National Center for Computational Hydroscience and Engineering

The University of Mississippi

Wave Model of CCHE2D-CoastFor Model Training Course

Yan Ding, Ph.D.

Research Assistant ProfessorNational Center for Computational Hydroscience and Engingeering

The University of Mississippi, Oxford, MS 38677

March, 2008

Deformation of Irregular Waves

Deformation of waves from offshore to onshore

• Shoaling

• Refraction

• Diffraction

• Reflection

• Wave Breaking

• Wave Transmission through structure

• Bottom Friction

• Wave-Current Interaction

•……

Incid

ent W

ave

Wave Transmission through a Nonsubmerged Structure

Wave transmission coefficient Kt= Hr/Hf

Transmission through and over a riprap structure

Hr = Wave height transmitted to the water body in the rear side of the structureHf = Wave height in front of the structure

Overtopping

Kt can be determined by means of the experimental studies on the features of structures; The values can be found from most of coastal textbooks and coastal engineering manuals

Irregular Wave Models

• Phase-averaged models1. Short-wave-averaged models dealing with irregular and

multidirectional waves developed on a statistical basis;2. Spectral Energy Balance Equation (SEB);3. The models can predict irregular wave transformation in a large-

scale region (1-100km), but not time-varying wave conditions

• Phase-resolving models1. Simulate the time-varying processes of short waves, and even

wave breaking process; 2. It’s suitable for small region and can give highly spatial

resolutions.

Multidirectional Wave Spectral Model (1)

• Energy Balance Equation + Diffraction The variations of wave energy density S(x,y,,f) under the

attack of irregular/multi-directional incident waves, can be represented as follows, (Mase 2001)

wave ray

shoreline

x

y

2

222 cos

2

1cos

2 y

SCC

y

SCC

yQ

Sv

y

Sv

x

Svgg

yx

where = wave direction (-0.5 – 0.5), v = energy transport velocity, Q = source term arisen from energy dissipation, e.g., wave breaking and bottom friction. = empirical coefficient (=2.0-3.0). C=wave celerity, Cg=wave group celerity

Diffraction Term

Fig. Coordinate System

y

C

x

C

C

CvCvCv g

gygx cossinsin,cos

f

S(f)

o fp

Wave Spectrum S(f,θ) and Wave Properties

D NarrowBroad

O

( , ) ( ) ( , )S f S f D f

/ 2

0 / 20

1( , )S f dfd

m

S(f)= Wave Frequency SpectrumD(θ,f)= Wave Directional Spreading Function

• Multidirectional Wave Spectrum Energy

• Significant Wave Height H1/3 Based on the Rayleigh Distribution

0

2

mT

m

/ 2

0 0 / 2( , )m S f dfd

1/3 04.0H m

• Total Wave Energy

• Mean Wave Direction

• Averaged Wave Period

Wave Spectral Model (2)Frequency Spectra S(f)

• Bretschneider-Mitsuyasu (1970) (B-M Spectrum)

• Texel Marsen Arsole (TMA) Spectrum (Bouws et al. 1985)

43/1

543/1

23/1 )(

05.1exp257.0)(

fTfTHfS

),(2

)(expln25.1exp

)2()(

22

24

54

2

hff

ff

f

f

f

gfS

p

pp

h=water depthfp=peak frequency= peak enhancement factor

21

21)2(5.01

1)(5.0

),( 2

2

h

hh

hh

for

for

for

hf

2/1)/(2 ghfh

ff

ff p

09.0

07.0

f

S(f)

o fp

D NarrowBroad

O

• Bretschneider-Mitsuyasu (B-M) Spectrum

• Texel Marsen Arsole (TMA) Spectrum (Bouws et al. 1985)

Wave Spectral Model (3)Directional Spreading Function D(q,f)

2cos),( 2

0

sGfD

J

jmm jjfD

1

2 )(cos)(5.0exp1

2

1),(

cedisdecaylongwithswellfor

cedisdecayshortwithswellfor

waveswindfor

S

tan75

tan25

10

max

)1(

)1(2 212

0

s

sG

s

ffsff

ffsffs

p

pp

max5.2max

5

)(

)(

m=mean wave direction; J=number of terms in the series (=20)m= spreading parameter

Wave Breaking Criteria

• Goda’s Criterion (Goda 1975)

)151(5.1exp(1 3/4

00

L

hA

L

Hb

Hb = Breaking Wave HeightL0 = Wave LengthA = Empirical Coefficient (0.12 – 0.18) = Sea Bed Slope

• Saturated Wave Breaking

bH hh = water depth γ = empirical coefficient, 0.6-0.8

Generation of Non-Orthogonal Mesh Covering Touchien Estuary

CCHE2D Mesh Generator

http://www.ncche.olemiss.edu/index.php?page=freesoftware#mesh

Close-up View of Mesh

Wave Spectrum Input

x

y

Onshore

Offshore

+θ

-θ

Offshore wave spectral properties:

Wave height (m)Period (s)Mean Direction (Deg)Tide Elevation (m)

Input Data (1)

Filename = *_wave.dat, where * = a project name, e.g. touchien

Input Data (2)

Filename = n_karl.dat

OutputFilename = wave_res.plt

Demonstration Dialogue Input

Contact Information

Yan Ding, Ph.DNational Center for Computational Hydroscience and EngineeringThe University of MississippiCarrier Hall, Room 102University, MS 38677U.S.A.

Email: ding@ncche.olemiss.eduPhone: +1 (662) 915-1339Website: http://www.ncche.olemiss.edu