Wind Energy

13 Gusts in Intermittent Wind Turbulence 75
Engineers [7]. However this scale belongs to the inertial range; it is usually
not a characteristic time scale, so that the results obtained here are expected
to be valid for any other scale τ belonging to the inertial range.
Here we consider the recurrent times of gust events: the times between
successive gust events. The recurrent times of meteorological events have
practical importance, and correspond to the knowledge of some dynamical
properties of wind fluctuations. Here we not only focus on the mean
return times, but also on their pdf. We consider the evolution of this pdf
with increasing velocity thresholds δ. For illustration purposes, we have
taken an atmospheric turbulent velocity data base: velocity measurements
taken 25 m from the ground in south-west France, with a sonic velocimeter
sampling at 10 Hz (see [8, 9]). We analyze here three portions of duration
55 min each, recorded under near-neutral stability conditions. A portion of the
data is shown in Fig. 13.1: this illustrates the intermittent behavior of wind
turbulence. The power spectrum of the 3 portions is shown in Fig. 13.2,
in log–log plot, indicating a very nice −5/3 scaling law over most of the
available dynamics (between 0.2s and about 10 min). We have then transformed
the velocity time series into an amplitude increment time series:
Y3(t) =|V (t + τ0) − V (t)| with τ0 =3s. The new time series is shown in
Fig. 13.3, together with an example of threshold (δ =1 m −1 ), and the associated
recurrent times. Successive return time form a new time series which
is represented in Fig. 13.4.
An interesting question is now to evaluate the tail behavior of the pdf of
return times: since gust events are associated to large return times, their
probability of occurrence is given by the tails. There are in fact many results
providing the form of the tail of the pdf of recurrent times (also called
first-passage times) for scaling processes. One of the most classical scaling
U (m/s)
6
5
4
3
2
1
0
0
50 100 150 200 250 300
t (s)
Fig. 13.1. A portion of the turbulent time series analyzed here for illustration
purposes