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INWAVE: THE INFRAGRAVITY WAVE DRIVER OF THE COAWST SYSTEM. Maitane Olabarrieta & John C. Warner. COAWST WORKSHOP Woods Hole, 23 rd -27 th July. OUTLINE INTRODUCTION AND MOTIVATION IG GENERATION AND DISSIPATION MECHANISMS IG MODELLING TECHNIQUES INWAVE - PowerPoint PPT Presentation
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INWAVE: THE INFRAGRAVITY WAVE DRIVER OF THE COAWST
SYSTEM
COAWST WORKSHOPWoods Hole, 23rd -27th July
Maitane Olabarrieta & John C. Warner
OUTLINE
1. INTRODUCTION AND MOTIVATION2. IG GENERATION AND DISSIPATION MECHANISMS3. IG MODELLING TECHNIQUES4. INWAVE
a. EQUATIONS AND NUMERICAL SCHEMEb. HOW IS IT LINKED TO THE VORTEX FORCE?c. APPLICATIONSd. FUTURE PLANS
OCEAN WAVES CLASIFICATION
Storms, tsunamis
WindSun, Moon
Frequency (Cycles per second)
24 h 12 h 5 min 30 s 1 s 0.1 s
Long Waves Short Waves
Coriolis
Gravity
Surface Tension
Restoring Force
Forcing
Tides Long Waves
Kind of Wave
Infra-gravity Waves
Gravity Waves Ultra-gravity Waves Capillarity Waves
Period
Ener
gy
IG WAVE CHARACTERISTICS
- They are generated by incoming wave groups.
- Account for 20-60% of the offshore energy.
- These long waves reflect from the shore to form cross-shore standing pattern (= minimal dissipation at
shoreline).
- They can propagate alongshore (edge waves),
sometimes forming standing pattern.
- Can significantly contribute to the surfzone circulation.
FIELD MEASUREMENTS OF IG WAVES
0
1
2
3
Hm
0 (m
)
0
2
4
6
8
Hm
0 (m
)
67 68 69 70 71 72 73 74 75 76 77 78 790
2
4
6
(m
)
Yearday
Ruessink, 2010sea-swell
infragravity
0 1 2 3 4 5 6 7 80
0.5
1
1.5
2
Hm0
offshore (m)
Hm
0,in
f bea
ch (
m) ≈ 15%
Herbers et al., 1995
SOME OF THE EFFECTS OF IG WAVES
RUNUP AND BEACH-DUNE EROSION
BEACH MORPHOLOGY ????
HARBOR RESONANCE
MOTIVATIONUnder storm conditions, in dissipative beaches, the
run up and swash zone dynamics are controlled mainly by the Infragravity Wave motion
(Raubenheimer and Guza, 1996)
We should include these processes if we want to solve the coastal
erosion, overwash and breaching
Hatteras Village, North Carolina
Frisco, North Carolina
IG GENERATION AND DISSIPATION MECHANISM
IG GENERATION MECHANISMS IN THE SURF ZONE
BOUND WAVE RELEASE (Munk, 1949; Tucker, 1950)
IG generation due to the breaking point movement (Symonds et al., 1984)
Pressure gradient
Radiation stress gradient
BOUND WAVE RELEASE (Munk, 1949; Tucker, 1950)
IG generation due to the breaking point movement (Symonds et al., 1982)
The dominance of each mechanism depends on the slope regime (Battjes, 2004)
With oblique wave incidence, free long waves can get trapped in the coast due to refraction as edge waves or be reflected offshore as leaky waves
Herbers et al., 1995
1 1 1, 1, 2 2 2, 2,sin( ) sin( )x y x ya t k dx k y a t k dx k y Incident waves
Su
rf z
one
Su
rf z
one
shoaling
Bound infragravity wave
0 0
,2 ,1 2 2 1 1( ) cos cosx x
x x x
x x
k x k k dx k k dx
arctan yb
x
k
k
5
2,ˆ ~l b h
1
4,ˆ ~l f h
released infragravity wave
(de)-shoaling
,
arctan yf
f x
k
k
2
2,f x yk k
gh
Trapping at:
0
,
arctan 90yf
f x
k
k
2
2turningy
hg k
Leaky if:
turning shelfh h
IG DISSIPATION MECHANISM
- Bottom friction.- IG wave breaking.- Energy transfer thru non-linear interactions to lower periods.
It is not clear which is the main dissipation mechanism and it might depend on the beach slope and on the frequency of the IG components.
IG MODELING TECHNIQUES
WAVE RESOLVING TECHNIQUES:BOUSSINESQ , PARTICLE TRACKING OR RANS MODELS
WAVE AVERAGED OR PHASE AVERAGED TECHNIQUES:WAVE ACTION BALANCE EQUATION + NLSW
Reniers, 2012 (long wave and runup Workshop)
FREE SURFACE ELEVATION AND WAVE ENERGY ENVELOPE TIME VARIATION
Time varyingWave forcings
Infragravity wave generation
, , where , ,
, ,yxc A E x y tc A c AA D
A x y tt x y x y t
Boundary condition for the wave action
conservation equation
, , , , , , , , , , , , , , ,xx xy yx yyS x y z t S x y z t S x y z t S x y z t
Vortex Force terms varying in wave group scale
SWAN domain: Wave spectral time scale
InWave domain: Wave group time scale
DIRECTIONAL WAVE SPECTRUM
Boundary region
- Random phases- Double summation technique- Hilbert transform
SWAN DOMAIN
INWAVE DOMAIN
BOUNDARY
How do we model IG?
Offshore incident wave conditions (frequency-
directional spectra)
Bound in-coming infragravity waves (e.g.
Hasselmann, 1963)
Infragravity wave generation thru VF and propagation of the bounded IG wave
Wave group energy (Hilbert transform)
Leaky, bound and trapped infragravity waves
SWAN + INWAVE + ROMS COUPLING
Short wave (group) transformation
SWAN
INWAVE
ROMS
, ,( )
1
ˆ( , , ) *j x j y j j
Ni t k x k y
jj
x y t e
Random phase model
JONSWAP, D() ~ coss() 21( , , ) | ( , , ) |
2w lowE x y t g A x y t
Hilbert Transform and low-pass filter
Wave group energy (Hilbert transform)
Short wave (group) transformation: INWAVE equations
Wave action balance equation in curvilinear coordinate system
, , ,g g g wC A C A C AA
m nt
D
, cosg gC C U
, sing gC C V
, sin cos cos sin cos sin sin cossinh 2g
h h U U V VC m n m n m n
kh
2
0.5 1sinh 2g
khC C
kh
tanhgk kh
w k u
Wave dispersion relation + Doppler relation
tanh
sinh 2
gk khC
kh
Eikonal equation
ak wm
t
ak wn
t
2 2kk k
b bD D Q Total energy dissipationD
Energy dissipation in a breaking wavebD
Fraction of breaking wavesbQ
2b rep wD f E
Coefficient O(1)
Representative frequencyrepf
Wave energy integrated over directionswE min 1,1 expn
b
HQ
h
Breaking parameter
Coefficientn
Roelvink (1993)
H= γh Breaking parameter
water depthh
wave heightH
Battjes and Janssen (1978)
Short wave (group) transformation: INWAVE equations
Wave breaking
INWAVE MODEL: Incoming bound wave definition at ROMS boundaries
Van Dongeren et al. (2003) -> Hasselman (1963) & Herbers et al. (1994)
1. The energy of the secondary forced elevation E3 (Df) for one particular pair of interacting primary waves can be computed following Herbers et al. (1994)
Amplitude of the bound wave for each interacting pair
2. Bound wave out of phase with the envelope formed by each interacting pair
4. The time series of the surface elevation of the bound wave is
3. The direction of the bound wave is give by
5. This process is repeated for every pair of short-wave components. The summation of all components gives the total bound wave.
1D CASE APPLICATION:DUCK 85 TEST CASE (LIST 1991)
H5H4H3H2R1
H1R2 R3R4VS
Sea surface measurements in station H5
INWAVE MODEL: INPUTS
H5H4H3H2R1
H1R2 R3R4VS
INWAVE MODEL: RESULTS
2D CASE APPLICATION: OBLIQUE INCIDENT BICHROMATIC WAVES IN A UNIFORM BEACH
BATHYMETRY (m)
(m) (m)slope=0.0125
REAL APPLICATION: HURRICANE ISABEL
Time varying wave spectra
INWAVE MODEL: PRELIMINARY RESULTS
SEA SURFACE ELEVATION DUE TO IG WAVES(m)
FUTURE PLANS
- Validate Inwave with more test cases.- In the current configuration we need to define the wave enevelope with a netcdf file, but the idea is that the model will directly recontruct this signal from the paren t swan grid.- Inwave is not capable of including wave spectral variations along its boundaries and future efforts will be directed to include these capabilities.- Within a few months, before the end of the year Inwave will be distributed with COAWST and available for the public use.
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