Animated Surf Science 'Teaser'

Where do waves come from?

When we see a wave breaking on a beach we are seeing the result of a long journey.  The traveller is a ‘packet’ of energy which started off as a tiny amount of solar radiation entering the atmosphere.

The energy from the Sun entering our atmosphere is the driving force behind our weather and wind, and is what eventually generates waves on the surface of the ocean.  The energy is transferred from one form to another and, for a brief moment, is manifest in a sloping lump of moving water that we can ride on a board.

Once the Sun’s energy enters the atmosphere, the atmosphere is set in motion by the uneven heating of the poles and equator.  Large swirling vortices of air, called low-pressure systems, form in the lower atmosphere over the ocean.  The air circulating around these systems moves along the surface of the water, transferring energy from the air to the water.   

The energy is now contained in the surface of the ocean in the form of waves, which begin to leave the generating area.  The energy now travels within the water in the form of free-travelling swell.  The swell crawls across the ocean surface, gradually organising itself into neat groups of undulations heading towards some coastline.

Once near the coast, these undulations are influenced by the shape of the sea floor, which bends and warps them into different shapes and sizes. Once the waves get really near the coast and start to travel over shallow water, they break. It is here where the energy carried by the waves is transformed into moving water. And it is here where we surfers can bleed off a small part of this energy and use it to push us along on our boards.

Wave fundamentals

The waves we ride have a lot of interesting and unique properties.  Below, I’m going to explain a few of them; but first, let me briefly clarify some of the simple terminology associated with a wave. If you keep seeing words like amplitude, height, period, wavelength and frequency, and don’t know what some of them mean, then this might be useful.

The amplitude is the vertical displacement of the water from its resting position (more precisely, its average position or the mean sea level).

The height is the distance from trough to crest, which is twice the amplitude.  For those of you cool enough to think that’s too big, sorry.

The period is the time taken between when any part of a wave passes a fixed point and when the same part of the next wave passes that point.  

The wavelength is the distance between the same parts of two successive waves.  Period and wavelength are only meaningful when you have a continuation of waves, not a solitary wave.

The frequency is the number of waves that pass a fixed point per second.  It is the inverse of the period, i.e. the frequency in Hertz (cycles per second) is one divided by the period in seconds.

One parameter you’ll see all the time when looking at wave measurements and predictions, is a thing called the significant wave height.  This was originally designed to correspond to the height an ‘experienced observer’ (usually aboard a ship) might guess the waves to be.  Because even experienced observers tend to focus their attention on the biggest waves, the statistical parameter found to be closest to the observed wave height was not just a simple average.  Instead, it was obtained by taking the average of the highest third of the waves observed over a short length of time.  

Terminology describing the ‘anatomy’ of a wave

Wave period: in the example, the period is five seconds

One of the most important things to understand about surface water waves is the fact that they transmit energy through the water but the water itself isn’t actually transported anywhere.  This can be demonstrated in lots of ways; for example, when you flick a piece of rope up and down and send a wave along it from one end to the other.  The energy needed for the up-and-down movement is transmitted along the rope, but the rope itself doesn’t go anywhere.  The wave does not ‘carry rope’ from one end to the other; it just carries energy.  Each particle along the rope describes a circular motion as the wave passes through it, but, eventually, every particle in the rope ends up in the same place.

In deep water a floating object traces an orbital path as a wave passes through.
After the wave has passed the object ends up in the same place

Wave generation

Apart from special waves such as tsunamis, the only thing that produces the waves we see on our coasts is the action of the wind blowing over the sea surface.  Waves arriving on a coast can be generated by local wind, in ‘real time’, in which case the waves are called windsea, or they can be the result of a wind that blew over the surface of the ocean thousands of kilometres away, up to several days before, in which case they are termed swell or groundswell. 

To produce waves, the air moving over the surface of the water has to somehow transmit its energy to the water.  Just how this happens is a very complicated process, still not well understood.  The most accepted theory is the one proposed in the 1950s by J.W. Miles and O.M. Phillips – the Miles-Phillips theory.  The theory describes how waves are generated from a flat sea using two mechanisms; the first of which produces tiny ripples called capillary waves, and the second of which produces bigger waves called gravity waves (those we ride). 

According to the Miles-Phillips theory, capillary waves first begin to grow from an entirely flat sea, and then gravity waves are subsequently formed from a sea already containing capillary waves.  Gravity waves and capillary waves are named as such because the restoring force (the force that returns the sea to an equilibrium position after the wind has lifted it up) is gravity in the case of a gravity wave and capillary action, or surface tension, in the case of a capillary wave.

The initial generation of capillary waves is due to variations in the surface wind, which cause irregularities in the water surface.  The wind does not blow completely horizontally all the time; it will naturally contain small vertical motions as well.  Sometimes, these vertical motions are enough to create tiny up and down motions on the surface of the water itself.

Air never blows exactly parallel to the water surface – it has random up-and-down motions too.
The pattern itself is advected across the ocean surface and only changes relatively slowly

Once the sea contains capillary waves, there is an increase in the ‘roughness’ of the water surface.  There is no longer any need for small vertical air movements – the horizontally-moving air can now push up the existing bumps in the water surface.  This second mechanism is self-perpetuating: the rougher the surface the more ‘grip’, the more grip the bigger the waves, the bigger the waves the rougher the surface, and so on. 

While the first mechanism causes the waves to grow at a rate which is linear with time, the second mechanism is exponential with time; the bigger they are the quicker they grow.

Now, it would be absurd to think that the waves keep on growing like this forever.  Therefore there must be one or more mechanisms that counteracts the wave growth and eventually stops them getting any bigger.  The most important one is called whitecapping, and this is where the waves become so steep in the deep ocean that they break at the top, releasing energy.  For any particular windspeed, there will be a wave height at which the energy removed by the whitecaps exactly matches the energy provided by the wind, at which point the waves will stop growing.  The stronger the wind, the larger the waves can grow before whitecapping stops them.

Exponential wave growth. The grey lines are streamlines, representing the air flow above the water surface.
The air speed is faster than the wave speed, so the pressure is higher (streamlines squashed together) on the
windward side of the wave and lower (streamlines pulled apart) on the leeward side of the wave,
which makes the wave grow. As the wave grows, these pressure anomalies increase, which
makes the wave grow even faster, which modifies the pressure anomalies even more, and so on

Swell propagation

When a swell is first generated in the storm centre, a whole continuum of different wave heights, periods and directions are produced at the same time.  As long as the wind continues to blow over that stretch of the ocean, the waves will continue to be mixed up.  This is a windsea. 

Once the waves leave the generating area, they no longer remain under the influence of the overlying wind, and propagate away as free-travelling swell.  As they travel away from the storm centre, several mechanisms act upon them to change their characteristics.  As long as they are still in deep water, the waves get progressively smaller and cleaner the further they travel away from the storm centre.

One of the things that makes water waves so complicated is that they do not all travel at the same speed – they are dispersive. The speed at which a wave travels in deep water is proportional to the period of that wave; in other words, waves with longer periods travel faster.  This is the principle of dispersion, and is probably the most important thing to know about the propagation of ocean waves. 

As the swell begins to propagate away from the storm centre, the waves of different periods begin to sort themselves out; the longer, faster ones racing out in front, and the shorter, slower ones lagging behind.  By the time the swell is some distance from the storm centre, the longer ones will have made their way right out in front and the shorter ones will have been left way behind.  The swell has ‘stretched out’, in a radial direction.

Depending on how far it has travelled, one swell can look quite different from another when it arrives on the coast.  If you were sitting on a coast a short distance from the storm centre you would see the whole swell arriving in a very short time.  Even though the long waves would arrive first, the short ones would not be very far behind.  But if you were much further away from the storm centre, the long waves, being way out in front, would clearly arrive before all the others.  Then all the other waves would turn up, the shortest ones coming in last.  The swell in this case would be cleaner and more lined up, with a smaller number of different periods arriving at any particular time. 

Swells can travel immense distances in the open ocean with very little overall energy loss, particularly when it comes to the long-period waves. Even though there is virtually no loss of energy overall, the waves do get smaller as they propagate away from the storm centre. This can be understood if we imagine a single wave crest being generated at some point on the ocean, from a wind blowing in a particular direction. As the wave front moves away from the generating position, it will spread out over a progressively wider area. This process is called circumferential spreading. But the height of the wave front also gets smaller as it spreads out. This is because the initial energy given to it when it was generated has to be shared over a progressively wider area. The only way this can be done is for the wave height to be reduced accordingly.

Swell propagating away from the storm centre.  As the swell propagates further away from the storm centre,
it will spread out in both directions, radially and circumferentially.  The radial spreading causes
dispersion of the different wave periods and the circumferential spreading causes the waves to reduce in height

Waves in shallow water

Once a swell starts getting near a coastline, its behaviour begins to change as it starts to propagate over shallower water.  Out in the open ocean, the water was deep enough compared with the height of the waves for the presence of the sea bed not to have any effect; but once the water becomes shallow enough, the configuration of the sea floor starts to seriously affect the waves.  This change in behaviour is based on the fact that waves slow down in shallow water, and the amount they slow down is dependent on the water depth.  If the sea floor is irregular, some parts of a wave will slow down more than others.

If a wave comes out of deep water and straight into really shallow water within a very short distance, the wave height will increase dramatically. This you can see happening at surf spots like Maverick’s, where powerful swells come out of deep water and suddenly ‘trip up’ onto a shallow rock shelf. As a wave begins to hit the shelf, the front part will slow down before the back, squashing the wave up horizontally and forcing it to grow vertically.

As a wave train approaches shallow water the waves at the front of the wave train slow down whilethe
ones at the back are still going at their original speed, which causes them to squash up together. 
The wavelength gets shorter but the waves get higher. The wave period, however, remains
the same. (Thanks to Régis Lachaume for the original diagram upon which this was based)

Now, the sea bed is never so regular that the water depth decreases uniformly as you get closer to the shore.  In reality, the depth will be deeper in some spots and shallower in others.  This means that, as a wave crest approaches the shore, some parts of it will slow down, and others will keep going at a faster speed.  For example, if there is a deep trench next to a shallow reef, the part of the wave crest propagating over the trench might keep going at its deep-water speed, while the part that hits the reef will slow down considerably.  This called refraction.  Refraction is when one part of a wave crest travels slower than another, making the wave bend towards the slower part.  A good analogy of refraction is if you are travelling along in your car and the brakes are binding on one side.  The car will tend to veer off to that side. By steering the waves in this way, refraction is a crucial factor in determining the characteristics of any surfing break: it can make the waves bigger, smaller, longer, shorter, faster, slower or hollower.

The simplest kind of refraction.  The part of the wave front that propagates over shallow water slows
down while the part in deep water keeps going at the same speed.  In the area between the deep and
shallow water the wave front bends towards the shallow water