Turbulence statistics from three different nacelle lidars

Atmospheric turbulence can be characterized by the Reynolds stress tensor, which consists of the second-order moments of the wind field components. Most of the commercial nacelle lidars cannot estimate all components of the Reynolds stress tensor due to their limited number of beams; most can estimate the along-wind velocity variance relatively well. Other components are however also important to understand the behavior of, e.g., the vertical wind profile and meandering of wakes. The SpinnerLidar, a research lidar with multiple beams and a very high sampling frequency, was deployed together with two commercial lidars in a forward-looking mode on the nacelle of a Vestas V52 turbine to scan the inflow. Here, we compare the lidar-derived turbulence estimates with those from a sonic anemometer using both numerical simulations and measurements from a nearby mast. We show that from these lidars, the SpinnerLidar is the only one able to retrieve all Reynolds stress components. For the two- and four-beam lidars, we study different methods to compute the along-wind velocity variance. By using the SpinnerLidar's Doppler spectra of the radial velocity, we can partly compensate for the lidar's probe volume averaging effect and thus reduce the systematic error of turbulence estimates. We find that the variances of the radial velocities estimated from the maximum of the Doppler spectrum are less affected by the lidar probe volume compared to those estimated from the median or the centroid of the Doppler spectrum.

One-point statistics for turbulent pipe flow up to

We study turbulent flows in a smooth straight pipe of circular cross-section up to friction Reynolds number $({\textit {Re}}_{\tau }) \approx 6000$ using direct numerical simulation (DNS) of the Navier–Stokes equations. The DNS results highlight systematic deviations from Prandtl friction law, amounting to approximately $2\,\%$ , which would extrapolate to approximately $4\,\%$ at extreme Reynolds numbers. Data fitting of the DNS friction coefficient yields an estimated von Kármán constant $k \approx 0.387$ , which nicely fits the mean velocity profile, and which supports universality of canonical wall-bounded flows. The same constant also applies to the pipe centreline velocity, thus providing support for the claim that the asymptotic state of pipe flow at extreme Reynolds numbers should be plug flow. At the Reynolds numbers under scrutiny, no evidence for saturation of the logarithmic growth of the inner peak of the axial velocity variance is found. Although no outer peak of the velocity variance directly emerges in our DNS, we provide strong evidence that it should appear at ${\textit {Re}}_{\tau } \gtrsim 10^4$ , as a result of turbulence production exceeding dissipation over a large part of the outer wall layer, thus invalidating the classical equilibrium hypothesis.

Understanding complex wind fields with single Doppler Lidar techniques

<p>Scanning Wind Doppler lidars are more and more used for operational applications for which the retrieval of wind vectors and the turbulence quantities at specific points or at high resolution in an area of interest can bring valuable information. For retrieving volume wind data, many techniques can be used to retrieve wind vectors from the combination of radial wind data at different distances and lines of sight, as the well-known Volume Velocity Processing (VVP) technique, developed formerly for Doppler Radars. Although More sophisticated techniques based on the coupling with computational fluid dynamic models exist. e, a processing based on the VVP technique, called the Volume Wind processing (VW) has been developed. This algorithm includes a Single Value Decomposition algorithm that ensures a robust filtering of the retrieved wind data, and then high accuracy and precision. In addition, radial velocity variance (RVV) algorithm has been developped to remove the constant wind speed over a scan to provide fields of turbulent radial wind speeds. Those fields can be averaged and their variances can be computed to determine the averaged turbulent radial wind speeds as well as its deviation.</p><p>In this study, the principle and the validation of the VW algorithm will be presented at different sites (offshore, rural, and urban) against reference anemometers will be firstly presented. The bias and precision on 10 minutes averaged wind speed obtained are both about 0.5 m/s. The results reveal that the accuracy is significantly better for winds along lidar beam and precision better for larger samples of instantaneous wind speeds in the averaging time. Finally, the Volume Wind and the Radial Velocity Variance algorithms have then been applied to datasets of several months measured with Windcube Scanning Lidars at two different sites characterized by complex terrain and buildings. The data processed by the algorithms are analyzed to better understand the heterogeneities of the wind fields and its variations in time. </p>

Numerical study on edge tone with compressible direct numerical simulation: Sound intensity and jet motion

A two-dimensional model of the edge tone is studied by a highly accurate and reliable method of direct numerical simulation of the compressible Navier-Stokes equations, and used to verify key features observed in previous experimental and numerical studies, and to discover new features related to the jet motion and the edge tone generation mechanism. The first and second modes of the edge tone that are numerically reproduced agree well with Brown’s equation. In the mode transition region, dynamical mode transition is observed at a fixed jet velocity. For both first and second modes, the pressure distributions are antisymmetric with respect to the edge plate, and the sound intensity is proportional to the fifth power of the jet velocity. These results are consistent with the edge tone being radiated from a dipole-like source. Spatial profiles of the velocity and the velocity variance of the oscillating jet are also investigated for each mode over a range of the jet velocity including the mode transition regime. The amplitude of the velocity oscillation becomes constant with increasing jet velocity, while a measure of the amplitude of the velocity variance profile, which is introduced to characterize the strength of the jet fluctuation and named the ’fluctuation strength’, is proportional to the third power of the jet velocity. Some properties of the fluctuation strength correspond to properties of the sound intensity, including the first mode having larger amplitude than the second mode, and the way of deviating from the power law at smaller values of jet velocity and in the mode transition region. It is proposed that the third-power law exhibited by behavior of the fluctuation strength could be related to the increase of the skewness observed in the velocity profile with increase of jet velocity, and a model calculation is used to support this proposal.

An approach to minimize aircraft motion bias in multi-hole probe wind measurements made by small unmanned aerial systems

A multi-hole probe mounted on an aircraft provides the air velocity vector relative to the aircraft, requiring knowledge of the aircraft spatial orientation (e.g., Euler angles), translational velocity and angular velocity to translate this information to an Earth-based reference frame and determine the wind vector. As the relative velocity of the aircraft is typically an order of magnitude higher than the wind velocity, the extracted wind velocity is very sensitive to multiple sources of error including misalignment of the probe and aircraft coordinate system axes, sensor error and misalignment in time of the probe and aircraft orientation measurements in addition to aerodynamic distortion of the velocity field by the aircraft. Here, we present an approach which can be applied after a flight to identify and correct biases which may be introduced into the final wind measurement. The approach was validated using a ground reference, different aircraft and the same aircraft at different times. The results indicate a significant reduction in wind velocity variance at frequencies which correspond to aircraft motion.

An Approach to Minimize Aircraft Motion Bias in Multi-Hole Probe Wind Measurements made by Small Unmanned Aerial Systems

Multi-hole probe mounted on an aircraft provide the air velocity vector relative to the aircraft, requiring knowledge of the aircraft spatial orientation, translation, and velocity to translate this information to an Earth-based reference frame and determine the wind vector. As the relative velocity of the aircraft is typically an order of magnitude higher than the wind velocity, the extracted wind velocity is very sensitive to multiple sources of error including misalignment of the probe and aircraft coordinate system axes, sensor error and misalignment in time of the probe and aircraft orientation measurements in addition to aerodynamic distortion of the velocity field by the aircraft. Here, we present an approach which can be applied after a flight to identify and correct biases which may be introduced into the final wind measurement. The approach was validated using a ground reference, different aircraft, and for the same aircraft at different times. The results indicate significant reduction in wind velocity variance at frequencies which correspond to aircraft motion.

A Method for Identifying Kolmogorov’s Inertial Subrange in the Velocity Variance Spectrum

Kolmogorov’s inertial subrange is one of the most recognized concepts in fluid turbulence. However, the practical application of this theory to turbulent flows requires identifying subrange bandwidth. In the atmospheric boundary layer, decades of investigation support Kolmogorov’s theory, but the techniques used to identify the subrange vary and no systematic approach has emerged. The algorithm for robust identification of the inertial subrange (ARIIS) has been developed to facilitate empirical studies of the turbulence cascade. ARIIS systematically and robustly identifies the most probable subrange bandwidth in a given velocity variance spectrum. The algorithm is a novel approach in that it directly uses the expected 3/4 ratio between streamwise and transverse velocity components to locate the onset and extent of the inertial subrange within a single energy density spectrum. Furthermore, ARIIS does not assume a −5/3 power law but instead uses a robust, iterative statistical fitting technique to derive the slope over the identified range. This algorithm was tested using a comprehensive micrometeorological dataset obtained from the Floating Instrument Platform (FLIP). The analysis revealed substantial variation in the inertial subrange bandwidth and spectral slope, which may be driven, in part, by mechanical wind–wave interactions. Although demonstrated using marine atmospheric data, ARIIS is a general approach that can be used to study the energy cascade in other turbulent flows.

The Universality of the Normalized Vertical Velocity Variance in Contrast to the Horizontal Velocity Variance in the Convective Boundary Layer

The vertical turbulent velocity variance normalized by the convective velocity squared as a function of the boundary layer depth–normalized height [i.e., ] in the convective boundary layer (CBL) over a homogeneous surface exhibits a near-universal profile, as demonstrated by field observations, laboratory experiments, and numerical simulations. The profile holds over a wide CBL stability range set by the friction velocity, CBL depth, and surface heating. In contrast, the normalized horizontal turbulent velocity variance increases monotonically with decreasing stability. This study investigates the independence of the profile to changes in CBL stability, or more precisely, wind shear. Large-eddy simulations of several convective and neutral cases are performed by varying surface heating and geostrophic winds. Analysis of the turbulent kinetic energy budgets reveals that the conversion term between and depends almost entirely on buoyancy. This explains why does not vary with shear, which is a source to only. Further analysis through rotational and divergent decomposition suggests that the near-universal profile of is fundamentally related to the dynamics and interactions of local and nonlocal CBL turbulence. Specifically, the preferential interactions between local wavenumbers and the downscale energy cascade of CBL turbulence offer plausible explanations to the universal profile of .

Inhomogeneous Turbulent Dispersion across the Nearshore Induced by Surfzone Eddies

In various oceanic regions, drifter-derived diffusivities reach a temporal maximum and subsequently decrease. Often, these are regions of inhomogeneous eddies, however, the effect of inhomogeneous turbulence on dispersion is poorly understood. The nearshore region (spanning from the surfzone to the inner shelf) also has strong cross-shore inhomogeneous turbulence. Nearshore Lagrangian statistics are estimated from drifter trajectories simulated with a wave-resolving two-dimensional Boussinesq model with random, normally incident, and directionally spread waves. The simulation is idealized and does not include other (wind, tidal, Coriolis) processes. The eddy field cross-shore inhomogeneity affects both the mean cross-shore drift and cross- and alongshore diffusivities. Short-time diffusivities are locally ballistic, and the mean drift is toward the eddy velocity variance maximum. The diffusivities reach a maximum and subsequently decrease, that is, are subdiffusive. The diffusivity maximum and time to maximum are parameterized taking into account the eddy field inhomogeneity. At long times, the cross- and alongshore diffusivities scale as t−1/2 and t−1/4, respectively, which is related to the offshore decay of the eddy intensity. A diffusion equation, with a space-dependent Fickian diffusivity related to the eddy velocity variance, reproduced the short-, intermediate-, and long-time behavior of the mean drift and cross-shore diffusivity. The small Middleton parameter, indicating fixed float dispersion, suggests the Eulerian time scale can parameterize the Lagrangian time scale in this region. Although this idealized simulation had no mean currents, and thus no shear dispersion or mixing suppression, inhomogeneous turbulence effects may be relevant in other regions such as the Antarctic Circumpolar Current (ACC) and western boundary current extensions.