SURFZONE WAVES I (PHASEAVERAGED)

Surf-Zone Wave Models I Phase-Averaged Models Existing Wave Decay Models • Battjes and Janssen 1978 • Thornton and Guza 1983 • Svendsen 1984 • Dally et al... Rayleigh pdf is normally a g

Surf-Zone Wave Models I

Phase-Averaged Models

Existing Wave Decay Models

• Battjes and Janssen (1978)

• Thornton and Guza (1983)

• Svendsen (1984)

• Dally et al (1985); Dally (1990, 1992)

• Larson (1995)

Energy dissipation from wave breaking:

2

2 2

s

gdH

P

d









(bore theory)

(Dally)

d

Dally Breaker Decay Model

(monochromatic waves)

2

2

cos

1

8

1

8

s

g

s

d



 

 

(Snell’s law yields change in wave angle)

(linear wave theory)

Random Waves

Wave-by-wave approach:

Transform each wave component representing the

pdf individually across the profile – add together

the components to obtain the statistical properties

of the wave field at any location (no need to

specify shape of the pdf except in the offshore).

Rayleigh pdf is normally a good

description in the offshore.

(Monte-Carlo simulation)

2

2

2

rms

p H

H

F H

H

Represent the Rayleigh pdf in the

offshore by N waves: H i , i = 1,N

Rms wave height is given by:

( ) ( )

n x q x N

n=number of non-breaking waves

q=number of breaking waves

1 ( )

1

1 1

n

i

q x

i

n

q













Let =q/N (ratio of breaking waves), then:

2 (1 ) 2 2

In the general case: non-breaking waves consists

of unbroken and reformed waves

1

     

 

cos

i

d

F

dx

d

 



non-breaking wave

breaking wave

Sum over all waves:

2

1

cos

n

i g

i

d

H C

dx

d



 





Add equations:

cos

q N

d



N

d



Interchange derivation and

summation, and develop:

1

1 cos

q

i



Substitute previous expressions:

d



Or:

d



2

2 2 2

1

8

1

8

rms rms g

2 cos 2

cos

go o

g

C

C







Wave transformation neglecting breaking:

Ratio of breaking waves:

2

x

d

H

Rms Wave Height for Unbroken Waves

2

2 0

0

b

b

d

H p H dH

H

p H dH











Solve for a Rayleigh pdf:

1

 

Wave Decay Over Non-Monotonic Profile

Breaking, unbroken, and reformed waves

occur in the general case.

1

1 8

If a negative slope is encountered, wave

reforming takes place.

2 2

b k gk k

d C

C

d k : smallest seaward depth

the ratio of reformed waves:

k r

rms r stab r





 = 0.5 (comparison with Monte-Carlo simulations)

Validation of Random Wave Model

SUPERTANK Laboratory Data Collection Project

DELILAH Field Experiment

SUPERTANK Data

Comparison Between Monte-Carlo Approach

and Random Wave Model