Post on 05-Jul-2015
description
SWAN Advanced Course1. General introduction to waves and wave modelling
Delft Software Days28 October 2014, Delft
28 Oct 2014
Introduction
- Waves
- SWAN wave model
- SWAN North Sea
x ySN N c N c N
x yN c ct
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Waves
k=1/L
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Waves
Type of wave Typical period [s] Cause
Tide 5*104 s = 12 hr moon, sun
Tsunami 104 s = 3 hr earthquake
Seiches 103 s = 20 min cold front
Surfbeat 102 s = 2 min wave groups
Swell 15 – 20 s storms far away
Wind waves (“Sea”) 2 – 10 s wind
Capillary waves 0.1 s turbulence in wind
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Waves
Figure courtesy Holthuijsen (TU-Delft)
Wave generation: by windPropagation: shoaling, refraction, reflection, diffraction
Transformation: non linear wave-wave interactionsDissipation: breaking, whitecapping, bottom friction
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Waves
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E(f): variance density spectrum [m2/Hz]
Eenergy(f) : energy density spectrum = * g * E(f)
wave harmonic frequencies waverecord analysis spectrum
1( ) sin 2
N
i i ii
t a f t
In the limit for N
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Waves
HE10 sometimes called ‘swell’Rather: low frequency wave height
Tp = peak period (=1/peak frequency)
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forfor
a p
pb
f ff f
Empirical forms based on fetch-limited observations
2
2 24 exp
242 5
Pierson-Moskowitz spectrum
5( ) 2 exp4
p
p
f
p
f
ffE f g ff
JONSWAP
1 ,pp
fT
Standard values:
From input:
3.3, 0.07, 0.09a b
determined from Hs
Waves
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Waves
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Direction
Swellm =100
wind seam = 4
m[-]
one sideddirectionalspreading
[°]
Type
1 37.5
4 24.9 wind sea
15 14.2
60 7.3
100 5.7 swell
800 2
( , ) ( ) ( , )E f E f D f( , ) cos ( )m
meanD f A f28 Oct 2014Delft Software Days 10
Waves
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SWAN
x y c Ex y
E c E c E St
bathymetry
offshore waves
wind
waterlevel
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SWAN
action density (instead of energy density)
propagation refraction
Sin = wind inputSnl = non linear wave-wave interactionsSds = dissipation
Sourceterms
frequencyshift(currents)
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SWAN
Sin ( , ) = A + B E( , )
•Linear wave growth: Caveleri and Malanotte-Rizzoli (1981):A = A ( , , w,U*)
•Exponential wave growth
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u
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SWAN
Sin ( , ) = A + B E( , )•Exponential wave growth:
• Komen et al. (1984), Snyder et al. (1981) [WAM-cycle3]
• Janssen (1989, 1991) [WAM-cycle4]
• Westhuysen (from Yan 1987, but with refitted coefficients D,E,F,H)
*max 0, 0.25 28 cos 1p
a
w h sw
a e
Uc
B
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22* max 0 , cos
phase
aw
w
Uc
B
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SWAN
2 2* 10DU C UU10 is input to SWAN
310
310 10
1.2875 10 for 7.5 m/s0.8 0.065 10 for 7.5 m/sD
UC
U UWu (1982):
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2 30.55 2.97 1.49 10DC U U
10 , 31.5m/sref refU U U U
Zijlema et al. (CE 2012):
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SWAN
2 2* 10DU C UU10 is input to SWAN
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SWAN
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
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SWAN
q or p =4 (tuned)n variable, to be set with .
If =0 -> n=1 -> was default until 2013If =1 -> n=2 -> more dissipation for larger k so
more energy at lower frequencies (larger T)‘Rogers’, default since 2013
( , ) ( , )qn
wc dsPM
k sS C Esk tots k EKomen et al. (1984):
1p
dsPM
k sCk s
, ,wcapkS Ek
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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 non breakS f S f S
121 1 ( )( ) tanh 10 1
2 2brr
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):
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SWAN
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SWAN
2
2 2, ,sinhbot bottomS C E
g kd
2 3
2 3
0.038 m s (swell)0.067 m s (fully-developed sea)bottomC
Bottom friction ‘Jonswap formulation’
now defaultwas default (till 2013)
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SWAN North Sea
SWAN North Sea within FEWS
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SWAN North Sea
Grid 1 (DCSM)RectangularArea:1500 km x 1700 kmCell size:3.6 km x 3.6 km
Grid 2 (ZUNO)CurvilinearArea:770 km x 750 kmCell size:200 m - 2 km x200 m - 2 km
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SWAN North Sea
In FEWS every 6 hour: SWAN-DCSM and SWAN-ZUNOResults in FEWS
Spectral wave boundary conditions for SWAN-DCSM:WAM model by ECMWF (30 freq x 24 dir) 0:00 6:00 12:00 18:00…
dt = 6 hrWind (equal for SWAN-ZUNO and SWAN-DCSM):HIRLAM11-v7.2 model 0:00 6:00 12:00 18:00…
dt = 1hrWaterlevels:WAQUA DCSMv6 (rectangular) 0:00 6:00 12:00 18:00…
dt = 1hrCurrents (SWAN-ZUNO only):WAQUA DCSMv6 0:00 6:00 12:00 18:00…
dt = 1hrBathymetry:based on WAQUA DCSMv6 and ZUNOv4
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SWAN North Sea
ca.5 km
2013:MV2
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SWAN North Sea
SWAN validation based on operational runs Nov 2012 – April 2013
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SWAN North Sea
Komen; delta=0(presently inSWAN North Sea)
Westhuysen
Komen; delta=1(present default inSWAN)
Observation
- - SWAN ZUNOSWAN DCSM
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SWAN North Sea
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