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r(1 +1/k) has the value V^/2 = 0.8862. A higher value of k, such as 2.5 or 3, indicates a site where the variation of hourly mean wind speed about the annual mean is small, as is sometimes the case in the trade wind belts for instance. A lower value of k, such as 1.5 or 1.2, indicates greater variability about the mean. A few examples are shown in Figure 2.2. The value of T(1 +1/k) varies little, between about 1.0 and 0.885 see (Figure 2.3).

k = —■- 1.25 —•— 1.5 —o- 2.0 —I— 2.5 —X—3.0

k = —■- 1.25 —•— 1.5 —o- 2.0 —I— 2.5 —X—3.0

Wind speed (m/s)

Figure 2.2 Example Weibull Distributions

Figure 2.2 Example Weibull Distributions

Shape factor, k Figure 2.3 The Factor T(1 + 1 /k)

The Weibull distribution of hourly mean wind speeds over the year is clearly the result of a considerable degree of random variation. However, there may also be a strong underlying seasonal component to these variations, driven by the changes in insolation during the year as a result of the tilt of the earth's axis of rotation. Thus in temperate latitudes the winter months tend to be significantly windier than the summer months. There may also be a tendency for strong winds or gales to develop around the time of the spring and autumn equinoxes. Tropical regions also experience seasonal phenomena such as monsoons and tropical storms which affect the wind climate. Indeed the extreme winds associated with tropical storms may significantly influence the design of wind turbines intended to survive in these locations.

Although a Weibull distribution gives a good representation of the wind regime at many sites, this is not always the case. For example, some sites showing distinctly different wind climates in summer and winter can be represented quite well by a double-peaked 'bi-Weibull' distribution, with different scale factors and shape factors in the two seasons, i.e.,

Certain parts of California are good examples of this.

2.5 Synoptic and Diurnal Variations

On shorter time-scales than the seasonal changes described in Section 2.4, wind speed variations are somewhat more random, and less predictable. Nevertheless these variations contain definite patterns. The frequency content of these variations typically peaks at around 4 days or so. These are the 'synoptic' variations, which are associated with large-scale weather patterns such as areas of high and low pressure and associated weather fronts as they move across the earth's surface. Coriolis forces induce a circular motion of the air as it tries to move from high- to low-pressure regions. These coherent large-scale atmospheric circulation patterns may typically take a few days to pass over a given point, although they may occasionally 'stick' in one place for longer before finally moving on or dissipating.

Following the frequency spectrum to still higher frequencies, many locations will show a distinct diurnal peak, at a frequency of 24 h. This is usually driven by local thermal effects. Intense heating in the daytime may cause large convection cells in the atmosphere, which die down at night. This process is described in more detail in Section 2.6 as it also contributes significantly to turbulence, on time-scales representative of the size of the convection cells. Land and sea breezes, caused by differential heating and cooling between land and sea, also contribute significantly to the diurnal peak. The daily direction reversal of these winds would be seen as a 12 h peak in the spectrum of wind speed magnitude.

2.6 Turbulence

2.6.1 The nature of turbulence

Turbulence refers to fluctuations in wind speed on a relatively fast time-scale, typically less than about 10 min. 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 above, which varies on a time-scale of one to several hours, with turbulent fluctuations superimposed. These turbulent fluctuations then have a zero mean when averaged over about 10 min. This description is a useful one as long as the 'spectral gap' 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 topographical features such as hills and mountains, and thermal effects which can cause air masses to move vertically as a result of variations of temperature, and hence of 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 which cannot be represented simply in terms of deterministic equations. Obviously it does obey certain physical laws, such as those describing the conservation of mass, momentum and energy. However, in order 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 which 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

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Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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