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From Lie-group (symmetry) analysis of the multi-point correlation equation Oberlack and Gunther (Fluid Dyn Res 33:453-476, 2003) found three different solutions for the behavior of shear-free turbulence: (i) a diffusion like solution, in which turbulence diffuses freely into the adjacent calm fluid, (ii) a deceleration wave like solution when there is an upper bound for the integral length scale and (iii) a finite domain solution for the case when rotation is applied to the system. This paper deals with the experimental validation of the theory. We use an oscillating grid to generate turbulence in a water tank and Particle Image Velocimetry (PIV) to determine the two-dimensional velocity and out-of-plane vorticity components. The whole setup is placed on a rotating table. After the forcing is initiated, a turbulent layer develops which is separated from the initially irrotational fluid by a sharp interface, the so-called turbulent/non-turbulent interface (TNTI). The turbulent region grows in time through entrainment of surrounding fluid. We measure the propagation of the TNTI and find quantitative agreement with the predicted spreading laws for case one and two. For case three (system rotation), we observe that there is a sharp transition between a 3D turbulent flow close to the source of energy and a more 2D-like wavy flow further away. We measure that the separation depth becomes constant and in this sense, we confirm the theoretical finite domain solution.

As a first step toward characterizing coherent structures within the atmospheric surface layer (ASL), measurements obtained via a large-scale particle tracking velocimetry (LS-PTV) system were validated against wind-measurement station data as well as canonical turbulent boundary layer studies. The LS-PTV system resolves three-dimensional, Lagrangian tracks over a 16 m^3 volume. Mean-velocity measurements, as well as vertical and shear Reynolds-stress measurements, generally agreed with wind-measurement station data and Reynolds-stress profiles referenced from literature. The probability distributions for streamwise, spanwise and vertical velocity-fluctuation components appear normally distributed about zero. Furthermore, the probability distributions for all three components of Lagrangian acceleration were exponential and followed the parametrization curve from LaPorta et al. (Lett Nat 409:1017–1019, 2001). Lastly, the vorticity probability distributions were exponential and symmetric about zero, which matches findings from Balint et al. (Fluid Mech 228:53–86, 1991). The vorticity intensity measured by the LS-PTV system was less than values from Priyadarshana et al. (Fluid Mech 570:307–346, 2007), which is attributed to the low spatial resolution. However, the average spacing of 0.5 m between tracer particles is deemed sufficient for the future characterization of vortical structures within the ASL.

An investigation into redistribution of vorticity for rapidly accelerating plates with varying kinematics and initial conditions has been performed. Both three-dimensional particle tracking velocimetry and direct force measurements were applied simultaneously. The effective velocity of the feeding shear layer has been identified as the appropriate characteristic velocity rather than the commonly used plunge or free stream velocity. Based on this new normalization for circulation, it has been demonstrated that the existence of initial boundary-layer vorticity on the plunging plate – at least in the near-midplane region – does not contribute to the eventual vortex formation process. In accordance with the literature, however, the tip vortex positioning relative to the plate surface has been identified as an important contributor in the overall force production, particularly once the plate acceleration has ceased.

An investigation into the interdependency between acceleration and vorticity fields for rapidly accelerating, AR=4 plates with varying kinematics and initial conditions has been performed. In addition, the vorticity redistribution and reorientation in the plate’s proximity has also been studied. The data was obtained simultaneously by means of a threedimensional particle tracking velocimetry (3D-PTV) system together with a six-component force sensor. The effective velocity of the feeding shear layer has been identified as the appropriate characteristic velocity rather than the more commonly-used plunge or freestream velocities. Based on these newly-normalized circulation histories, it has been demonstrated that the existence of initial boundary-layer vorticity on the plunging plate - at least in the near midplane region - does not contribute to the eventual vortex formation. The comparison of identical plate kinematics with and without a superimposed uniform freestream velocity revealed a close interdependency of vorticity and Lagrangian acceleration fields. Consequently, a separation and/or superposition of circulatory and non-circulatory effects leads to an oversimplified description of such separated flows. In accordance with literature, the tip vortex has been identified to be an important contributor in the overall force production. Tip-vortex strength as well as its relative positioning to the plate surface influences the instantaneous force. As such, the orientation of the tip vortex becomes the critical contributor to lift once the acceleration of the plate has ceased.

The interaction between leading-edge-vortex and tip-vortex development on a low-aspect-ratio plate has been investigated and compared to a nominally two-dimensional rectangular flat plate. Simultaneous to force measurements, three-dimensional particle tracking velocimetry (3D-PTV) was used to characterize the instantaneous flow field on the suction side. An integration of the spanwise circulation distribution for the two-dimensional case indicates that the leading-edge-vortex formation process is correlated with the convective time and not with the instantaneous pitch angle. However, for the finite plate, it is found that the tip-vortex formation process is correlated with the instantaneous pitch angle instead. Since leading-edge vorticity is convected inboard by tip-vortex-induced spanwise velocity, leading-edge-vortex growth is found to be retarded in the tip region. Finally, with the aid of Lagrangian particle tracks, the leading-edge and tip vortices are found to grow distinct from one another, that is, no leading-edge vorticity is drawn into the tip vortex. However, the tip vortex is found to influence the leading-edge-vortex dynamics through inboard transport of leading-edge vorticity and is therefore responsible for vortex compression at the mid-span.

In preparation of simultaneous large-scale / small-scale 3D Particle Tracking Velocimetry (3D-PTV) experiments in a developing turbulent flow we performed two types of measurements separately: (i) the velocity and coarse-grained velocity derivatives were measured in a large observation volume with focus on the large-scale flow features and (ii) spatially resolved velocity derivatives were measured in a small observation volume with the goal to obtain small-scale quantities associated with vorticity and strain. In this contribution we demonstrate that the characteristic flow structures were captured and velocity derivatives were accessed with sufficient accuracy. The problem of measuring velocity derivatives both in the Lagrangian and Eulerian frame of reference is also addressed. Although comparable accuracies in both settings could be achieved with our method, only statistics obtained from the spatially resolved measurement were found to be practically the same in both settings.

We analyze the flow field within an array of 18 counter-rotating, vertical-axis wind turbines (VAWTs), with an emphasis on the fluxes of mean and turbulence kinetic energy. The turbine wakes and the recovery of the mean wind speed between the turbine rows are derived from measurements of the velocity field using a portable meteorological tower with seven, vertically-staggered, three-component ultrasonic anemometers. The data provide insight to the blockage effect of both the individual turbine pairs within the array and the turbine array as a whole. The horizontal and planform kinetic energy fluxes into the turbine array are analyzed, and various models for the roughness length of the turbine array are compared. A high planform kinetic energy flux is measured for the VAWT array, which facilitates rapid flow recovery in the wake region behind the turbine pairs. Flow velocities return to 95% of the upwind value within six rotor diameters downwind from each turbine pair. This is less than half the recovery distance behind a typical horizontal-axis wind turbine (HAWT). The observed high level of the planform kinetic energy flux is correlated with higher relative roughness lengths for the VAWT array as compared to HAWT farms. This result is especially relevant for large wind farms with horizontal dimensions comparable to the height of the atmospheric boundary layer. As shown in recent work and confirmed here, the planform kinetic energy flux can be the dominant source of energy in such large-scale wind farms.