Features of the turbulent cascade are investigated for various datasets from three different turbulent flows, namely free jets as well as wake flows of a regular grid and a cylinder. The analysis is focused on the question as to whether fully developed turbulent flows show universal small scale features. Two approaches are used to answer this question. Firstly, 2-point statistics, namely structure functions of longitudinal velocity increments and secondly, joint multi-scale statistics of these velocity increments are analysed. The joint multi-scale characterisation encompasses the whole cascade in one joint probability density function. On the basis of the datasets, evidence of the Markov property for the turbulent cascade is shown, which corresponds to a three point closure that reduces the joint multi-scale statistics to simple conditional probability density functions (cPDF). The cPDF are described by the Fokker-Planck equation in scale and its Kramers-Moyal coefficients (KMCs). KMCs are obtained by a self-consistent optimisation procedure from the measured data and result in a Fokker-Planck equation for each dataset. The knowledge of these stochastic cascade equations enables to make use of the concepts of non-equilibrium thermodynamics and thus to determine the entropy production along individual cascade trajectories. In addition to this new concept, it is shown that the local entropy production is nearly perfectly balanced for all datasets by the integral fluctuation theorem (IFT). Thus the validity of the IFT can be taken as a new law of the turbulent cascade and at the same time independently confirms that the physics of the turbulent cascade is a memoryless Markov process in scale. IFT is taken as a new tool to prove the optimal functional form of the Fokker-Planck equations and subsequently to investigate the question of universality of small scale turbulence in the datasets. The results of our analysis show that the turbulent cascade contains universal and non-universal features. We identify small scale intermittency as a universality breaking feature. We conclude that specific turbulent flows have their own particular multi-scale cascade, with other words their own stochastic fingerprint.

Wind turbines operate in the atmospheric boundary layer, where they are exposed to the turbulent atmospheric flows. As the response time of wind turbine is typically in the range of seconds, they are affected by the small scale intermittent properties of the turbulent wind. Consequently, basic features which are known for small-scale homogeneous isotropic turbulence, and in particular the well-known intermittency problem, have an important impact on the wind energy conversion process. We report on basic research results concerning the small-scale intermittent properties of atmospheric flows and their impact on the wind energy conversion process. The analysis of wind data shows strongly intermittent statistics of wind fluctuations. To achieve numerical modeling a data-driven superposition model is proposed. For the experimental reproduction and adjustment of intermittent flows a so-called active grid setup is presented. Its ability is shown to generate reproducible properties of atmospheric flows on the smaller scales of the laboratory conditions of a wind tunnel. As an application example the response dynamics of different anemometer types are tested. To achieve a proper understanding of the impact of intermittent turbulent inflow properties on wind turbines we present methods of numerical and stochastic modeling, and compare the results to measurement data. As a summarizing result we find that atmospheric turbulence imposes its intermittent features on the complete wind energy conversion process. Intermittent turbulence features are not only present in atmospheric wind, but are also dominant in the loads on the turbine, i.e. rotor torque and thrust, and in the electrical power output signal. We conclude that profound knowledge of turbulent statistics and the application of suitable numerical as well as experimental methods are necessary to grasp these unique features and quantify their effects on all stages of wind energy conversion.

Turbulence plays an important role in our everyday life, yet it is still not well understood. Wind tunnel experiments can help to develop generalized descriptions of turbulent flows. However, creating turbulent flows with suitable characteristics for various experiments is still challenging. In this work, fractal and active grids were used to generate multi-scale turbulent flows. Using hot-wire measurements we investigated the influence of different boundary conditions, bar sizes and solidity for fractal grids. We found that the evolution of the flow generated by a fractal grid does not depend on the considered boundary conditions. An alternative to these rigid structured grids is an active grid, which allows for a dynamical generation of flow fields with comparable properties. Experiments were conducted with an active grid in which the distribution of the local solidity was actively changed. A transition between classical and fractal grid type decaying turbulence depending on the active grid excitation protocol was observed. We conclude that the distribution of the local solidity of these grids has a strong influence on the evolution of the generated turbulent flow.

Abstract. The effect of intermittent and Gaussian inflow conditions on wind energy converters is studied experimentally. Two different flow situations were created in a wind tunnel using an active grid. Both flows exhibit nearly equal mean velocity values and turbulence intensities but strongly differ in their two point statistics, namely their distribution of velocity increments on a variety of timescales, one being Gaussian distributed, and the other one being strongly intermittent. A horizontal axis model wind turbine is exposed to both flows, isolating the effect on the turbine of the differences not captured by mean values and turbulence intensities. Thrust, torque and power data were recorded and analyzed, showing that the model turbine does not smooth out intermittency. Intermittent inflow is converted to similarly intermittent turbine data on all scales considered, reaching down to sub-rotor scales in space. This indicates that it is not correct to assume a smoothing of intermittent wind speed increments below the size of the rotor.

Emergent extreme events are a key characteristic of complex dynamical systems. The main tool for detailed and deep understanding of their stochastic dynamics is the statistics of time intervals of extreme events. Analyzing extensive experimental data, we demonstrate that for the velocity time series of fully-developed turbulent flows, generated by (i) a regular grid; (ii) a cylinder; (iii) a free jet of helium, and (iv) a free jet of air with the Taylor Reynolds numbers Reλ from 166 to 893, the interoccurrence time distributions P(τ) above a positive threshold Q in the inertial range is described by a universal q- exponential function, P(τ) = β(2 − q)[1 − β(1 − q)τ]1/(1−q), which may be due to the superstatistical nature of the occurrence of extreme events. Our analysis provides a universal description of extreme events in turbulent flows.