Wave Modeling

Local Wave Transformations

Billy L. Edge & Margery Overton

CVEN 695-02

Bathymetric Data

Why do we need wave models?

• Wave climate assessment at the project site is important to most coastal & ocean engineering projects, including- navigation and channel studies- on/offloading of ships- optimization of harbor layouts- design of structures (breakwaters, etc.)- shoreline erosion projects, etc.

• Nearshore wave conditions are normally determined from deepwater conditions- long-term nearshore wave data are usually unavailable- transform offshore wave data to nearshore (wind-generation, shoaling, refraction, breaking, dissipation, bottom friction) – regional scale models- investigate local scale phenomena (refraction, wave reflection, diffraction,

nonlinear wave-wave and wave-current interaction) –local scale models

Regional Scale Wave Modeling

• Scale O(100 km~5000 km)– Spectral wind-wave models (WAM)

• Scale O(10 km ~100 km)– Spectral wind-wave models (STWAVE and SWAN)– Dominant process: wind input, shoaling and refraction– Wave action: conservation equation– Assume phase-averaged wave properties vary slowly

over distances of the order of a wavelength– Cannot accurately resolve rapid variations that occur at

sub-wavelength scale due to wave reflection/diffraction

Local Scale Wave Modeling

• Scale O(1 km ~ 10 km)– Elliptic mild-slope model (CGWAVE)– Parabolic mild-slope model (REFDIF)– Boussinesq wave model (BOUSS-2D)– Dominant processes: shoaling, refraction, breaking,

reflection, diffraction, wave nonlinearities due to interactions of different frequencies and ambient currents and structures

– All models use vertically integrated eqns for wave propagation in 2D horizontal plane

– CGWAVE assumes hyperbolic cosine variation of the velocity potential over depth, and BOUSS-2D assumes a quadratic variation

Summary of Model Features

Phase resolvingPhase averagingPhase averaging

Diffraction/Reflection

Nonlinear Interactions

Wave-Current Interaction

Wave Breaking

Shoaling/Refraction

BOUSSCGWAVE/

REFDIFSTWAVE

Spectral Wind-Wave Models

• Advantages– wind-wave generation– shoaling, refraction, breaking– wave-current interaction– applicable to large domains (deep to shallow water)

• Disadvantages– reflection, diffraction– steady-state

Elliptic Mild-Slope Models

• Advantages– well suited for long-period oscillations– shoaling, refraction, breaking, bottom friction– reflection, diffraction– wave-current interaction (in future version)– flexibility of finite elements

• Disadvantages– nonlinear interactions in shallow water (in future

version)

Parabolic Mild-Slope Models

• Advantages– shoaling, refraction, breaking, bottom friction– Refraction, reflection, diffraction– wave-current interaction

• Disadvantages– Grid limitations in size and regular gridding

Boussinesq Wave Models

• Advantages– shoaling, refraction, breaking, bottom friction– reflection, diffraction, nonlinear interactions– wave-induced currents, wave-current interaction

• Disadvantages– computationally intensive– 2-D very computationally intensive

Applicability

• STWAVE:– ideal for wave propagation in open water

• SWAN:– time dependent, larger domain

• Mild-Slope:– ideal for long-period oscillations in harbors (CGWAVE)– suited for strong diffraction & reflection– more flexibility with finite element method(CGWAVE)– rapid solutions(REFDIF)

• BOUSS-2D:– ideal for wave transformation near entrance channels

and harbors – nonlinear interactions in shallow water– wave-induced currents near structures and surfzone

Engineering Practice - 1

• CORPS wave models have good physics to provide reliable estimates to projects

• Integrated with tools (SMS,etc.)• Used in support of a variety of research and engineering studies• Have strengths & weaknesses – no one model can do it all!• Validated with field/lab data & checked against analytical

solutions

• MIKE21 wave models …

• DELFT3D wave models …

• Wind forcing• Current forcing• Wave-current• Regional modeling• Deepwater wave

transformation up to pre-breaking depths

• Finite difference• Spectral, steady

state• Quick to run• Good front end

STWAVE computed wave Heights

STWAVE

CGWAVE

• Diffraction • Reflection• Refraction• Breaking• Bottom friction• Entrance losses• Finite element mesh• Spectral sea state• Wave-current

Interaction (in testing)

• Wave-wave Interaction (in testing)

• No wind Input CGWAVE Sea state for Morro Bay, CA

BOUSS-2D

• Time-dependent• Open coast, harbor

and surf zone waves• Shoaling, refraction,

reflection, diffraction,dissipation and run-up

• Finite difference• Random spectral sea

state modeling• Wave-induced

currents• Nonlinear waves,

sub- and super-harmonics BOUSS-2D Simulation for Everglades project

Engineering Practice -3

• Have to use models if no nearshore field data available

• Using models that are in common practice and have acceptance in the engineering community is preferred to one of a kind models

• Project-specific problems must determine the type of model for a study

• Detailed model documentation is necessary

Grays Harbor, Washington

Grays Harbor, Washington

Entrained Sand

Regions of Application of Wave Models

Solitary/Cnoidal Waves

Wave Prediction (Deep Water)

Combined Refraction and Shoaling(Dean and Dalrymple)

http://www.ndbc.noaa.gov/

Random Waves

• Analysis Methods– Eye– ZUC– ZDC– Spectral

Random Wave Spectra

JONSWAP

Wave Spectra

2

2 2

( )4exp

22 4 5

JONSWAPmax

Pierson Moskowitzmax

5( ) (2 ) exp

4

where

0.07 ,

0.09,

and

peak frequency

0 0081, Phillips Constant

E

E

m

m

f f

f

m

m

m

m

fE f g f

f

f f

f f

f

α .

TMAPierson MoskowitzOther

JONSWAP

Mild Slope Equation

http://www.coastal.udel.edu/refdif/img20.htm

CONCLUSIONS

• BOUSS-2D is a powerful nonlinear model for estimating waves in shallow and intermediate water depths where wave diffraction and nonlinearities are important

• Model is ready for project applications

• SMS interface of BOUSS-2D

• MAKE THINGS AS SIMPLE AS POSSIBLE BUT NO SIMPLER!!! – “Albert Einstein”

REFDIF