# Diffraction Of Water Waves

The following types of transformation are mainly related to wave phenomena occurring in the natural environment. When the waves approach the shoreline, they are affected by the seabed through processes such as refraction, shoaling, bottom friction and wave-breaking. However, wave-breaking also occurs in deep water when the waves are too steep. If the waves meet major structures or abrupt changes in the coastline, they will be transformed by diffraction. If waves meet a submerged reef or structure, they will overtop the reef. These phenomena will be further explained in the following.The following types of wave transformation occur mainly in connection with ports and the like. If the waves meet a steep structure, reflection will take place, and if the waves meet a permeable structure, partial transmission will take place.

For a more detailed treatment of wave transformation in the nearshore the reader should consult Shallow-water wave theory and Swash zone dynamics.

Diffraction If you observe straight wave fronts in a ripple tank, you can see that they travel in a straight line if the water depth is constant and no obstacles are in the way. If, however, the waves pass by an edge of an obstacle or through a small opening, the waves spread out. Diffraction is the bending of a wave as the wave passes through an.

• Diffraction of water waves is observed in a harbor as waves bend around small boats and are found to disturb the water behind them. The same waves however are unable to diffract around larger boats since their wavelength is smaller than the boat. Example 1 A number of straight and parallel water waves are shown in the figure below.
• Generate plane water waves and use a barrier to demon-strate diffraction at an edge. Then, form a slit and observe diffraction behind the slit. Repeat this experiment for a double-slit. By using the integrated wave generator as well as the external wave generator, generate two circular waves.

• 1Summary of transformation types

## Summary of transformation types

The following is a summary of the transformation types to be found in nature.

### Refraction

Fig 1. Wave refraction (and breaking).

Depth-refraction is the turning of the direction of wave propagation when the wave fronts travel at an angle with the depth contours at shallow water. The refraction is caused by the fact that the waves propagate more slowly in shallow water than in deep water. A consequence of this is that the wave fronts tend to become aligned with the depth contours. Currents can also result in refraction and this is termed current refraction.

Fig. 2. Wave diffraction in a port (from a numerical simulation with a short wave model).

### Diffraction

Diffraction can be seen when there are sheltering structures such as breakwaters. Diffraction is the process by which the waves propagate into the lee zone behind the structures by energy transmittance laterally along the wave crests.

Fig. 3. Shoaling

### Shoaling

Shoaling is the deformation of the waves, which starts when the water depth becomes less than about half the wavelength. The shoaling causes a reduction in the wave propagation velocity as well as shortening and steeping of the waves.

### Bottom friction

Bottom friction causes energy dissipation and thereby wave height reduction as the water depth becomes more and more shallow. Friction is of special importance over large areas with shallow water.

### Depth-induced wave-breaking

Depth-induced wave-breaking of individual waves starts when the wave height becomes greater than a certain fraction of the water depth. As a rule of thumb, the wave height of an individual wave at breaking is often said to be around 80% of the water depth, but this is a very approximate figure. Breaking waves are generally divided into three main types, depending on the steepness of the waves and the slope of the shoreface:

• Spilling takes place when steep waves propagate over flat shorefaces. Spilling breaking is a gradual breaking which takes place as a foam bore on the front topside of the wave over a distance of 6– 7 wavelengths.
• Plunging is the form of breaking where the upper part of the wave breaks over its own lower part in one big splash whereby most of the energy is lost. This form of breaking takes place in cases of moderately steep waves on moderately sloping shorefaces.
• Surging is when the lower part of the wave surges up on the foreshore in which case there is hardly any surf-zone. This form of breaking takes place when relatively long waves (swell) meet steep shorefaces.
Fig. 4. Depth-induced wave-breaking: spilling, plunging and surging.
Fig. 5. White capping can be seen on these irregular directional storm waves
Fig. 6. Wave-overtopping of breakwater in a flume test.
Fig. 7. Wave-overtopping of breakwater in nature.

### Wave set-up

Wave set-up is a very important phenomenon in the surf-zone hydrodynamics. This is a local elevation in the mean water level on the foreshore, caused by the reduction in wave height through the surf-zone. The wave set-up is proportional to the wave height at breaking. As a rule of thumb, the wave set-up is 20% of the offshore significant wave height. Gradients in wave set-up, e.g. in partly sheltered areas near port entrances, will generate local circulation in the surf-zone towards the sheltered area.

### Wave swash

Wave swash or Wave uprush is the propagation of the waves onto the beach slope. The swash consists of an onshore phase with decelerating upwards flow (uprush or swash) and an offshore phase with accelerating downwards flow (downrush or backwash)

### Wave run-up

Wave run-up is the sum of the wave set-up and the wave swash. The wave run-up is this the maximum level the waves reach on the beach relative to the still water level. The run-up height exceeded by 2% of the run-up events is denoted [math]R_{2%}[/math]. Relationships for estimating [math]R_{2%}[/math] are given in Swash zone dynamics. For typical storm waves this gives: [math]R_{2%} approx 6 H_0 tan beta [/math]. Here is [math]tan beta[/math] the beach slope, and [math]H_0[/math] and [math]T[/math] are the significant wave height and period at deep water.

### White-capping

White-capping or top-breaking is steepness-induced wave-breaking, which occurs in deeper water when the wave height becomes too large compared to the wavelength. (see Fig. 5.)

### Wave overtopping

Wave-overtopping takes place when waves meet a submerged reef or structure, but also when waves meet an emerged reef or structure lower than the approximate wave height. During over-topping, two processes important to the coastal processes take place: wave transmission and the passing of water over the structure. (see Fig. 6.)

## References

Mangor, K., Drønen, N. K., Kaergaard, K.H. and Kristensen, N.E. 2017. Shoreline management guidelines. DHI https://www.dhigroup.com/marine-water/ebook-shoreline-management-guidelines.

 The main author of this article is Mangor, KarstenPlease note that others may also have edited the contents of this article. Citation: Mangor, Karsten (2020): Wave transformation. Available from http://www.coastalwiki.org/wiki/Wave_transformation [accessed on 5-05-2021] For other articles by this author see Category:Articles by Mangor, KarstenFor an overview of contributions by this author see Special:Contributions/Karsten

All waves behave in certain characteristic ways. They can undergo refraction, reflection, interference and diffraction. These basic properties define the behaviour of a wave – anything that reflects, refracts, diffracts and interferes is labelled a wave.

These behaviours of waves can help us understand how water waves interact with land. Out in the deep ocean, tsunamis and wind-generated waves settle to quite steady predictable wave patterns. However, as they approach the complex coastline of New Zealand, they can refract, diffract, be reflected and interfere with one another. Together, these behaviours direct the course and effects of waves around New Zealand’s coast.

## Refraction: when waves slow down and change direction

Refraction is the change in direction of a wave as it slows down. In shallower water near the coast, waves slow down because of the force exerted on them by the seabed. If a wave is approaching the coast at an angle, the nearshore part of the wave slows more than the offshore part of the wave (because it’s in shallower water). This is why the wavefront changes direction.

Refraction is the reason why surf waves often line up parallel to the beach. Even if waves are coming in from deep water at an angle to the beach, the move to shallower water means that the waves will slow down and curve around (refract) so they are more parallel as the surf hits the beach.

Refraction is very important for tsunamis because (unlike other waves) they interact with the seabed even in deep water – so they are always undergoing refraction. This affects the direction that the tsunami travels through the ocean. Tsunamis also refract around land masses.

## Reflection: when waves bounce back

Reflection of water waves at a coast is usually not an important part of their behaviour, unless the coast has a steep cliff or a seawall. However, reflected waves tend to interfere with the oncoming waves, and these patterns can be studied.

A tsunami wave can reflect off continental shelves, ocean ridges and large reefs under the sea. Reflected tsunami waves off an ocean ridge to the west of Sri Lanka and south-west of India contributed to the damage on the western side of Sri Lanka during the 2004 Boxing Day tsunami.

## Interference: when waves affect each other

When two waves travelling in different directions meet, they combine their energies and form interference patterns. This can result in regions of very high waves when they add up (constructive interference) alternating with regions of diminished or no waves when they cancel out (destructive interference).

Interference is important for surfers because it affects the size of surf waves. When two sets of swells with similar frequencies interact, they interfere with each other and form groups. Within the groups, interference means that the wave height will vary. Surfers can tell from the interference pattern which wave will be the biggest (and the best to surf!), for example, every 7th wave.

## Resonance: when waves ‘slosh’ to and fro

### Diffraction Of Water Waves

A tsunami wave coming into a bay can cause the water in the whole bay to ‘slosh’ backwards and forwards. This is called resonance, and it happens when the frequency of the tsunami wave is similar to the natural oscillating frequency (resonant frequency) of the body of water in the bay. Resonance can push the water level really high, making the effect of the tsunami greater.

Different bodies of water have different resonant frequencies – it depends on their size and shape. Lyttelton Harbour and Mercury Bay (Coromandel) are both prone to ‘sloshing’. Mercury Bay has a resonant frequency of 1 hour – once it gets disturbed by a tsunami, it will slosh backwards and forwards every hour, sometimes for several days, before it dissipates.

Bigger, more open areas of water like the North Canterbury Bight and the South Taranaki Bight can also amplify tsunami waves through resonance, but with longer periods (for example, 2.5 hours in the North Canterbury Bight).

## Diffraction: when waves bend

When waves get to a barrier such as an offshore rock or a small gap such as the opening to a harbour, they don’t go straight past the barrier or carry on straight after going through the gap. Instead, they bend – they curve outwards after passing through a gap and spread around an object. This is diffraction. It happens when the wavelength of the wave and the size of the gap or barrier are similar.

Diffraction is interesting to wave researchers because it means that wave energy reaches ‘shadow zones’ where you wouldn’t otherwise expect energy to be. It’s an important part of wave behaviour at ports, harbours, built structures and offshore islands. Diffraction is more important in shallow water than it is in deep water.

## Nature of science

Common scientific concepts can connect seemingly disparate areas of science. For instance, water waves, sound waves and electromagnetic radiation all exhibit similar behaviours. Some of the scientific knowledge obtained in one of these areas can therefore be applied to the others.

### Diffraction Of Water Waves

Published 2 May 2011

### Diffraction Of Water Waves Around A Log

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