1. INWAVE: THE INFRAGRAVITY WAVE DRIVER OF THE COAWST SYSTEM
Good morning.
First of all I would like to thank John for organizing this workshop and my apologizes for not being able to be in person to present this work.
In this talk I will describe the Infragravity wave driver that we are including in the COAWST modeling system.
Maitane Olabarrieta & John C. Warner
COAWST WORKSHOP
Woods Hole, 23rd -27th July

2. OUTLINE INTRODUCTION AND MOTIVATION
IG GENERATION AND DISSIPATION MECHANISMS
IG MODELLING TECHNIQUES
INWAVE
a. EQUATIONS AND NUMERICAL SCHEME
b. HOW IS IT LINKED TO THE VORTEX FORCE?
c. APPLICATIONS
d. FUTURE PLANS
Although the Inwave driver is still being tested, I will explain you why we decided to include this new driver in COAWST.
For those how are not that familiar with what Infragravity waves are, I will explain the generation and dissipation of this long waves and I will briefly mention which are the implications of the existence of these waves in coastal areas.
I will also describe which numerical techniques can we use to model these kind of waves, their advantages and disadvantages.
I will describe how Inwave works, I will show some applications and tests of Inwave.
Finally I will point out which is the current situation of Inwave and which are our future plans.

3. OCEAN WAVES CLASIFICATION
Long Waves
Short Waves
24 h
12 h
5 min
30 s
1 s
0.1 s
Period
Infra-gravity Waves
Gravity Waves
Ultra-gravity Waves
Tides
Long Waves
Capillarity Waves
Kind of Wave
Storms, tsunamis
Sun, Moon
Wind
Forcing
Coriolis
Surface Tension
This graph shows the ocean waves energy distribution in function of the frequency.
We can see how most of the energy of the ocean waves corresponds to the wind waves or gravity waves, with periods between 1 and 30 s. There is another strong peak that corresponds to the astronomic tides and tsunamis, with periods from tens of minutes to several hours.
We can see how the energy in between these kind of wave motions in not negligible. This frequency band, with periods between 30 s and 5 minutes more or less, is what is known as the Infragravity wave band. The generation mechanism is the wind and the restoring force the gravity.
Gravity
Restoring Force
Energy
Frequency (Cycles per second)

4. 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.
The main characteristic of these waves is that they are created by incoming wind wave groups.
As they propagate onshore, their energy increases and they can dominate the water motion on dissipative beaches
These waves reflect on the shore to form cross-shore standing pattern
And they can also propagate alongshore to form standing wave patterns.

5. FIELD MEASUREMENTS OF IG WAVES
Ruessink, 2010
≈ 15%
sea-swell
infragravity
Herbers et al., 1995
As shown by different field measurements, the IG wave energy in the nearshore depends on the offshore wave energy.
These are the data collected by Ruessink 2010 in Truc Vert Beach (France).
In this first graph, we can see the time variation of the water level and the offshore wave height.
There was a strong storm event in the measurements.
What we can see is that offshore wave energy in dissipated in the beach, we can see how the wave energy is water limited and the consequence is this short wave height modulation.
We can also see the existence of the IG wave band in the surf zone. We can see how the IG wave height is also tidally modulated and how it increases when the offshore wave energy is higher.
Ruessink, found that in this beach around 15% of the offshore wave height is in general transferred to the IG motion.
But this relation between the offshore wave energy and the IG wave energy has also been detected in other beaches such as in Duck and Oahu and in lost of places around the world.

6. SOME OF THE EFFECTS OF IG WAVES
BEACH MORPHOLOGY ????
RUNUP AND BEACH-DUNE EROSION
So, which are some of the consequences of the IG wave generation?
Well, during storm conditions, in dissipative beaches especially, the surfzone dynamics and the swash motions are dominated by the IG wave motion. And is believed that this is a processes that contributes in a great manner to the runup in the coast, possible overtopping and the erosion in the swash- dune region.
Another possible effect if the beach morphology. This point is not that clear but there is still an open discussion of the possible relation between the rhythmic patterns in the hydrodynamics created by IG wave motions and rhythmic morphological patterns.
Another important effect of IG waves is the harbor resonance. This images show a harbor in the north coast of Spain, in the Village of Lastres. Periodically this harbor resonates in response to the external IG wave forcing. This forcing period is about s. The resonance creates strong water level variations inside the harbor and strong current velocities (as you can see in this image), damaging the boats and creating lost of economical looses.
HARBOR RESONANCE

7. MOTIVATION
Under storm conditions, in dissipative beaches, the run up and swash zone dynamics are controlled mainly by the Infragravity Wave motion (Raubenheimer and Guza, 1996)
Hatteras Village, North Carolina
We should include these processes if we want to solve the coastal erosion, overwash and breaching
Frisco, North Carolina
Our main goal of including the IG generation processes in COAWST was the improvement of the flooding and erosion simulation during storm conditions.
As I mentioned earlier, under storm conditions, in dissipative beaches the runup and swash dynamics are controlled mainly by the infragravity wave band.
The short wave energy in the surf zone gets saturated and the energy is transferred to the IG wave motion.
For this reason, if we want to simulate the coastal erosion, overtopping and breaching we should include these processes in the COAWST modeling system.
At this moment the wave driver in COAWST is SWAN. SWAN is designed to work in a time scale in which all wave groupiness processes are averaged.
For this reason it is not designed to include the wind wave energy modulation and therefore the IG wave generation.
For this reason we decided to include a new wave driver (Inwave) that considered the possible wave groupies.

8. BOUND WAVE RELEASE (Munk, 1949; Tucker, 1950)
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)
Before I start to talk about Inwave, I think it is important to mention which are the possible Infragravity wave generation and dissipation mechanisms.
Basically InfraGravity waves can be generated by two mechanisms:
The bound wave generation and its release in the surf zone.
The breaking point movement in the surf zone that acts like a paddle for long Infragravity waves.

9. BOUND WAVE RELEASE (Munk, 1949; Tucker, 1950)
Radiation stress
gradient
Pressure
gradient
In the offshore, wave groupiness, due to variations on the radiation stress gradients creates a bounded long wave, that travels with the group velocity.
As the wave group propagated towards the shore, this bounded wave shoals and when the wave group is destroyed the bound wave get released and starts to propagate as a free long wave. This free long wave can be reflected in the shore or in the breaking point, producing an outgoing free long wave.

10. IG generation due to the breaking point movement (Symonds et al
The other IG wave generation mechanism is the breaking point movement. Within a wave group, the highest waves will break more offshore and shorter waves more onshore.
This creates a variation on the extension of the surf zone, within a wave group. This variation acts like a wave maker creating an onshore directed free long wave and an offshore directed break point forced long wave.

11. The dominance of each mechanism depends on the slope
regime (Battjes, 2004)
The dominance of this generation mechanims depends on the slope regime defined by Battjes in 2004.
The slope regime depends on the beach slope, the wave frequency, the water depth and the gravitational acceleration,
For steep slope regimens the breakpoint variation mechanism seems to be more important, while in mild slope regimes the bound wave release is more relevant.
Anyway, both mechanisms can occur and we should consider both when modeling IG waves.

12. 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
In 2 dimensions the problem is even more complex. With oblique wave incidence or high directional spreading, the free IG waves in the surf zone can be trapped due to refraction propagation as edge waves or they can be reflected propagation offshore as leaky waves.

13. 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.
Bottom friction, IG wave breaking and non linear energy transfers are the main mechanisms of IG wave dissipation.
However, it is still not clear which is the relative importance of each process and more reach is needed in this direction.
In summary, we want with inwave is to create a wave driver able to create the forcing to simulate all this processes.

14. IG MODELING TECHNIQUES
WAVE RESOLVING TECHNIQUES:
BOUSSINESQ , PARTICLE TRACKING OR RANS MODELS
WAVE AVERAGED OR PHASE AVERAGED TECHNIQUES:
WAVE ACTION BALANCE EQUATION + NLSW
With respect to the IG wave modeling techniques I would say that there are 2 main types of models:
The first type are the wave resolving models, such as the bousinnesq, RANS and particle tracking models.
The advatage of these models is that they consider the long wave- short wave non linear interactions and that the wave nonlinearities are implicitly included in the models. The main problem of these models is that they are computationally expensive, especially the RANS and particle tracking models. The use of boussinesq models would be an option, but the problem is that these are vertically averaged so we would not be able to simulate 3D processes such as undertows, that in the surfzone are important.
2. The second type of models are the phase averaged wave models coupled to the NLSW equations. These are computationally less expensive but they have more physical limitations. For example the effect of short wave non linearities are not consider.

15. Reniers, 2012 (long wave and runup Workshop)
This is a summary of the IG wave model references, indicating if they are 1, 2 or 3 dimensional models and which types of equations the solve. This was presented by Reniers in the Long Wave Run Up workshop 2012.
What we can see is that there are very few 3D models that include IG waves, the one presented by Reniers in 2009 (which is based on xbeach coupled to Delft 3D) and the model presented by Steeling and Zilejma (2010) which is the swash model.

16. How do we model IG? 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
Due basically due to computational restrictions, and because we wanted to be able to simulate 3 D processes such as undertows, we decided to configure Inwave in a similar way to xbeach. We also want to take advantage of the nesting capabilities of COAWST in a wave that we just model the IG wave motion in the finest grids.
Basically what Inwave does is:
It takes a directional wave spectrum in the boudaries where Inwave is going to be run. And from this directional spectrum, by assuming random phases, making an inverse Fourier Transform, it recontructs the free surface elevation signal of the wind waves.
Since the propagation of these waves would be very time consuming, what we do is use the Hilbert transform to obtain the envelope of the wave energy. This envelope includes the effect of the wave groupiness.
Then we use the wave action balance equation to solve the wave group varying wave energy in the Inwave domain and we feed ROMS with the Vortex Force to generate the IG waves. We also need to define the bound wave in ROMS grid to include the effects of the bound wave that is propagating from the offshore.
Boundary condition for the wave action conservation equation
Vortex Force terms varying in wave group scale
FREE SURFACE ELEVATION AND WAVE ENERGY ENVELOPE TIME VARIATION
Time varying
Wave forcings
Infragravity wave generation

17. SWAN + INWAVE + ROMS COUPLING
Offshore incident wave conditions (frequency- directional spectra)
INWAVE
Wave group energy (Hilbert transform)
Bound in-coming infragravity waves (e.g. Hasselmann, 1963)
Short wave (group) transformation
ROMS
Infragravity wave generation thru VF and propagation of the bounded IG wave
Leaky, bound and trapped infragravity waves

18. Wave group energy (Hilbert transform)
Hilbert Transform and low-pass filter
JONSWAP, D() ~ coss()
Random phase model

19. Short wave (group) transformation: INWAVE equations
Wave action balance equation in curvilinear coordinate system
Wave dispersion relation + Doppler relation
Eikonal equation

20. Short wave (group) transformation: INWAVE equations
Wave breaking
Battjes and Janssen (1978)
Roelvink (1993)
H= γh

21. 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)
2. Bound wave out of phase with the envelope formed by each interacting pair
3. The direction of the bound wave is give by
4. The time series of the surface elevation of the bound wave is
5. This process is repeated for every pair of short-wave components. The summation of all components gives the total bound wave.
Amplitude of the bound wave for each interacting pair

22. 1D CASE APPLICATION:DUCK 85 TEST CASE (LIST 1991)R2 H1 R3 R1 VS R4 H2 H3 H4 H5
Sea surface measurements in station H5

23. INWAVE MODEL: INPUTS R2 H1 R3 R1 VS R4 H2 H3 H4 H5

24. INWAVE MODEL: RESULTS

25. 2D CASE APPLICATION: OBLIQUE INCIDENT BICHROMATIC WAVES IN A UNIFORM BEACH
slope=0.0125
(m)
(m)
BATHYMETRY
(m)

26. REAL APPLICATION: HURRICANE ISABEL
Time varying wave spectra

27. INWAVE MODEL: PRELIMINARY RESULTS
SEA SURFACE ELEVATION DUE TO IG WAVES
(m)

28. 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.