Ocean wave

Ocean surface waves are the result of forces acting on the ocean. The predominant natural forces are pressure or stress from the atmosphere (especially through the winds), earthquakes, gravity of the Earth and celestial bodies (the Moon and Sun), the Coriolis force (due to the Earth's rotation) and surface tension. The characteristics of the waves depend on the controlling forces. Tidal waves are generated by the response to gravity of the Moon and Sun and are rather large-scale waves. Capillary waves, at the other end of the scale, are dominated by surface tension in the water. Where the Earth's gravity and the buoyancy of the water are the major determining factors we have the so-called gravity waves.

Waves may be characterized by their period. This is the time taken by successive wave crests to pass a fixed point. The type and scale of forces acting to create the wave are usually reflected in the period. Figure 1.1 illustrates such a classification of waves.

On large scales, the ordinary tides are ever present but predictable. Less predictable are tsunamis (generated by earthquakes or land movements), which can be catastrophic, and storm surges. The latter are associated with the movement of synoptic or meso-scale atmospheric features and may cause coastal flooding.

Wind-generated gravity waves are almost always present at sea. These waves are generated by winds somewhere on the ocean, be it locally or thousands of kilometres away. They affect a wide range of activities such as shipping, fishing, recreation, coastal and offshore industry, coastal management (defences) and pollution control. They are also very important in the climate processes as they play a large role in exchanges of heat, energy, gases and particles between the oceans and atmosphere. It is these waves which will be our subject in this Guide.

To analyse and predict such waves we need to have a model for them, that is we need to have a theory for how they behave. If we observe the ocean surface we note that the waves often form a rather complex pattern. To begin we will seek a simple starting model, which is consistent with the known dynamics of the ocean surface, and from this we will derive a more complete picture of the wind waves we observe.

The model of the ocean which we use to develop this picture is based on a few quite simple assumptions: • The incompressibility of the water. This means that the density is constant and hence we can derive a continuity equation for the fluid, expressing the conservation of fluid within a small cell of water (called a water particle); • The inviscid nature of the water. This means that the only forces acting on a water particle are gravity and pressure (which acts perpendicular to the surface of the water particle). Friction is ignored; • The fluid flow is irrotational. This means that the individual particles do not rotate. They may move around each other, but there is no twisting action. This allows us to relate the motions of neighbouring particles by defining a scalar quantity, called the velocity potential, for the fluid. The fluid velocity is determined from spatial variations of this quantity.

From these assumptions some equations may be written describe the motion of the fluid