Page 43 - Wind Energy Handbook

TURBULENCE 17

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

ó
I ¼ (2:6)
U
where ó is the standard deviation of wind speed variations about the mean wind
speed U, usually defined over 10 min or 1 h. Turbulent wind speed variations can
be considered to be roughly Gaussian, meaning that the speed variations are
normally distributed, with standard deviation ó, about the mean wind speed U.
However, the tails of the distribution may be significantly non-Gaussian, so this