The waves we ride have a few interesting and unique properties. Below, I'm going to explain just 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, frequency and phase, 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.
The phase is the relative starting position of one wave compared with another. If two waves start at the same position (or time) they are in phase; if they start at slightly different positions (or times) they are out of phase.
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.
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.
As long as the wave isn't just about to break, a particle on the surface will describe a complete circle as the wave passes through it. If the wave is near breaking point, however, the particle will spiral forward slightly, resulting in a very small net movement of water towards the shore. This surface motion is transmitted downwards to the other particles below the surface, which also take on a circular motion, but the circles quickly become smaller and smaller with distance from the surface. In deep water, a point is reached below the surface where the motion of the particles is practically zero. In shallower water, the theoretical position of this point might be further from the surface than the bed itself " in this case, the particles near the bed start to take on an elliptical motion and, right on the bed they just move backwards and forwards.
Another interesting property of waves in deep water is the way they behave in relation to the wave groups, or sets. After having propagated some distance away from the storm centre, waves tend to organise themselves into groups (of course we all know that because waves arriving on our coasts from a long-travelled swell always come in sets). In deep water, as the group travels along, each individual wave in the group travels at twice the speed of the group. This has the strange effect that, as the group is crawling along the surface of the ocean, all the waves in it are constantly moving from the back of the group to the front. Each wave is born at the back of the group, moves through to the front and then vanishes; in other words, each wave only lives for as long as it takes to get from the back of the group to the front. So, although you could track a wave group across the ocean for some distance, you couldn't do this with a single wave. It follows that energy that the swell is carrying travels at the group speed, not the individual wave speed.
Closely related to the above is the fact that waves are dispersive. This means that, in deep water, they travel at a speed directly proportional to their period" the longer the period, the faster it goes. As waves start to come into shallower water, the presence of the sea bed gradually starts to influence their motion, and the wave speed becomes increasingly dependent upon the water depth. In really shallow water, the wave speed is dependent on the depth and nothing else. Also, as the waves come into shallow water, the ratio between wave speed and group speed gradually reduces. In really shallow water this ratio is 1, i.e. the wave speed is equal to the group speed.