Upload
delftsoftwaredays
View
352
Download
6
Embed Size (px)
DESCRIPTION
SWAN Advanced Course
Citation preview
SWAN Advanced Course3. Model physics in SWAN
Delft Software Days28 October 2014, Delft
Contents
• SWAN, a third generation wave model
• SWAN, fully spectral
• Physics in SWAN: source terms
2
3
First, second and third generation models
• First generation:> parameters only (Hs, Tp, m)> without nonlinear interactions
• Second generation (Hiswa):> Per discrete direction, Hs and Tp.> crude parametric form of nonlinear interactions
• Third generation (Swan):> Spectral shape as function of frequency and direction> Approximations of Boltzman integral for nonlinear
interactions
Phase-averaged wave models
Gen Sin Snl Sds
1 • based on growthrate meas.
• large inmagnitude
• saturationlimit (on/offlimitspectrum)
2 • based on fluxmeasurements
• smaller than 1stgeneration
• parametricform
• limitedflexibility
• saturationlimit (as in1stgeneration)
3 • based on fluxmeasurements
• stress coupled tosea state
• approximateform ofBolzmannintegral
• explicit form
source term representation: dE/dt = Sin + Snl + Sds
4
Physics in SWAN
Figure courtesy Holthuijsen (TU-Delft)
Generation: wave growth by windPropagation: shoaling, refraction, reflections, diffraction
Transformation: non-linear wave-wave interactionsDissipation: wave breaking, whitecapping, bottom friction
5
In shallow water the Eulerian energy balance equation becomes:
refractionincl. shoaling incl. shoaling
Energy balance equation
x y c Ex y
E c E c E St
6
SWAN: fully spectral E( , )
Based on action balance equation (Action ):
x ySN N c N c N
x yN c ct
refraction (depth, current),diffraction (depth, obstacles)
shoaling (depth) frequency shift (current)
Wave propagation based on linear wave theory
Dispersion relation 2 tanh ,gk kh k U
Action N is conserved in presence of current, energy is NOT !
7
12
2
1 12 1
1
ag
a
g g a
ga
g
C Cm m
C c
cc acc a
Holthuijsen et al. (2003)
Diffraction in SWAN
8
3rd-generation formulations:• Input by wind (Sin)• Wave-wave interactions:
> quadruplets (Snl4)> triads (Snl3)
• Dissipation:> white-capping (Swcap)> depth-induced breaking (Sbr)> bottom friction (Sbot)
Source terms in SWAN
S = Sin + Snl4 + Swcap + Snl3 + Sbr + Sbot
deep shallow
9
Physics in SWAN: Wind input
Sin ( , ) = A + B E( , )
•Linear wave growth: Caveleri and Malanotte-Rizzoli (1981):• A = A ( , , w,U*)
•Exponential wave growth:• Komen et al. (1984), Snyder et al. (1981) [WAM-cycle3]
• Janssen (1989, 1991) [WAM-cycle4]
*max 0, 0.25 28 cos 1p
a
w h sw
a e
Uc
B
22* max 0 , cos
phase
aw
w
Uc
B
( : Miles constant) 10
Alternative for exponential wave growth
Yan (1987):
Courtesy:Van der Westhuysen
11
Physics in SWAN: Wind input
2 2* 10DU C UTransformation:
310
310 10
1.2875 10 for 7.5 m/s0.8 0.065 10 for 7.5 m/sD
UC
U U1. Wu (1982):
2. Zijlema et al. (CE 2012):2 30.55 2.97 1.49 10DC U U
10 , 31.5m/sref refU U U U
12
Critical issues:• Effect of gustiness on wind input?• Is wave growth linearly or quadratically proportional to wind
speed?• Is there a limit to momentum transfer from atmosphere to wave
field at extreme wind speeds?• Does wind input depend on wave characteristics in shallow
water (steepness?) ?
Physics in SWAN: Wind input
13
Physics in SWAN: Whitecapping
1p
dsPM
k sCk s
, ,wcapkS Ek
52.36 10 , 0, 4dsC p
Whitecapping is represented by pulse-based model of Hasselmann(1974), reformulated in terms of wave number (for applicability in finite-water depth) by Komen et al. (1984):
with
Tunable coefficients:
• Komen et al. (1984, WAM-cycle3) :
• Janssen (1992, WAM-cycle4):54.10 10 , 0.5, 4dsC p
14
Physics in SWAN: Whitecapping
( , ) ( , )qn
wc dsPM
k sS C Esk tots k EKomen et al. (1984):
1. Underprediction of mean wave period (mean and peak)under wind-sea conditions
2. Overprediction of wind-sea when a bit of swell is added
15
Saturation-based whitecapping
( , ) ( , )qn
Komen dsPM
k sS C Esk
3( ) ( )gB k c k E
tots k E,
1 12 2
/ 2( )( , ) ( , )
p
Break dsr
B kS C g k EB
,
, ( , ) ( ) 1 ( )wc SB br Break br KomenS f S f S1
21 1 ( )( ) tanh 10 12 2br
r
B kfB
*up fc
Saturation based whitecapping by Van der Westhuysen et al. (2007),related to nonlinear hydrodynamics within wave groups :
Komen et al. (1984):
Adjusted by Van der Westhuysen (2007):
16
Saturation-based formulation
Wind-sea part no longer affected byaddition of swell
17
Pure wind sea: Lake George, Australia
20 km
Stronger wave growth and betterprediction in spectrum tail bysaturation-based model
18
Fetch-limited situations
20 m/s
measured
SWAN default
SWAN saturationbased wcap
19
• Deep water, fetches > 5km• position spectral peak improved (used to be at frequencies too
high), low-frequency part better predicted• wave energy in high-frequency tail correctly predicted (used to
be too much)• wave energy better predicted
• Deep water, fetches < 5km• strong overprediction of low-frequency energy (used to be
closer to measurements)
• Shallow water• computed spectral shape deviates from measured spectral
shape (pronounced spectral peak, onset to secondary peak)
Fetch-limited situations
20
Physics in SWAN: Quadruplets
Computation of quadruplets is based on Boltzmann integral forsurface gravity waves;
1 2 3 4 1 2 3 4,k k k k
resonance condition:
1 2 3 4 1 2 3 4,
1 2 3 4 1 2 3 4k k k k
21
DIA
Xnl
Van der Westhuysen etal. (2005):
• DIA (default) vs. Xnl
• accuracy vs. CPU
Physics in SWAN: Quadruplets
22
• Exact methods to solve Boltzmann integral are not suitable foroperational wave models;
• (Initially deep-water) DIA is rather inaccurate, but less time-consuming (Hasselmann et al., 1985);
• Depth effects have been included by WAM scaling.• Quadruplets are of relative importance in relative deep water in
concert with white-capping and wind input.
Physics in SWAN: Quadruplets
Compared to exact method:• DIA provides lower significant wave heights and higher
mean wave periods;• Directional spreading is larger for DIA.
23
and proportionality coefficient, fraction of breaking wavesand maximum wave height:
Physics in SWAN: Depth-induced wave breaking
214 2tot BJ b mD Q H
,,br tot
tot
ES D
E
1BJ
Energy dissipation due to depth-induced breaking is modelled by thebore-based model of Battjes and Janssen (1978) :
with
mHbQ
0.73 defaultmH d
24
Problem over nearly horizontal beds
Default BJ78( BJ = 0.73)
Physics in SWAN: Depth-induced wave breaking
Apparent upper limit of Hm0/d in SWAN,due to fixed value of
25
0.76( ) 0.29BJ pk d
Dependencies of BJ on local variables (vd Westhuysen 2010)
Ruessink et al. (2003):
26
Depth breaking based on shallow water nonlinearityBiphase model by Van der Westhuysen, 2010)
3301
04m
tot bfBD H p H dHd
bp H W H p H
From Thornton & Guza (1983):
4,9
n
refref
W H
Introduce a biphase-dependentweighting function on the pdf:
Eldeberky(1996)
33013
16
n
mtot rms
ref
B fD Hd
loc loc44 arctann S S
Boers (1996):
27
Calibration and validation of biphase model
Biphase model yields similarimprovement as Ruessink et al.parameterization, but withphysical explanation of modelbehaviour.
28
Calibration and validation of biphase model
Amelander Zeegat (18/01/07, 12:20)
Wave growth limit reduced bybiphase model over nearlyhorizontal areas
29
Critical issues wrt depth-induced wave breaking
• Does wave breaking depend on local wave characteristics, suchas local wave steepness?
• Is the dissipation rate frequency dependent?
• What is influence of long waves on breaking of shorter waves?
• Knowing that Battjes-Janssen model (BJ) hampers wave growth inshallow water, there is no breaker formulation for the entirespectrum of bottom slopes (ranging from horizontal to reef-type ofslopes) other than the recently implemented but highly empiricalformulation of Salmon et al. (ICCE, 2012).
30
Physics in SWAN: Bottom friction
• JONSWAP (Hasselmann et al., 1973):
• Collins (1972):drag-law type
• Madsen et al. (1988):eddy-viscosity type
2bottom w rmsgC f U
2 3
2 3
0.038 m s (swell)0.067 m s (fully-developed sea)bottomC
2
2 2, ,sinhbot bottomS C E
g kd
( 0.015 default)bottom f rms fC C gU C
, 0.05 defaultw w bot N Nf f a K K
31
• Triads modelled by Lumped Triad Interaction (LTA) method ofEldeberky (1996).
• In shallow water triads have a significant influence on waveparameters for non-breaking and breaking waves over asubmerged bar or on a sloping beach.
• Present formulation does not include energy transfer to lowerfrequencies. Transfer to higher frequencies oftenoverestimated. Conclusion: Modelling of triads in 2D waveprediction models needs improvement.
Physics in SWAN: Triads
32
ENERGY DENSITY SPECTRA (2.61)
0
10
20
30
40
0.0 0.1 0.2 0.3 FREQUENCY (Hz)
EN
ER
GY
DE
NS
ITY
(m2 /H
z)
DEEPMP3MP5MP6TOE
ENERGY DENSITY SPECTRA (2.61)
0
10
20
30
40
0.0 0.1 0.2 0.3
FREQUENCY (Hz)
ENER
GY
DEN
SITY
(m2 /H
z)
DEEPMP3MP5MP6TOE
Measured (flume) Computed (SWAN)
FORESHORE - PETTEN
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
-40 -35 -30 -25 -20 -15 -10 -5 0 5
FORESHORE (m)
ELE
VA
TIO
N(m
)
1:30
1:25 1:20 1:1001:25
1:4.5
1:20
1:3
MP3 MP5 MP6DEEP BAR
• No energy transfer to lowfrequencies
• Exaggeration of energy transfer tohigher harmonics
Physics in SWAN: Triads
33
Hm0 Tm-1,0
With triads
No triads
Physics in SWAN: Triads
34
Depth profile nearPetten Sea defence Tm-1,0 (with triads)Tm-1,0 (no triads)
Physics in SWAN: Triads
35