Wind Energy

13
Gusts in Intermittent Wind Turbulence
and the Dynamics of their Recurrent Times
François G. Schmitt
Summary. Regions interesting for the installation of windmills possess large mean
wind velocity, but this is also associated to large Reynolds numbers and huge velocity
fluctuations. Such fully developed turbulence is generally characterized by intermittent
fluctuations on a wide range of scales. There are many gusts (large fluctuations
of the wind velocity at small scales), producing extreme loading on wind turbine
structure. Here we consider the dynamics of gusts: the recurrent times of large
fluctuations for a fixed time increment, and also “inverse times” corresponding to
the times needed to have wind fluctuations larger than a fixed threshold. We discuss
theoretically these two different quantities, and provide an example of data
analysis using wind data recorded at 10 Hz. The objective here is to provide theoretical
relations that will help for the interpretation of available data, and for their
extrapolation.
13.1 Introduction
Wind turbines need theoretically large and constant wind velocities to be
optimally efficient. However, this is not possible since large velocities correspond
to high Reynolds numbers and fully developed turbulence situations,
characterized by intermittent fluctuations of the wind velocity having highly
nonlinear and non-Gaussian properties [1–3]. Turbulent wind fluctuate at all
scales in intensity and in direction, producing high loading on wind turbine
structure, large fluctuations on wind turbine force and moments, and high
variability on wind turbine power output. Here we focus on small-scale wind
fluctuations called wind gusts, which produce most of the fatigue loading on
turbine structures; we consider theoretically, with data analysis applications,
the dynamics of these gusts: the recurrent times of large fluctuations for a fixed
small time increment (also called “return times” or “waiting times”), and also
“inverse times” corresponding to the times needed to have wind fluctuations
larger than a fixed threshold.