Coastal & Marine
Environment
Chapter
7
Coastal & Marine Environment
Wave
Transformation
Mazen Abualtayef
Assistant Prof., IUG, Palestine
Coastal & Marine
Environment
Chapter
7
Wave Transformation
Wave transformation describes what happens to
waves as they travel from deep into shallow water
Diffraction
Shoaling
Deep
Refraction
Shallow
Coastal & Marine
Environment
Chapter
7
Wave Transformation
Wave transformation is concerned with the
changes in H, L, C and a, the wave angle
with 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 wave
transformation 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.
Coastal & Marine
Environment
Shoaling
b0
Chapter
H0
7
H
E is the wave energy density
Ks is the shoaling coefficient
Coastline
Coastal & Marine
Environment
Chapter
7
Wave refraction
• As waves approach shore, the part
of the wave in shallow water slows
down
• The part of the wave in deep water
continues at its original speed
• Causes wave crests to refract
(bend)
• Results in waves lining up nearly
parallel to shore
• Creates odd surf patterns
Coastal & Marine
Environment
Chapter
7
Wave refraction
Coastal & Marine
Environment
Wave refraction
Chapter
7
We can now draw wave rays (lines representing
the direction of wave propagation) perpendicular
to the wave crests and these wave rays bend
Coastal & Marine
Environment
Chapter
7
Wave refraction
When the energy flux is conserved between the wave
rays, then
where b is the distance between adjacent wave rays.
Kr is the refraction coefficient
Coastal & Marine
Environment
Chapter
7
Another way to calculate Kr using the wave direction of
propagation by Snell’s Law
Coastal & Marine
Example 7.1
Environment
Simple Refraction-Shoaling Calculation
Chapter
7
A wave in deep water has the following
characteristics: H0=3.0 m, T=8.0 sec and
a0=30°. Calculate H and a in 10m and 2m of
water depth.
Answer:
L0 = gT2/2π = 100m
For 10m depth:
d/L0 = 0.10 and from wave table,
d/L = 0.14, Tanh(kd) = 0.71 and
 Ks = 0.93
 a = 20.9°
 Kr = 0.96
 H = 2.70 m
n = 0.81
Coastal & Marine
Environment
Chapter
7
Coastal & Marine
Environment
Chapter
7
Wave breaking
Wave 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.
Coastal & Marine
Environment
Wave breaking
Chapter
7
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 in
the wave height is used to define the breaking
point and determines the breaking parameters
(Hb, db and xb).
Coastal & Marine
Environment
Chapter
7
Wave breaking
The breaker type is a function of the beach
slope m and the wave steepness H/L.
Miche, 1944
 b = 0.78
McCowan, 1894; Munk, 1949
Kamphuis,1991
(7.32)
Coastal & Marine
Environment
Chapter
7
Example 7.2 - RSB spreadsheet
Refraction-Shoaling-Breaking
6.00
Wave Height (m)
5.00
H (rs)
Hb (H/L)
Hb (d/L)
4.00
3.00
2.00
1.00
0.00
0.00
5.00
10.00
15.00
Depth (m)
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.
Coastal & Marine
Environment
Problem
Chapter
7
Given: T=10 sec, H0=4 m, a0=60°
Find: H and a at the depth of d =15.6 m
Check if the wave is broken at that depth
Assume  b  0.78
Coastal & Marine
Environment
Chapter
7
Wave diffraction
Wave diffraction is concerned with the transfer
of 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 solves
for sudden changes in wave conditions such
as obstructions that cause wave energy to be
forced across the wave rays.
Coastal & Marine
Environment
Wave diffraction
Propagation of a wave around an obstacle
Chapter
7
Coastal & Marine
Environment
Chapter
7
Wave diffraction
Coastal & Marine
Environment
Chapter
7
Wave diffraction
• Semi infinite rigid impermeable breakwater
• Through a gap
Coastal & Marine
Environment
Chapter
7
Wave diffraction
Coastal & Marine
Environment
Wave diffraction
The calculation of wave diffraction is quite complicated. For preliminary
calculations, however, it is often sufficient to use diffraction templates. One such
Chapter
template is presented in Fig. 7.10.
7
Coastal & Marine
Environment
Chapter
7
Wave diffraction
Coastal & Marine
Environment
Wave diffraction
Chapter
7
When shoaling, refraction and diffraction all
take place at the same time, wave height may
be calculated as
Coastal & Marine
Environment
Wave reflection
Chapter
7
H r  Cr .H i
2
r
aI
Cr 
2
b  Ir
Ir 
m
H i / L0
Coastal & Marine
Environment
Chapter
7
Reflection
The Wedge, Newport Harbor, Ca
Wave energy is
reflected
(bounced back)
when it hits a solid
object.
waves
Coastal & Marine
Environment
Chapter
7
Summary
What can affect the way that waves travel?
Wave refraction: the slowing and bending of
waves in shallow water.
Wave diffraction: propagation of a wave
around an obstacle.
Wave reflection: occurs when waves “bounce
back” from an obstacle they encounter.
Reflected waves can cause interference with
oncoming waves, creating standing waves.
Standing waves: are found in inlets and bays
They remain in a fixed position