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

14

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):

16

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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