1. Coastal system
A system is may be defined as all the inputs, outputs and interactions that affect a physical process or event.
Appropriate design considers only as many systems as necessary. To arrive at a technically and environmentally satisfactory design, we must understand each element and its interactions, the inputs and outputs, and how they affect the system and neighboring systems.

2. Data requirements
It is obvious that for coastal design and management we need data that fit the requirements of our design (synthesis) and the concepts of simplification, systems and engineering time. Most coastal data are difficult to measure, which means that they contain large inherent uncertainties. Such uncertainties mean that even the best designs and solutions will be approximate.

3. Coastal design
Coastal engineering is a field for which there are no design codes. Some standard procedures exist but solutions are generally site specific. Thus every project becomes a unique challenge. Input conditions cannot be defined with sufficient accuracy and the “strength of materials” is uncertain. Therefore, normal design, as one might design a bridge for example, is not possible.
Design by full-scale trial and error is socially and economically also not acceptable. Hence, coastal projects are normally designed using models, which are essentially trial and error tools. The two basic types of models are physical (or hydraulic) models and numerical (or computer) models.

4. 2.1.1 Description of waves
Water waves are fluctuations of the water level, accompanied by local currents, accelerations and pressure fluctuations. Their simplest form is sinusoidal and we will use it here to define the most basic wave properties. The high water levels are the wave crests, the low levels are the wave troughs. The vertical distance between a crest and a trough is the wave height H. The distance over which the wave pattern repeats itself is the wave length L. The waves propagate with a velocity C, and the time that is required for a wave to pass a particular location is the wave period T. The inverse of the wave period is the wave frequency f.
Still water level
Orbital motion
Orbital size decreases with depth to zero at wave base

5. 2.1.1 Description of waves
The subject of water waves covers phenomena ranging from capillary waves that have very short wave periods (order 0.1 sec.) to tides, tsunamis (earthquake generated waves) and seiches (basin oscillations), where the wave periods are expressed in minutes or hours. Waves also vary in height from a few millimeters for capillary waves to meters for the long waves.

6. Wave classification Ocean waves can be classified in various ways:
Disturbing Force:
The forces which generate the waves:
Meteorological forcing (wind, air pressure); sea and swell belong to this category.
Earthquakes; they generate tsunamis, which are shallow water or long waves.
Tides (astronomical forcing); they are always shallow water or long waves.

7. Restoring Force:
Force necessary to restore the water surface to flatness after a wave has formed in it
Capillary waves- wavelength < 1.73 cm
Gravity waves- wavelength > 1.73 cm

8. 2.1.2 Wind and waves
Wind Waves: gravity waves formed by the transfer of wind energy into water
Wave height, H: usually <3m
Wave length, L: m
Factors that affect wind wave development:
Wind strength
Wind duration
Fetch: the uninterrupted distance the wind blows
In general, wind speed and wave activity are closely related. There are other important variables to consider such as depth of water, duration of the storm and fetch (the distance the wind blows over the water to generate the waves). The resulting waves are called fully developed sea.
The relationship between wind and waves in the open sea is so predictable that sailors have for centuries drawn a close parallel between wind and waves. The Beaufort Scale in Table 2.1 is a formalized relationship between sea state and wind speed, and we can use it to obtain an estimate of waves in the open sea when wind speed is known.

9. 2.1.2 Wind and waves Length on which the wind effects (Fetch)
Duration of wind
Depth of water
Wind speed
Example
U = 20 m/sec
Fetch = 20 km
Duration = 3hrs, 2hrs

10. Ho = 1.40 m
Wind speed U, m/s
Fetch Length km

11. 2.1.3 Sea and swell Waves originate in a “sea” area
Swell describes waves that:
have traveled out of their area of origination
exhibit a uniform and symmetrical shape
Waves generated locally by wind are known as sea. It consists of waves of many different wave heights and periods. These waves propagate more or less in the wind direction. Local peaks in the water level occur where the two wave train add and lower water levels exist where they subtract, resulting in the irregular wave pattern at any particular location.
On large bodies of water, the waves will travel beyond the area in which they are generated. For example, waves generated by a storm off the coast of Alexandria may travel in an easterly direction and eventually arrive in Gaza. While the waves travel such long distances, the energy of the individual waves is dissipated by internal friction and wave energy is transferred from the higher frequencies to lower frequencies. The resulting waves arriving in Gaza will be more orderly than the initial sea generated off Alexandia, with longer wave periods (10-20 sec), smaller wave heights and more pronounced wave grouping. Waves, generated some distance away are called swell.

12. Interference and rogue waves
Interference waves: when waves from different storm systems overtake one another. They add (constructive interference) or subtract (destructive interference) from the other.
Constructive
Destructive
Mixed

13. Deep-, transitional, and shallow-water Waves
Wave length: determines the size of the orbits of water molecules within a wave
Water depth: determines the shape of the orbits
Deep-water waves
Water depth > wave base
More circular orbits
Shallow-water waves
Water depth < 1/20 L
Orbits are more flattened
Transitional waves
Water depth < wave base but also > 1/20 L
Intermediate-shaped orbits
L is the wavelength

14. Irregular / Regular waves

16. Waves approaching shore
Types of Breaking Waves:
Spilling breaker
Plunging breaker
Surging breaker
Factors that determine the position and nature of the breaking wave:
Slope
Contour
Composition

17. 2.1.4 Introduction of small amplitude wave theory
In this chapter a simplified method of representing wave motion will be introduced, called small amplitude wave theory.
Small amplitude wave theory can be confidently applied to both sea and swell, basically because it is consistent with
other design considerations and with the uncertainty in wave data

18. 2.1.4 Introduction of small amplitude wave theory
The basis for small amplitude wave theory is the sinusoidal wave. The sinusoidal water surface may be described by
where a is the amplitude of the wave, x is distance in the direction of wave propagation, t is time, k is the wave number, w is the angular wave frequency, L is the wave length, T is the wave period and

19. Linear wave theory (Airy 1845)
The fluid is homogenous and incompressible
Surface tension is negligible
Coriolis effect is neglected
Pressure at the free surface is uniform and constant
The bed is horizontal, fixed and impermeable
The wave amplitude is small relative to the water depth

20. Wave characteristics
Wave Celerity :
Wave Length :

21. Wave characteristics Example Given : T=10 sec, h1=200 m, h2=3 m
Find : C and L
Note: h = d = water depth

22. 2.2 Small amplitude wave theory

23. 2.2 Small amplitude wave theory

25. 2.3.2 Small amplitude expressions
Waves propagate with velocity C, but the individual water particles do not propagate; they move in particle orbits as shown in Fig For small amplitude wave theory, such particle orbits are elliptical and if the water is 'deep', they become circular. Their size decreases with depth.

26. Example 2.1 Use of the wave table
We will now calculate the wave characteristics for a wave of period T = 8 sec and a wave height H = 1.5 m in a depth of water d = 6 m. We use small amplitude wave theory (Table 2.2) and the wave table (Table 2.3). It is first necessary to calculate the deep water wave length and relative depth
The wave table (Table 2.3) now yields the following
From the value of d/L, the wave length in 6 m of water and wave number, k, may now be calculated
From these, the following parameters may be computed; r is assumed to be 1035 kg/m for seawater.

28. 3. Short-term wave analysis
Significant Wave Height (Hs) is the most important. It is defined as the average of the highest 1/3 of the waves in a wave train, H1/3. In terms of significant wave height, four commonly used relationships based on the Rayleigh distribution are
The expected value of the maximum wave in a wave train of Nw, waves could be estimated by Q =1/Nw.
A more accurate estimate is
where m(x) denotes "expected value" of x, g is the Euler constant (=0.5772) and O(x) denotes terms of order greater than x, i.e. small terms.

31. Short-term statistics
Stochastic variable (H)
Hmean
Hrms
Significant wave height HS
The mean value of the highest 1/3 waves
Hs = 1.41 Hrms
Hmean = Hrms
Hs = Hmean

32. Significant wave height
No. H
Sorted H
first 1/3 1
1.2
Hs  2
0.3
1.1 3
0.5 4
0.6
0.7
  Hrms 5
 0.75 6 7
0.4
Hmean  8
0.2
0.67  9
Hs = 1.41 Hrms
Hmean = Hrms
Hs = Hmean

33. Short-term statistics
Theoretical distribution model
Reyleigh Distribution

35. Long-term statistics Stochastic variable (Hs) Weibull Distribution
Extrapolate
Return Period
Example
Find Hs for the return period of 25 years
Given: Analyzed wave data (Graph)

36. f = 1/25
P(Hs) = 2.7 × 10-5
Hs = 15.7m

37. 5. Wave generation 5.2.3 Jonswap Parameters
The Jonswap method of wave hindcasting uses the following dimensionless expressions.

38. Simple Jonswap wave hindcast
Example 5.1
Simple Jonswap wave hindcast
Let us use the Jonswap method to calculate the wave conditions resulting from an effective wind speed U=20m/s blowing for 6hrs (t=21,600sec) over a fetch of 100km (F=100,000m). Q. A.
U=20m/s and F=100km  Hmo=3.2m, Tp=7.9sec, Storm period=7hrs
U=20m/s and Storm period=6hrs  Hmo=2.9m, Tp=7.2sec, F=78km

39. 6hr U=20m/s and F=100km  Hmo=3.2m, Tp=7.9sec, Storm period=7hrs
U=20m/s and Storm period=6hrs  Hmo=2.9m, Tp=7.2sec, F=78km

40. U=20m/s and F=100km  Hmo=3.3m, Tp=6.5sec, Storm period=8.5hrs
U=20m/s and Storm period=6hrs  Hmo=2.5m, Tp=5.5sec, F=60km

41. Wave Hindcast for Gaza Fetch = 2000 km Wind speed 30 m/s
Return Periods
Wind Speed (m/s)
(years) 1
23.6 50
31.5
100
32.6
500
35.7

42. U=30m/s and Storm period=6hrs  Hmo=4.3m, Tp=7.5sec, F=78km
U=30m/s and F=600km  Hmo=11m, Tp=>10sec, Storm period=22hrs