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INWAVE: THE INFRAGRAVITY WAVE DRIVER OF THE COAWST SYSTEM COAWST WORKSHOP Woods Hole, 23 rd -27 th July Maitane Olabarrieta & John C. Warner

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OUTLINE 1.INTRODUCTION AND MOTIVATION 2.IG GENERATION AND DISSIPATION MECHANISMS 3.IG MODELLING TECHNIQUES 4.INWAVE a. EQUATIONS AND NUMERICAL SCHEME b. HOW IS IT LINKED TO THE VORTEX FORCE? c. APPLICATIONS d. FUTURE PLANS

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OCEAN WAVES CLASIFICATION Storms, tsunamis Wind Sun, Moon Frequency (Cycles per second) 24 h 12 h5 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 Energy

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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.

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FIELD MEASUREMENTS OF IG WAVES Ruessink, 2010 sea-swell infragravity ≈ 15% Herbers et al., 1995

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SOME OF THE EFFECTS OF IG WAVES RUNUP AND BEACH-DUNE EROSION BEACH MORPHOLOGY ???? HARBOR RESONANCE

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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) We should include these processes if we want to solve the coastal erosion, overwash and breaching Hatteras Village, North Carolina Frisco, North Carolina

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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)

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Pressure gradient Radiation stress gradient BOUND WAVE RELEASE (Munk, 1949; Tucker, 1950)

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IG generation due to the breaking point movement (Symonds et al., 1982)

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The dominance of each mechanism depends on the slope regime (Battjes, 2004)

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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

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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.

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IG MODELING TECHNIQUES WAVE RESOLVING TECHNIQUES: BOUSSINESQ, PARTICLE TRACKING OR RANS MODELS WAVE AVERAGED OR PHASE AVERAGED TECHNIQUES: WAVE ACTION BALANCE EQUATION + NLSW

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Reniers, 2012 (long wave and runup Workshop)

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FREE SURFACE ELEVATION AND WAVE ENERGY ENVELOPE TIME VARIATION Time varying Wave forcings Infragravity wave generation Boundary condition for the wave action conservation equation 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 - Random phases - Double summation technique - Hilbert transform SWAN DOMAIN INWAVE DOMAIN BOUNDARY How do we model IG?

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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

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Random phase model JONSWAP, D( ) ~ cos s ( ) Hilbert Transform and low-pass filter Wave group energy (Hilbert transform)

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

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

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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 E 3 ( f) 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.

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1D CASE APPLICATION:DUCK 85 TEST CASE (LIST 1991) H5H4 H3H2R1 H1R2 R3 R4VS Sea surface measurements in station H5

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INWAVE MODEL: INPUTS H5H4 H3H2R1 H1R2 R3 R4VS

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INWAVE MODEL: RESULTS

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

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REAL APPLICATION: HURRICANE ISABEL Time varying wave spectra

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

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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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