Wave

Refraction

Lessen Outcomes

• To explain wave refraction effect at nearshore• To perform wave refraction analysis

Wave front - A curve in the horizontal plane through adjacent crest points.

Wave orthogonal/ray – Path perpendicular to the wave fronts at every point.

Wave Advance

Wave Front

Orthogonal

Wave

Front

Horizontal Plane

Wave front

Wave Advance

Wave refraction is the bending effect of wave crest in order to align with bottom contours as waves are moving over different depths.

During refraction, the wave crest/front bends to align themselves with the bottom contour and the wave ray becomes more perpendicular to the shore.

Wave Refraction

Oblique Waves Refracting across a

Uniformly Sloped Shelf

At deep water (d/L > 0.5), the wave celerity (C) is constant. o

is the angle between wave crest and bed contour OR between the orthogonal and a normal to the bed contour.

At intermediate depths (d/L < 0.5), the wave crests bend. o

reduce to .

Refraction of a Wave over a Step

L

d

C

C 2tanh

0

ooo L

L

L

d

C

C

sin

sin2tanhSnell’s Law:

Snell’s Law

L

d

L

L

C

C

oo

2tanh

sin

sin

0

The amount of reduction or amplification of waves due to refraction depends on:a. bathymetryb. the initial angle of approachc. wave period

Wave Refraction

Wave convergence or divergence, which is determined by the shape of the bottom topography, causes energy to be concentrated or spread out.

Where there are points or promontories projecting into the sea, wave fronts on both sides turn toward the point. A greatly increased amount of wave energy will be focused toward the point, and will tend to wear it away over time.

Wave Refraction

Energy Distribution

Wave refraction analysis provides:

(1) Pattern of wave transformation from deepwater to shallow water.

(2) Determination of the near-shore wave properties and the energy distribution along the coast.

Refraction Analysis

Consider the principle of energy conservation, the power transmitted forward between the two orthogonals is assumed to be constant, so that:

PPo

ggooo C

bgHC

bgH

88

22

ggoo ECCE

rso

g

goo

g

go

o

KKC

C

b

b

C

C

H

H

5.05.05.05.0

cos

cos

Kr = Refraction Coefficient

Refraction Analysis

Refracted wave height, H is given by

Ho’ = Unrefracted deepwater wave heightKs = Shoaling coefficientKr = Refraction coefficient

Refraction Analysis

'o

sH

HK

4

2

0

2

1

sin1

sin1

cos

cos

oor

B

BK

rs

o

KKH

H

Variation of Wave Celerity and

Angle with Depth

L

d

L

L

C

C

oo

2tanh

sin

sin

0

d/Lo

Parallel Contour:

Refraction Relationship

between d/Lo, Cd/Co,

o and

A wave in deep water has the following characteristics:

Ho = 3 m, T = 8 sec, m = 0.02 and o = 30o

a. Calculate Ks, , Kr and H in 10 m of water depth.b. Determine db and Hb.c. Locate the breaker line.

Problem