C O A S T A L W A V E S

Any perturbation of the interface between air and water is considered a wave. [ Internal waves : on interface between layers of water, e.g. between saltwater and fresh water]

Waves impart forces on: o structures o beach > sediment transport

Basic terminology:
L = wave length; H = wave height; T = wave period (remains same) f = 1/T = frequency; Amplitude, a = H/2; Wave number, k = 2

/L
Circular frequency,

= 2

/T; Wave speed (celerity), C = L/T

Wind wave generation:
- primary forcing function is wind > wind waves
- other forcing functions: earthquake > Tsunamis
- wind wave generation process:
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Dr. M.S. Khan


Factors determining wave height:
- wind speed: higher wind speed > higher waves
- fetch : distance over which wind blows
(smaller waves at the upstream end of fetch; cyclones, Nor’westers have longer fetch)
- Duration of wind: longer duration > higher waves
- Water depth: shallower water > higher waves

Spatial and temporal variation in wave height:
- Ocean waves are actually irregular w.r.t. x and t
(needs statistical analysis)
- However, individual ocean waves can be assumed to be regular (for simplicity of analysis)
- Significant wave height , H s
: Average height of the highest 1/3 of waves
Example of Significant Wave Height (Hs) Calculation
Measurement
No.
1
H (ft)
2.3
Highest 1/3 wave hts. (ft)
6.2
Ave height (ft)
Hs
5.3
2
3
4
1.5
1.1
4.5
6.0
5.9
5.6
5
6
7
8
9
10
5.2
6.2
1.8
4.2
2.3
3.4
5.2
5.1
4.8
4.7
4.6
4.5
17
18
19
20
21
22
11
12
13
14
15
16
23
24
25
26
27
28
29
30
3.2
4.4
5.1
4.1
3.8
2.9
4.3
2.8
3.7
4.7
4.6
5.9
2.4
1.9
1.6
2.4
5.6
4.8
6.0
1.4
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Dr. M.S. Khan

Linear Wave Theory
(also known as ‘Airy’ wave theory)

Free surface elevation,
  a cos
 kx
  t

(sinusoidal variation in both space and time) a = amplitude = H/2 x = horizontal distance t = time

Wave length, L
 gT
2
2
 tanh
2
 d
L g = acceleration of gravity
(needs trial and error solution for L!) d = water depth tanh = hyperbolic tangent
* L and H changes with d, but T remains the same.

Deep water (d/L > 0.5) wave length, L o
 gT
2


Shallow water (d/L < 0.04) wave length, L

2
T

Water particle excursion under waves: gd
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Dr. M.S. Khan


Wave energy:
Energy in by: wind
Energy out by: - wave breaking
- bottom friction
- internal turbulence

Wave transformation (from deep to shallow water)
- Shoaling : change in wave height.
Shoaling coefficient,
K
S

1 C o
2 C g
C o
= L o
/T; C = L/T
C g
= nC n

1
2

 1

2 sinh kd
2 kd

 sinh = hyperbolic sine
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Dr. M.S. Khan

- Refraction : change in angle between the shoreline and the wave crest line.
Refraction coefficient,
K
R
 cos cos

 o

Wave height at depth d,
H = H o
K
S
K
R
H o
= deep water wave height

Breaking waves:
- wave energy is dissipated by breaking when H/d > 0.78
- breaking causes intense turbulence and erosion
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Dr. M.S. Khan

Surging
- major ‘breaker’ types:
- Spilling
- Plunging
- Collapsing
- Surging
Spilling
Plunging
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Dr. M.S. Khan

Other Wave Theories
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Tsunami special type of ocean waves; Japanese, meaning 'harbor waves'
Tsunami propagation: animation
Tsunami Generation:
May generate from:

vertical displacement of ocean floor because of earthquake

submarine landslide

underwater volcanic eruption

impact of meteorite
Characteristics:

Relatively long wave length (200 - 300 km in deep sea, compared to normal wave length of 50 - 100 m in shallow water)

Relatively high velocity (700 - 800 km/hr)

Wave height increases in shallow water ('shoaling')
Threat to Bangladesh:

Historical evidence indicates that tsunami effects reached as far inland as the
Buriganga near Dhaka

The most devastating tsunami for Bangladesh coast originated near the
Myanmar coast

December 2004 earthquake in Indonesia caused subduction of India Plate beneath Burma Plate

Caused sudden release of energy and vertical displacement up to 30 m along a
1200-km long region

Waves propagated mostly in the East-West directions to Indonesia, Thailand, Sri
Lanka and Southern India. Waves reached as far as the Eastern coast of Africa!

Local waters along the Bangladesh coast was disturbed for several hours

Two deaths and several capsized boats were reported

The wave energy of a tsunami generated near Indonesia or Andaman Islands may have insignificant impact on Bangladesh coast, because of: o Relatively long and shallow continental shelf (200-km long, 10 - 20m deep) o Most energy would be dissipated near the origin in the shallow waters of the
Andaman and Indonesia coasts o Most energy would propagate in the E-W directions because of the existing faultline orientation

However, tsunami generated elsewhere (e.g. Myanmar coast) or at other energy release orientation may have severe impact on Bangladesh coast.

Tsunami modeling of the northern Bay of Bengal (report).
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Dr. M.S. Khan

3.00
2.50
2.00
1.50
1.00
0.50
0.00
0:00 4:48
Hiron point (26 Dec)
9:36 14:24
Tim e (m in)
19:12
Predicted
Observed
0:00 4:48
Fig.1: Water level fluctuation at Hiron Point.
Char Chenga (26 Dec)
3.00
Predicted
Observed
2.50
2.00
1.50
1.00
0.50
0.00
0:00 4:48 9:36 14:24
Tim e (m in)
19:12 0:00
Fig.2: Water level fluctuation at Char Chenga.
4:48
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Tsunami Modeling and Hazard Assessment
Tsunami Hazard Assessment in the Northern Bay of Bengal
Final Report
March 2011
Institute of Water and Flood Management,
Bangladesh University of Engineering and Technology
Institute of Water Modelling
In Collaboration with:
Bangladesh Water Development Board
Geological Survey of Bangladesh
Department of Geology, University of Dhaka
Jadavpur University, Kolkata, India
Fault source map
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Geological classification of tsunami hazard (tsunami vulnerability regions) (Karim et al., 2005)
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Initial surface
Wave transformation across the continental shelf
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Tsunami travel time to four locations on the Bangladesh coast
Case/
Source
FS 1
FS 2
FS 3
FS 4
FS 4’
Swatch of
No Ground
Travel Time (min)
Borguna Meghna
Coast Estuary
80 90 40
100
130
120
110
140
130
100
140
110
90 90 90
Cox’s
Bazaar
10
70
110
100
80
Transect
Maximum wave height of tsunamis for different cases
Swatch of
No Ground
Borguna
Coast
Meghna
Estuary
Cox’s
Bazaar
Location Maximum Wave Height (m)
FS 1 FS 2 FS 3 FS 4
FS 4’
Cont. Shelf 0.11 0.17 0.06 0.01 0.14
Shoreline 0.09 0.03 0.02 0.01 0.05
Cont. Shelf 0.33 0.16 0.27 0.06 0.14
Shoreline 0.14 0.05 0.04 0.02 0.06
Cont. Shelf 0.83 0.21 0.11 0.07 0.01
Shoreline 0.33 0.14 0.11 0.06 0.02
Cont. Shelf 0.85 0.23 0.09 0.06 0.03
Shoreline 0.98 0.12 0.04 0.02 0.02
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Maximum inundation map for scenario FS 1
Combined inundation map of tsunami in the coastal region of Bangladesh
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Dr. M.S. Khan

Random Waves: Wave spectra
Periodic Composite Waves
(Superposition)
- Ocean waves can be assumed to be combination of a huge number of sinusoidal waves of different amplitude and frequency.
Wave Spectra
Ocean waves are random in terms of wave height and period. This randomness can be represented by wave height or energy spectrum.
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Various design spectra have been proposed based on assumptions that the spectrum is narrow-band and sea surface elevations are Gaussian.
Pierson-Moskowitz Spectrum
(empirical eqn. For shape) s
 

H
2 s
4



2
T
 z


4
 
5 exp






2
T
 z


4 


4
T z
= zero-crossing period
= T p
/1.408
T p
= peak period


JONSWAP Spectrum
(Joint North Sea Wave Program; for deep water waves)
E
 

2

  g
4
2 f 5 exp



5
4

 f f m



4 

 exp

= fct. of wave height

= a parameter f m
= peak frequency

= peakedness factor

 f
 f m

2
2
 2 f
2 m
Currents o Ocean Currents: Originate in open ocean, but intrude into nearshore zone. o Tidal Currents: Act through estuaries, tidal inlets, straits between land masses, etc. o Nearshore currents:
- Wind induced: currents created in shallow water caused by wind shear stress on surface
- Wave induced: longshore currents, rip currents.

Longshore current:
- alongshore component of incident waves
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Dr. M.S. Khan

- causes longshore sediment transport ( littoral drift )

Rip-current:
- Offshore-directed release of accumulated incident
wave energy
- Usually present when incident waves are shore-perpendicular
- Can be identified by less wave action
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Orthogonals : Nearshore redistribution of wave energy
Diverging Converging
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Homework 1
Homework 2
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