Wind Generated Waves

As wind passes over the water’s surface, small ripples are formed. These ripples grow exponentially and form fully developed waves. This phenomenon is illustrated in the figure below.

As wind passes over the surface of the water, small fluctuations in the wind speed cause variations in air pressure on the surface which produce Capillary waves. These pressure variations with fluctuations in velocity are best explained using Bernoulli’s Equation:

From this equation it can be seen that faster moving winds produce lower pressure, whereas, slower moving winds produce higher pressures. Furthermore, the effects of the pressure fluctuations are magnified because as the wind moves over the crests of the waves, the velocity profile near the water surface increases and cause the pressure to decrease. Similarly, as the wind moves over the trough of the wave, the velocity profile near the water surface decreases and causes the pressure to increase. These pressure effects are illustrated in the figure below.

2. Shear Effect:

As wind passes over the surface of the water, the surface is stretched which causes the surface to wrinkle. This is similar to the wrinkles that are formed by stretching a piece of Saran Wrap. Furthermore, the friction forces between the air and the water surface allow for shear forces to develop within the water. These shear forces push the water molecules and form small hills of water which are held down by surface tension and gravity forces. These shear effects are illustrated in the figure below.

There are three main factors that influence wave growth: wind speed, wind duration, and fetch (length over which wind blows). The effects of these factors are best explained by the following main theories:

Turbulent eddies in wind field exert a fluctuating pressure on the water surface. Pressure fluctuations very in magnitude and frequency and move forward at a range of speeds. Pressure fluctuations cause water surface undulations to develop and grow. The key to their growth is that a resonant interaction occurs between forward moving pressure fluctuations and free waves that propagate at the same speed as the pressure fluctuations.

As wind blows over a forward moving wave, a complex air flow patterns develop over the wave. This involves a secondary air circulation that is set up around an axis that is parallel to wave crest, by the wind velocity profile acting over a moving wave surface profile. Below a point on the velocity profile where the wind velocity equals the wave celerity, air flow is reversed relative to the forward moving wave profile. Above this point, air flow is in the direction of the wave motion. This results in a relative flow circulation in a vertical plane above the wave surface that causes a pressure distribution on the surface that is out of phase with the surface displacement. The result is a momentum transfers to the wave that selectively amplifies the steeper waves.

There are many other theories that attempt to explain how waves grow but the one that is most logical says that the ripples on the water’s surface create more friction which allows for more energy to be transferred from the wind to the waves. The wind energy is then continually transferred to the waves causing the ripples to increase in size (height and period).

As wind energy is transferred to the water, there comes a point where the water waves reach their maximum wave height and there is no more growth. These waves can either be fully developed or non-fully developed (fetch limited or duration limited). These maximum wave growths are defined as follows:

The wind energy is continually transferred to the waves until it is balanced with the friction and gravity forces acting on the water molecules.

The distance over which the wind is blowing is not enough to allow for full development of the waves.

The wind has not been in contact with the water surface long enough to allow for full development of the waves.

Theories of Wind Generated Waves