2. • A surface wave is an oscillatory disturbance
that moves across the sea surface.
What is the surface wave?
Porf. Dr. Khaled Alam El-Din
3. When a wave travels, it propagates the wave form
(energy) but there is no real transfer of mass.
Energy traveling along the interface between ocean
and atmosphere
Wave Motion
5. The wave crest is the highest part of the wave above
mean sea-level.
The wave trough is the lowest part under mean sea-
level.
The wavelength, L [m], is the horizontal distance
between two successive crests, or troughs.
The wave height, H (m), is the vertical distance
displacement between a crest and the adjacent trough
The amplitude, a [m], is the maximum displacement
from the mean sea-level.
The wave period, T [s], is the time interval between
the passage of two successive crests at a fixed point.
The frequency, f [Hz], is the number of crests
passing a fixed point per second
The Wave Parameters
7. Wave Energy
• Wave energy is directly proportional to
wave height squared.
• where:
E = wave energy per unit area (J/m2)
= water density (kg/m3)
g = gravity (m/s2)
H = wave height (m)
8. Significant wave height
• Hs is the mean height of the highest one third of the
waves passing a point.
• Mean H = Average wave height
Hs or H1/3 = Significant wave height
H1/10 = Average of the highest one-tenth wave height
Hmax = Maximum probable wave height for a large
sample of waves
Other wave height can
be computed from Hs,
• H1/10 = 1.27 Hs
Hmean = 0.64 Hs
Hmax = 1.87 Hs,
9. The wave steepness is the ratio of wave
height to wavelength (= H/L).
• When H/L is larger than or equals 1/7 (H/L
1/7), or when the angle of wave crest is less
than 120°, the wave becomes unstable.
Wave steepness and stability
10. The relative depth is the ratio of water
depth to wavelength (= h/L).
• When h/L is greater than or equal ≥ (1/2) the
wave denotes Deep-water waves
• When h/L is less than or equal ≤ (1/20) the
wave denotes Shallow-water waves
• When (1/20) < h/L < (1/2) the wave denotes
Transitional waves
Relative Depth
& deep and shallow water waves
11. a- Deep-water waves
Water depth is greater than
wave base ≥ (1/2)L
No interaction with the
bottom
Water particles move in
circle,
Diameter of orbital motion
decreases with depth of
water
Wave speed (celerity)
proportional to wavelength
For deep-water waves,
long waves are fast waves
Wave speed (C) = 1.25 L
Wave speed (C) = 1.56 x T
Wavelength (L) = 1.56 x T 2
12. b-Shallow-water wave
Water depth is < (1/20)L
Orbital motion getting
squished by the Bottom into
ellipses that approximate
Back and forth motion near
bottom.
Wave speed (celerity)
proportional to depth of
water.
Wave speed (C) = g h
For shallow water waves,
the deeper the water, the
faster the wave
13. 1. Deep water wave has a wave height 2 m and wave
period 11 sec, find out the depth at which the motion of
the water particles diminish & the wave energy and
power.
2. Calculate the wave energy and power of shallow water
wave has a height 2.5 m at a water depth 5 m.
3. A surface wave has a wave period 11 sec and wave
height 2.2 m in deep water find out:
a- The wave speed
b- Wave energy
c-Wave power.
d- Wave steepness and discuss the stability.
14. 1. If you know that a surface wave has a height 2.4 m and
wave length 150 m is approaching to a shallow water of
a depth 6m find out:
a- The relative depth and determine the wave type.
b- the wave speed
c- Wave energy.
d- Wave power.
15. Factors that control wave energy
(generation and growth)
1. Wind speed
The faster the wind blows, the more energy they
possess, and the bigger the waves will appear.
2. Wind duration- Length of time that the wind
blows
The longer the duration - length of time that the wind blows- the
bigger the waves.
3. Fetch- Distance over which the wind blows in a
single direction
The same goes for the fetch – the larger the area of
wind/water interaction, the bigger the waves.
16. When the wind blows for - theoretically - unlimited
fetch and duration, the sea reaches the maximum
wave height, wavelength for particular wind speed at
equilibrium conditions “fully developed sea” .
Waves cannot grow further because they are losing
energy through breaking whitecaps.
When the fetch is small and/or the period is short the generated
waves become limited and called limited in fetch and/or duration.
Fully developed sea
17. Sea waves and Swell
Swell
Uniform, symmetrical waves that
travel outward from storm area
Travel faster than the wind outside
the storm, so wave heights decrease
Longer wavelength transport
energy long distances
Sea waves
Random waves inside the storm
area under the wind action
Has different wave heights,
lengths, periods, and directions.
Height increases faster than the
length …. Hence the wave become
unstable and breaks (whitecaps)
18. Current Effect on Waves
Same direction
• Wave speed increases
• Wavelength increases
• Wave height decreases
• Wave steepness
decreases
• Wave becomes More
stable
Opposite direction
• Wave speed decreases
• Wavelength decreases
• Wave height increases
• Wave steepness
increases
• Wave becomes unstable
and break
Wave Current Wave Current
20. Wave Refraction (2)
• Energy focused
on headland
– Headland
eroded
• Energy
dissipated in bay
– Bay filled up
with sediment
21. Wave Diffraction
A. When waves approach barriers with gaps, the wave will be
observed to spread or disperse upon passing through the gap.
B. If waves approach a barrier with multiple gaps, wave diffraction will
occur as the wave passes through each gap, and the spreading
waves may interact both destructively and constructively. Thus,
barriers with many gaps can efficiently scatter wave energy, often
diminishing the height and power of waves.
22. Wave Reflection
& Standing wave
Waves and wave energy bounced back
from barrier
Reflected wave can interfere with next
incoming wave and make a standing wave
23. Wave Breaking
Top of wave topples over base because of
decrease in wave speed due to friction with
seafloor until
The particle speed become faster than the
wave speed or celerity (u > C) ,
The wave steepness (H/L) > 1/7 or
The wave height equal 0.78 of water depth
(H ≥ 0.78h).
Different types of breakers associated with
different slope of seafloor
24. Breaker types
a- Spilling breaker
Water slides down
front slope of wave
Gently sloping
seafloor (1:50)
Wave energy
expended over
longer distance
Best for Recreation
25. b- Plunging breaker
Curling crest
Moderately steep
seafloor (1:20)
Wave energy
expended over
shorter distance
Best for board
surfers
Breaker types
26. c- Surging breaker
Breakers on shore
Steepest seafloor
Energy spread over
shortest distance
Best for body
surfing
Breaker types
27. a- Long-shore Current
Current in surf zone
Flows parallel to the shore
Moves substantially more sediment than
beach drift
28. b- Rip Current
Current in surf
zone
Narrow and
strong current
flows offshore
direction.
Transport
sediment
offshore.
29. • Geometry of the basin controls the period of the standing wave.
A basin can be closed or open.
• Resonance amplifies the oscillation and occurs when the
period of the basin is similar to the period of the force
producing the standing wave.
Seiches
30. For n order seiches in
Seiches
2. open basin
T = 4 * l / (2 n - 1) √ (g * h)
Where T : wave period, l : Length of the basin, g : gravity acc.
h : Average depth and n = Oscillation mode
n = 1 for the main frequency and 2 for the 1st harmonic frequency and so on.
Example:
A longitudinal lake has a length of 220 km and an
average depth of about 10m. Calculate the period of the
main and fist order natural frequency.
Solution:
l = 220 km = 220 000 m, n = 1, g = 9.8 m/s2, h = 10 m
T main = 2 * l / (n √ (g * h)) = 2 * 220,000 / √ 9.8 * 10
= 44446.7 sec = 12.3 hr
T 1st = 2 * 220,000 / 2 * √ 9.8 * 10 = 6.15 hr
1. close basin
T = 2 * l / (n √ (g * h))
31. • Internal waves form on the interface between two layers
of different densities (the surface of density
discontinuity)
• Thus, Internal waves form within the water column on the
pycnocline.
• Any disturbance to the pycnocline can generate internal
waves, including: Flow of water related to the tides., Flow of
water masses past each other, Storms, or Submarine
landslides.
• Internal waves display all the properties of progressive waves
including reflection, refraction, interference, breaking, etc.
• Because of the small density difference between the water
masses above and below the pycnocline, wave properties
are different compared to surface waves.
Internal waves
32. • An internal wave propagating on the interface between two layers.
Water particles are shown as yellow and magenta dots. Yellow dots
sit in the middle of the water column and move only up and down.
Magenta dots sit at the top and bottom of the water column and
move only in the horizontal.
By watching a yellow dot you can see how a water particle in the
middle of the water column moves up and down, but does not move
horizontally, as the wave passes through.
Internal waves
33. • Storm surge is the rise in sea level resulting from
low atmospheric pressure associated with storms
and the accumulation of water driven shoreward
by the winds.
• Storm surge is especially severe when
superimposed upon a high tide.
• Storm surge is become danger in Lower coastal
areas located in a shallow sea
Storm Surge
34. Tsunami
The word tsunami comes from the Japanese word
meaning "harbor wave.“
A tsunami (pronounced sue-nahm-ee) is a series of
huge waves that can cause great devastation and loss of
life when they strike a coast.
Tsunamis were previously called tidal waves, but are
unrelated to tides.
They only become a danger when reaching coastal
areas where wave height can reach 30 m.
36. Tsunami characteristics
• Long wavelengths (> 200 km or 125 miles)
• Shallow-water wave
• Speed proportional to water depth so very fast in open
ocean. Maximum speed = 800 km/hr
• Sea level can rise up to 40 m (131 ft) when tsunami
reaches shore
• Usually creates a surging front of water at the shoreline
instead of breaking wave
– Like a sudden extreme high tide (hence originally called tidal
waves)
– Preceded be a sudden recession of water (the trough)
– The recession and surge are separated by several minutes.
Why?
– Several surges…series of waves
37. C= √ (g * h)
Where, C : the speed of tsunami, g : gravity acc.
h : depth of the earthquake
Example:
Calculate the speed of the tsunami caused by an
earthquake occurred at 5000 m depth. Then, calculate the
time interval to reaches an island at a distance 500 km from
the center of the earthquake
Solution:
g = 9.8 m/s2, h = 5000 m & l =500 km
C = √ (9.8 * 5000) = 221.4 m/s = 796.9 km/hr
T = Distance / speed = 500/796.9 = 0.62 hr = 37.64 min
Tsunami
Because of their large wave length, tsunamis are
shallow-water waves as they travel across the
ocean basin. The wave velocity depend on depth
38. Review
Discuss the following, draw when possible:
1.Factors affecting wave generation and growth.
2.Compare between sea waves and swell.
3.Wave refraction phenomenon.
4.Movements of the water particle under waves in shallow
and deep water.
5.Types of wave breaker.
6.Effect of currents on the wave characteristics.
7.Near-shore currents
8.Seiches.
9.Storm surge.
10.Tsunami.
39. Review
Rewrite the following sentences after doing the
necessary changes:
1.When a wave propagates towards shallow water, its period
will decrease and length will increase.
2.The rip current is fast and (narrow) wide current moves
parallel to the coast (offshore) .
3.The sea level increases by about (5) 50cm when the
atmospheric pressure (decreases) increases by 5 mb.
40. Review
Complete the following:
1.Water particles move under deep water waves in a ……….. orbit, that
decreases in ……. With depth. Particles at a depth greater than ½
wavelength have no motion.
2.Factors affected the generation and growth of the gravity waves are
…………, ………………. & …………….
3.The wave breaking on beaches has three types which are…Spilling……,
plugging……….. & …Surging…….
4.…… Surging ……. breaker occurs at steep slope beaches and these
coasts are characterized by a small width of … surf zone ……
5.Surging……….. breaker occurs at steep slope beaches and these coasts
are characterized by a …Narrow……. surf zone width.
6.…Spilling…….. breaker occurs at gentle slope beaches and these coasts
are characterized by a wide width of …… surf zone ……..
7.The sea level rises by about …1…… cm when the atmospheric pressure
decrease……. by 1 mb.
41. Review
1. Deep water wave has a wave height 2 m and wave period
11 sec, find out the depth at which the motion of the water
particles diminish & the wave energy and power.
2. Calculate the wave energy and power of shallow water
wave has a height 2.5 m at a water depth 5 m.
3. A surface wave has a wave period 11 sec and wave height
2.2 m in deep water find out: i- The wave speed ii- Wave
energy iii-Wave power. iv- Wave steepness and discuss
the stability.
4. If you know that a surface wave has a height 2.4 m and
wave length 150 m is approaching to a shallow water of a
depth 6m find out: i- The relative depth and determine the
type. ii- the wave speed iii- Wave energy. iv- Wave power.
42. Review
1. A longitudinal lake has a length of 220 km and an average
depth of about 10m. Calculate the period of the main
natural frequency.
2. Calculate the speed of Tsunami at the center of an
earthquake located at Mindanao Trench (11524m) west
the Pacific Ocean. Then, find the estimated time for that
wave to arrive an Island 200 km away from the center of
the earthquake.
3. Calculate the speed of Tsunami waves at the center of an
earthquake located at a depth of 5500 m in the Indian
Ocean. Then, find the approximate time for that wave to
arrive a coast 400 km away from the center of the
earthquake.
