5
4.5
5.5
31/03/01 30/04/01 30/05/01 30/06/01 30/07/01 30/08/01 29/09/01 29/10/01 29/11/01 29/12/01
Hm
0 (
m)
Buoy data Simulation results
Year 2001
0
1
2
3
4
5
0 1 2 3 4 5Hm0 TOMAWAC (m)
Hm
0 b
uo
y (
m)
.
not calibrated
calibrated
Wave energy resource estimation
Mean monthly wave power over the Réunion finer
model domain
Mean monthly values of the
wave power off Saint Pierre,
at a different water depths
Spectral formulation of wave power (kW/m) :
1000/),(),(2
0 0
qq dfdfFhfcgP gW
Long-term and homogeneous time series
Characterization of the wave energy resource on annual, seasonal
and monthly basis
e
2
0me
2
0m
2
w TH49.0TH64
gP
Alternative wave power
formulation, valid in the deep
water case
Sea-state simulation: other ocean energy
applicationsAccessibility studies:
Statistical analyses of the spectral parameter time series to evaluate the occurrence of
time windows necessary for installation, operation and maintenance.
Detailed local sea-state propagation modelsMean or extreme wave conditions issued from the database are set as boundary
conditions for more refined local models.
Paimpol-Bréhat tidal
turbine demonstration
farm project: detailed
sea-state propagation
model
©2007 SHOM. Realised with the
authorisation of SHOM.
Contract number 67/2007
4/13/2017 13
Regional model for LMDCZ (Tomawac-Telemac2D-Sisyphe)(see presentation of Thong Nguyen, HCM City Univ. of Technology)
303,000 elements
Max = 9 km
Min = 8 m
Coastal = 2.5 km
