07 chapter 7 wave transformation

7/28/2019 07 Chapter 7 Wave Transformation

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Coastal & Marine

Environment

Wave

Transformation

Coastal & Marine Environment

Mazen Abualtayef

Assistant Prof., IUG, Palestine


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Wave TransformationWave transformation describes what happens to

waves as they travel from deep into shallow water

Deep

Shallow

Refraction

Shoaling

Diffraction


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Environment Wave TransformationWave transformation is concerned with the

changes inH

,L,C

and a, the wave anglewith the bottom contours; wave period T

remains constant throughout the process. To

derive the simpler solutions, wave

transformation is separated into wave

refraction and diffraction. Refraction is wavetransformation as a result of changes in

water depth. Diffraction is specifically not

concerned with water depth and computes

transformation resulting from other causes,such as obstructions. Discussions about

wave refraction usually begin by calculating

depth related changes for waves that

approach a shore perpendicularly. This is

called wave shoaling.


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b0

Shoaling

Coastline

H0

H

Eis the wave energy density

Ks is the shoaling coefficient


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Environment Wave refraction

As waves approach shore, the part

of the wave in shallow water slowsdown

The part of the wave in deep watercontinues at its original speed

Causes wave crests to refract(bend)

Results in waves lining up nearlyparallel to shore

Creates odd surf patterns


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We can now draw wave rays (lines representingthe direction of wave propagation) perpendicular

to the wave crests and these wave rays bend


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When the energy flux is conserved between the wave

rays, then

Wave refraction

where bis the distance between adjacent wave rays.

Kris the refraction coefficient


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EnvironmentAnother way to calculate K

rusing the wave direction of

propagation by Snells Law


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Environment Example 7.1Simple Refraction-Shoaling Calculation

A wave in deep water has the following

characteristics: H0=3.0 m, T=8.0 sec and

a0=30. Calculate Hand a in 10m and 2m of

water depth.

Answer:

L0= gT2/2 = 100m

For 10m depth:

d/L0= 0.10 and from wave table,

d/L = 0.14, Tanh(kd) = 0.71 and n= 0.81

Ks

= 0.93

a = 20.9

H = 2.70 m K

r= 0.96


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Environment Wave breakingWave shoaling causes wave height to increase to

infinity in very shallow water as indicated in Fig. 7.1.

There is a physical limit to the steepness of the waves,H/L. When this physical limit is exceeded, the wave

breaks and dissipates its energy. Wave heights are a

function of water depth, as shown in Fig. 7.7.


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7Chapter

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Environment Wave breaking

Wave shoaling, refraction and diffraction

transform the waves from deep water to the

point where they break and then the wave

height begins to decrease markedly, because

of energy dissipation. The sudden decrease inthe wave height is used to define the breaking

point and determines the breaking parameters

(Hb, d

band x

b).


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7Chapter

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Environment Wave breaking

The breaker type is a function of the beach

slope mand the wave steepness H/L.

Miche, 1944

McCowan, 1894; Munk, 1949

Kamphuis,1991

(7.32)

b

=


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Environment Example 7.2 - RSB spreadsheet

For this example with the beach slope m=0.02, Hb=2.9m

(Eq. 7.32) with ab=15.3, in a depth of water of 4.9 m.

Refraction-Shoaling-Breaking

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0.00 5.00 10.00 15.00Depth (m)

WaveHeig

ht(m) H (rs)

Hb (H/L)

Hb (d/L)

i


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Problem

Given: T=10 sec, H0=4 m, a

0=60

Find: Hand aat the depth ofd =15.6 m

Check if the wave is broken at that depth

Assume 0.78b

C t l M i


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Wave diffraction is concerned with the transferof wave energy across wave rays. Refraction

and diffraction of course take place

simultaneously. The only correct solution is to

compute refraction and diffraction together

using computer solutions. It is possible,however, to define situations that are

predominantly affected by refraction or by

diffraction. Wave diffraction is specifically

concerned with zero depth change and solvesfor sudden changes in wave conditions such

as obstructions that cause wave energy to be

forced across the wave rays.

Wave diffraction

C t l & M i


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Environment Wave diffractionPropagation of a wave around an obstacle

C t l & M i


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Environment Wave diffraction

C t l & M i


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Environment

Semi infinite rigid impermeable breakwater Through a gap

Wave diffraction

C t l & M i


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C t l & M i


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Environment Wave diffractionThe calculation of wave diffraction is quite complicated. For preliminary

calculations, however, it is often sufficient to use diffraction templates. One such

template is presented in Fig. 7.10.

Coastal & Marine


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Coastal & Marine


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When shoaling, refraction and diffraction all

take place at the same time, wave height may

be calculated as

Wave diffraction

Coastal & Marine


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Environment Wave reflection

2

2

0

.

/

r r i

r

r r

r i

H C H

aI mC I

b I H L

Coastal & Marine


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Environment Reflection The Wedge, Newport Harbor, Ca

waves

Wave energy is

reflected

(bounced back)

when it hits a solid

object.

Coastal & Marine


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What can affect the way that waves travel?

Wave refraction: the slowing and bending of

waves in shallow water.

Wave diffraction: propagation of a wavearound an obstacle.

Wave reflection: occurs when waves bounce

back from an obstacle they encounter.

Reflected waves can cause interference withoncoming waves, creating standing waves.

Standing waves: are found in inlets and bays

They remain in a fixed position

Summary

07 chapter 7 wave transformation

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