Scotland is at the forefront of research and technological development in the field of wave and tidal energy and is home to leading companies such as Pelamis and Aquamarine. These companies are producing a whole new generation of wave and current devices which are starting to feed energy into the grid.
Scale model tests on these machines under controlled conditions is crucial in the design process and these are best carried our in a wave tank. The larger the scale the more reliable is the data obtained. Generating sea states in a tank that are representative of real sea conditions represents its own challenges and this is the main focus of ‘Making Waves’.
In order to generate realistic sea states in a tank we first need to carefully examine the form of waves in the real ocean and how they are generated. When most people talk about waves in the sea they are referring to the ones which are easily visible to the naked eye. These are generated by the wind blowing over the water surface and have wavelengths from a couple of centimetres up to many hundreds of metres.
The amount of energy transferred to the water by the wind depends on the distance over which it blows, known as the fetch. This is why when the wind is blowing from the land the waves near to the shoreline are relatively small, whereas the same wind velocity blowing from the sea direction generates large waves close to the beach.
If we look more closely at the water surface we see that there are many tiny waves of wavelength just a couple of centimetres or less. These are known as capillary waves and their dynamics is determined by surface tension effects, rather than being gravity- dominated like their larger brothers and sisters.
Although capillary waves don’t contain a lot of energy in their own right they are nonetheless very important. For example they increase the surface roughness of the sea surface and they also alter the spectrum of reflected light picked up by satellite imaging systems. At the other end of the spectrum are the very long-period tidal waves.
The speed of travel
In the deep ocean the speed at which waves travel, known as the celerity, is independent of the depth as waves do not ‘feel the bottom’. Waves of low frequency and correspondingly long wavelength then travel faster than their opposite numbers with high frequency and short wavelength.
However, the speed of travel of a group of waves, known as the group velocity, is slower than the celerity; in fact equal to half the celerity in deep water. In the real sea there is always a spread of frequencies and corresponding wave lengths and also of directions of travel, defined by the directional wave spectrum.
Laboratory waves are most frequently generated by moving a flap at the end of a long water channel or flume. Sinusoidal movements of the flap generate monochromatic waves of a single frequency and corresponding wave length. If the input signal to the wave maker is in the form of many superimposed sine waves, or equivalently filtered white noise, then a random sea can be produced with a defined spectrum. Breaking waves can be produced by first moving the flap quickly and then slowing it down, timing the motions so that the different wavelengths all catch up on each other at a prescribed point in the flume.
It’s important to have some mechanism at the end of a flume to absorb the waves. If there was just a vertical wall then the waves would be reflected back down the tank and standing waves would be set up.
This absorption is usually in the form of wedges of fine mesh material, rather like the wedges used for sound absorption in an acoustic anechoic chamber. Alternatively it is possible to absorb the waves with a second paddle at the end of the flume fitted with force transducers which detect the incoming waves.
Waves and currents
In the real ocean, wave energy is absorbed by the breaking process at the beach. As waves approach the shoreline they come into shallower water and start to ‘feel the bottom’. In shallow water the celerity decreases in proportion to the square root of the depth so the waves become steeper and eventually turn over and break: a process known as shoaling.
To a first approximation the effect of a current on a wave can be predicted by considering how the wave looks from a frame of reference moving with the current velocity. If the current is in the same direction of the wave then the wavelength becomes stretched out and the steepness is reduced. If the current is against the direction of wave motion then the wavelength is contracted so the waves become steeper, often to an extent that they start breaking.
Testing in a wave tank
Wave flumes are not usually adequate for testing complex three-dimensional machines or arrays of devices but it is possible to recreate a fully three-dimensional sea by using multiple paddles round the edge of a tank. By suitably phasing the motions of the paddles one can reproduce either a monochromatic wave moving in a specified direction or a fully directional random sea state..
Most early tanks were rectangular and had a line of wave makers along one side with wave absorbers on the opposite side. One of the problems here is that this scheme gives rise to a limited wedge of sea in which testing can be done.
By having absorbing wave makers around the whole periphery of a circular tank it is possible to generate a much greater usable area of sea. The new Flowave tank, shortly to be opened at the University of Edinburgh, incorporates both a complete circle of wave makers and also current-generating impellers.
In order to use the results from tank tests the scaling laws must be known. For waves there is a square-root relationship between velocities in the tank and the corresponding velocities in the real ocean. For example, for a 1:25 scale model tank the velocities will all be 5 times smaller than they are in the real ocean and things will happen five times more quickly.
Accelerations, on the other hand, are the same in the real sea as in the model. Scaling combined waves and currents though is a little more complex.
For small-amplitude waves, the form of the sea surface and the velocities under the surface can be predicted with reasonable accuracy using linear addition of sine wave components. The basis of linear theory dates back to early eighteenth-century mathematicians such as Laplace, and as long ago as 1802 Gerstner had produced a nonlinear theory for water waves.
Despite these early advances, even today the theoretical and numerical prediction of flow patterns around complex structures in the ocean and the related forces often turns out to be intractable. It’s fortunate that the technology for producing waves and currents in test facilities and the development of velocity and force measuring instruments has reached such a high degree of sophistication.