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
STWAVE
CGWAVE/
REFDIF
BOUSS
Shoaling/Refraction



Wave Breaking



Wave-Current Interaction



Nonlinear Interactions

Diffraction/Reflection


Phase averaging Phase averaging

Phase resolving
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 …
STWAVE
•
•
•
•
•
•
•
•
•
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
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 runup
• Finite difference
• Random spectral sea
state modeling
• Wave-induced
currents
• Nonlinear waves,
sub- and superharmonics
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)
Random Waves
• Analysis Methods
– Eye
– ZUC
– ZDC
– Spectral
Random Wave Spectra
JONSWAP
Wave Spectra
JONSWAP
E ( f )   g (2 ) f
2
 5 f  
exp      
 4  f m  
4
4
5
  ( f  f m )2 
exp 
2 2 
 2  f m 
where
 0.07 , f  f m

 0.09, f f m
and
f m  peak frequency
α  0.0081, Phillips Constant

E JONSWAP
max
Moskowitz
E Pierson
max
TMA
Pierson Moskowitz
Other
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