SWAN Advanced Course

1. SWAN Advanced Course
1. General introduction to waves and wave modelling
Delft Software Days
28 October 2014, Delft
28 Oct 2014

2. Introduction
- Waves
- SWAN wave model
- SWAN North Sea
N c c
t
w
N N c N c N S
w w w w

3. V V T T V
w x y
x y
w w w w
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4. Waves
k=1/L
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5. 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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6. Waves
Wave generation: by wind
Propagation: shoaling, refraction, reflection, diffraction
Transformation: non linear wave-wave interactions
Dissipation: breaking, whitecapping, bottom friction
Figure courtesy Holthuijsen (TU-Delft)
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7. Waves
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8. wave harmonic frequencies wave
record analysis spectrum
¦

9. N
K ( t ) a sin 2
S f t M
1
i i i
i
In the limit for N o f
E(f): variance density spectrum [m2/Hz]
Eenergy(f) : energy density spectrum = ȡ * g * E(f)
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10. Waves
HE10 sometimes called ‘swell’
Rather: low frequency wave height
Tp = peak period (=1/peak frequency)
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11. Empirical forms based on fetch-limited observations
ª § · º
( ) 2 exp 5

12. « ¨ ¸ » « ¨ ¸ » ¬ © ¹ ¼
for
for
p
p
f
«¬ »¼
f f
f f
V
V
a p
b p
V
­ d
® ! ¯

13. 2
ª º « »
« 2 2
»
4 exp
2 4 5 2
4
Pierson-Moskowitz spectrum
V
D S J
p
f
E f g f f f
f
JONSWAP
1 , D p
p
f
T
Standard values:
From input:
J 3.3,V 0.07,V 0.09 a b
determined from Hs
Waves
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14. Waves
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
Swell
m =
100
Direction
wind sea
m = 4
m
[-]
one sided
directional
spreading
[°]
Type
1 37.5
4 24.9 wind sea
15 14.2
60 7.3
100 5.7 swell
800 2
E( f ,T ) E( f )D( f ,T )
( ,T ) cosm T T ( )

15. mean D f A f
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16. Waves
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17. SWAN
Ec
Tw w

18. T
w

19. w
w c E

20. w x w y w
E cE S
x y
t
offshore waves
bathymetry
wind
waterlevel
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21. SWAN
action density (instead of energy density)
propagation refraction
Sin = wind input
Snl = non linear wave-wave interactions
Sds = dissipation
Source
terms
frequency
shift
(currents)
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22. SWAN
Sin (V,T) = A + B E(V,T)
•Linear wave growth: Caveleri and Malanotte-Rizzoli (1981):
A = A (V,T,Tw,U*)
•Exponential wave growth
Delft Software Days 28 Oct 2014
u
14

23. SWAN
Sin (V,T) = A + B E(V,T)
•Exponential wave growth:
• Komen et al. (1984), Snyder et al. (1981) [WAM-cycle3]
ª U
­° ½°º « ® ¾»
U
c
max 0, 0.25 28 * cos

24. 1
a
w h s
U
w
«¬ °¯ p a e
°¿»¼
B
• Janssen (1989, 1991) [WAM-cycle4]
T T V
• Westhuysen (from Yan 1987, but with refitted coefficients D,E,F,H)
Delft Software Days 28 Oct 2014

25. 2
* max 0 , cos 2
UE
T T V
U
§ ·
¨¨ ¸¸ ª¬ º¼
© phase ¹
a
w
w
U
c
B
15

26. SWAN
2 2
* D 10 U10 is input to SWAN U C U
­° ˜
3
U
® °¯
˜ t 1.2875 10 for 7.5m/s

27. 10
D 0.8 0.065 10
3
for 7.5 m/s
10 10
C
U U
Wu (1982):
Zijlema et al. (CE 2012):
0.55 2.97 i 1.49 i2

28. 10 3 D C
U U ˜
i
10 , 31.5m/s ref ref U U U U
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29. SWAN
2 2
* D 10 U10 is input to SWAN U C U
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30. SWAN
Whitecapping is represented by pulse-based model of Hasselmann
(1974), reformulated in terms of wave number (for applicability in finite-water
S k E
V ,T

31. *V V ,T

32. wcap
k
· * C § ¨ ·§ 1 G

33. G
k s
¸¨ ¸
© ¹© ¹
p
ds
PM
k s
2.36˜105 ,G 0, 4 dsC p
depth) by Komen et al. (1984):
with
Tunable coefficients:
• Komen et al. (1984, WAM-cycle3) :
• Janssen (1992, WAM-cycle4): 4.10˜105 ,G 0.5, 4 dsC p
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34. SWAN
n q
§ · § · ¨ ¸ ¨ ¸
S C k s E
Komen et al. (1984): ( V , T ) V ( V , T
)
s k E
wc ds
tot S k E
q or p =4 (tuned)
n variable, to be set with į.
© ¹ © PM
¹
k s
· * C § ¨ ·§ 1 G

35. G
k s
¸¨ ¸
© ¹© ¹
If į=0 - n=1 - was default until 2013
If į=1 - n=2 - more dissipation for larger k so
more energy at lower frequencies (larger T)
‘Rogers’, default since 2013
p
ds
PM
k s
V ,T

36. *V V ,T

37. wcap
k
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38. Saturation-based whitecapping
n q
§ · § · ¨ ¸ ¨ ¸
S C k s E
( , ) ( , )
V T V V T
Komen ds
k s
© ¹ © PM
¹
tot , s k E
Saturation based whitecapping by Van der Westhuysen et al. (2007),
related to nonlinear hydrodynamics within wave groups :
( ) 3 ( ) g B k c k E V
ª ( ) º
/ 2 ( , ) ( , )
S C B k g 1 2 k 1
2
E
p
« »
V T V T
Break ds
r
B
¬ ¼
,

39. , ( , ) ( ) 1 ( ) wc SB br Break br non break S V T f V S f V S ˜ ˜
1
1 1 ( ) 2 ( ) tanh 10 1
f B k
2 2 br
B
r
V
§ ª º · ¨ « » ¸ ¨ ¬ ¼ ¸ © ¹
*p f u
§ · ¨ ¸
c
© ¹
Komen et al. (1984):
Adjusted by Van der Westhuysen (2007):
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40. SWAN
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41. SWAN
Bottom friction ‘Jonswap formulation’
2
V

44. V T V T bot bottom S C E
2 2 , ,
g kd
sinh
2
3
2 3
0.038 m s (swell)
0.067 m s
(fully-developed sea)
­
®¯
bottom C
now default
was default (till 2013)
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45. SWAN North Sea
SWAN North Sea within FEWS
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46. SWAN North Sea
Grid 1 (DCSM)
Rectangular
Area:
1500 km x 1700 km
Cell size:
3.6 km x 3.6 km
Grid 2 (ZUNO)
Curvilinear
Area:
770 km x 750 km
Cell size:
200 m - 2 km x
200 m - 2 km
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47. SWAN North Sea
In FEWS every 6 hour: Ɣ SWAN-DCSM and SWAN-ZUNO
Ɣ Results 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 hr
Wind (equal for SWAN-ZUNO and SWAN-DCSM):
HIRLAM11-v7.2 model 0:00 6:00 12:00 18:00…
dt = 1hr
Waterlevels:
WAQUA DCSMv6 (rectangular) 0:00 6:00 12:00 18:00…
dt = 1hr
Currents (SWAN-ZUNO only):
WAQUA DCSMv6 0:00 6:00 12:00 18:00…
dt = 1hr
Bathymetry:
based on WAQUA DCSMv6 and ZUNOv4
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48. SWAN North Sea
ca.5 km
2013:
MV2
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49. SWAN North Sea
SWAN validation based on operational runs Nov 2012 – April 2013
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50. SWAN North Sea
Komen; delta=0
(presently in
SWAN North Sea)
Westhuysen
Komen; delta=1
(present default in
SWAN)
Observation
- - SWAN ZUNO
SWAN DCSM
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51. SWAN North Sea
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