Identification of Markov process within a wind turbine array boundary layer

The Markovian properties within a wind turbine array boundary layer are explored for data taken in a wind tunnel containing a model wind turbine array. A stochastic analysis of the data is carried out using the mathematics of Markov processes. The data were obtained using hot-wire anemometry thus providing point velocity statistics. The theory of Markov process is applied to obtain a statistical description of longitudinal velocity increments inside the turbine wake. Comparison of two- and three-scale conditional probability density functions indicates the existence of Markovian properties in longitudinal velocity increments for scale differences larger than the Taylor microscale. This result is quantified by use of the Wilcoxon rank-sum test which verifies that this relationship holds independent of initial scale selection outside of the near-wake region behind a wind turbine. Furthermore, at the locations which demonstrate Markovian properties, there appears to be a well defined inertial subrange which follows Kolmogorov's −5/3 scaling behavior. The results show that directly behind the tips of the rotor and the hub, the complex turbulent interactions and large scale structures of the near-wake affect the Markovian nature of the field. The presence of a Markov process in the remaining locations leads to characterization of the development multiscale statistics of the wind turbine wakes using the most recent states of the flow.