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Turbulence refers to fluctuations in wind speed on a relatively fast timescale, typically less than about 10 minutes. In other words, it corresponds to the highest frequency spectral peak in Figure 2.1. It is useful to think of the wind as consisting of a mean wind speed determined by the seasonal, synoptic, and diurnal effects described previously, which varies on a timescale of one to several hours, with turbulent fluctuations superimposed. These turbulent fluctuations then have a zero mean when averaged over about 10 minutes. This description is a useful one as long as the ‘spectral gap’ as illustrated in Figure 2.1 is reasonably distinct.

Turbulence is generated mainly from two causes: ‘friction’ with the earth's surface, which can be thought of as extending as far as flow disturbances caused by such topographical features as hills and mountains, and thermal effects, which can cause air masses to move vertically as a result of variations of temperature and hence in the density of the air. Often these two effects are interconnected, such as when a mass of air flows over a mountain range and is forced up into cooler regions where it is no longer in thermal equilibrium with its surroundings.

Turbulence is clearly a complex process and one that cannot be represented simply in terms of deterministic equations. Clearly it does obey certain physical laws, such as those describing the conservation of mass, momentum, and energy. However, to describe turbulence using these laws it is necessary to take account of temperature, pressure, density, and humidity as well as the motion of the air itself in three dimensions. It is then possible to formulate a set of differential equations describing the process, and in principle the progress of the turbulence can be predicted by integrating these equations forward in time starting from certain initial conditions and subject to certain boundary conditions. In practice of course, the process can be described as ‘chaotic’ in that small differences in initial conditions or boundary conditions may result in large differences in the predictions after a relatively short time. For this reason it is generally more useful to develop descriptions of turbulence in terms of its statistical properties.

There are many statistical descriptors of turbulence that may be useful, depending on the application. These range from simple turbulence intensities and gust factors to detailed descriptions of the way in which the three components of turbulence vary in space and time as a function of frequency.

The turbulence intensity is a measure of the overall level of turbulence. It is defined as

(2.6)

where σ is the standard deviation of wind speed variations about the mean wind speed , usually defined over 10 minutes or an hour. Turbulent wind speed variations can be considered to be roughly Gaussian, meaning that the speed variations are normally distributed, with standard deviation σ, about the mean wind speed . However, the tails of the distribution may be significantly non‐Gaussian, so this approximation is not reliable for estimating, say, the probability of a large gust within a certain period.

The turbulence intensity clearly depends on the roughness of the ground surface and the height above the surface. However, it also depends on topographical features, such as hills or mountains, especially when they lie upwind, as well as more local features, such as trees or buildings. It also depends on the thermal behaviour of the atmosphere: for example, if the air near to the ground warms up on a sunny day, it may become buoyant enough to rise up through the atmosphere, causing a pattern of convection cells that are experienced as large‐scale turbulent eddies.

Clearly as the height above ground increases, the effects of all these processes that are driven by interactions at the earth's surface become weaker. Above a certain height, the air flow can be considered largely free of surface influences. Here it can be considered to be driven by large‐scale synoptic pressure differences and the rotation of the earth. This air flow is known as the geostrophic wind. At lower altitudes, the effect of the earth's surface can be felt. This part of the atmosphere is known as the boundary layer. The properties of the boundary layer are important in understanding the turbulence experienced by wind turbines.