Turbulent boundary layer flow over regularly and irregularly arranged truncated cone surfaces

Aiming to study the rough-wall turbulent boundary layer structure over differently arranged roughness elements, an experimental study was conducted on flows with regular and random roughness. Varying planform densities of truncated cone roughness elements in a square staggered pattern were investigated. The same planform densities were also investigated in random arrangements. Velocity statistics were measured via two-component laser Doppler velocimetry and stereoscopic particle image velocimetry. Friction velocity, thickness, roughness length and zero-plane displacement, determined from spatially averaged flow statistics, showed only minor differences between the regular and random arrangements at the same density. Recent a priori morphometric and statistical drag prediction methods were evaluated against experimentally determined roughness length. Observed differences between regular and random surface flow parameters were due to the presence of secondary flows which manifest as high-momentum pathways and low-momentum pathways in the streamwise velocity. Contrary to expectation, these secondary flows were present over the random surfaces and not discernible over the regular surfaces. Previously identified streamwise-coherent spanwise roughness heterogeneity does not seem to be present, suggesting that such roughness heterogeneity is not necessary to sustain secondary flows. Evidence suggests that the observed secondary flows were initiated at the front edge of the roughness and sustained over irregular roughness. Due to the secondary flows, local turbulent boundary layer profiles do not scale with local wall shear stress but appear to scale with local turbulent shear stress above the roughness canopy. Additionally, quadrant analysis shows distinct changes in the populations of ejection and sweep events.

Short- and long-term predictions of chaotic flows and extreme events: a physics-constrained reservoir computing approach

We propose a physics-constrained machine learning method—based on reservoir computing—to time-accurately predict extreme events and long-term velocity statistics in a model of chaotic flow. The method leverages the strengths of two different approaches: empirical modelling based on reservoir computing, which learns the chaotic dynamics from data only, and physical modelling based on conservation laws. This enables the reservoir computing framework to output physical predictions when training data are unavailable. We show that the combination of the two approaches is able to accurately reproduce the velocity statistics, and to predict the occurrence and amplitude of extreme events in a model of self-sustaining process in turbulence. In this flow, the extreme events are abrupt transitions from turbulent to quasi-laminar states, which are deterministic phenomena that cannot be traditionally predicted because of chaos. Furthermore, the physics-constrained machine learning method is shown to be robust with respect to noise. This work opens up new possibilities for synergistically enhancing data-driven methods with physical knowledge for the time-accurate prediction of chaotic flows.

Statistical Model of Turbulent Dispersion Recapitulated

A comprehensive summary and update is given of Brouwers’ statistical model that was developed during the previous decade. The presented recapitulated model is valid for general inhomogeneous anisotropic velocity statistics that are typical of turbulence. It succeeds and improves the semiempirical and heuristic models developed during the previous century. The model is based on a Langevin and diffusion equation of which the derivation involves (i) the application of general principles of physics and stochastic theory; (ii) the application of the theory of turbulence at large Reynolds numbers, including the Lagrangian versions of the Kolmogorov limits; and (iii) the systematic expansion in powers of the inverse of the universal Lagrangian Kolmogorov constant C0, C0 about 6. The model is unique in the collected Langevin and diffusion models of physics and chemistry. Presented results include generally applicable expressions for turbulent diffusion coefficients that can be directly implemented in numerical codes of computational fluid mechanics used in environmental and industrial engineering praxis. This facilitates the more accurate and reliable prediction of the distribution of the mean concentration of passive or almost passive admixture such as smoke, aerosols, bacteria, and viruses in turbulent flow, which are all issues of great societal interest.

Measurement of turbulent boundary layer unsteady wall pressures beneath elastomer layers of various thicknesses on a plate

The attenuation of turbulence-inducedwall pressure fluctuations through elastomer layers is studied experimentally and analytically. Wall pressure statistics are measured downstream from a backward facing step, with no elastomer present and beneath 2-, 3- and 4-mm-thick elastomers in a water tunnel facility. In the absence of an elastomer layer, the wall pressure spectra, cross-spectra and velocity statistics measured at the various locations downstream from the backward facing step are in excellent agreement with those reported in the archival literature. The streamwise coherence measured beneath the elastomer layers is higher than that measured in the absence of an elastomer layer, an effect which increases with increasing elastomer thickness. It is speculated that this increase in coherence level is due to the ability of the elastomer to support shear stresses, which effectively increases the area over which an eddy influences the normal stresses measured by the pressure sensors. The high-frequency filtering of the elastomers is also observed in the coherence at the smallest streamwise separation. The attenuation of the turbulent boundary layer wall pressure fluctuations through the elastomer layer using an analytical elastomer transfer function is in excellent agreement with the attenuation measured experimentally through all thicknesses of elastomer and at all the free stream velocities at which the experiments are performed.

Experimental observation of the elastic range scaling in turbulent flow with polymer additives

A minute amount of long-chain flexible polymer dissolved in a turbulent flow can drastically change flow properties, such as reducing the drag and enhancing mixing. One fundamental riddle is how these polymer additives interact with the eddies of different spatial scales existing in the turbulent flow and, in turn, alter the turbulence energy transfer. Here, we show how turbulent kinetic energy is transferred through different scales in the presence of the polymer additives. In particular, we observed experimentally the emerging of a previously unidentified scaling range, referred to as the elastic range, where increasing amount of energy is transferred by the elasticity of the polymers. In addition, the existence of the elastic range prescribes the scaling of high-order velocity statistics. Our findings have important implications to many turbulence systems, such as turbulence in plasmas or superfluids where interaction between turbulent eddies and other nonlinear physical mechanisms are often involved.

LiSBOA (LiDAR Statistical Barnes Objective Analysis) for optimal design of lidar scans and retrieval of wind statistics – Part 2: Applications to lidar measurements of wind turbine wakes

The LiDAR Statistical Barnes Objective Analysis (LiSBOA), presented in Letizia et al. (2021), is a procedure for the optimal design of lidar scans and calculations over a Cartesian grid of the statistical moments of the velocity field. Lidar data collected during a field campaign conducted at a wind farm in complex terrain are analyzed through LiSBOA for two different tests. For both case studies, LiSBOA is leveraged for the optimization of the azimuthal step of the lidar and the retrieval of the mean equivalent velocity and turbulence intensity fields. In the first case, the wake velocity statistics of four utility-scale turbines are reconstructed on a 3D grid, showing LiSBOA's ability to capture complex flow features, such as high-speed jets around the nacelle and the wake turbulent-shear layers. For the second case, the statistics of the wakes generated by four interacting turbines are calculated over a 2D Cartesian grid and compared to the measurements provided by the nacelle-mounted anemometers. Maximum discrepancies, as low as 3 % for the mean velocity (with respect to the free stream velocity) and turbulence intensity (in absolute terms), endorse the application of LiSBOA for lidar-based wind resource assessment and diagnostic surveys for wind farms.

Wake Unsteadiness and Tip Vortex System of Full-Scale Helicopters in Ground Effect

The main rotor wakes of the free-flying DLR test helicopters Airbus Bo105 and EC135 were investigated in ground effect during hover, vertical takeoff, and forward flight. A high-speed schlieren system tracked the blade tip vortices at about 60 images per revolution. In addition, a constant temperature anemometry system utilized arrays of fiber film sensors, providing velocity statistics and spectra in the rotor flow. The overall wake structure agreed to preceding studies, but the velocity profiles and tip vortex trajectories were sensitive towards the environmental wind conditions. The tip vortices were observed in the schlieren images up to an age corresponding to about two revolutions below the rotor plane, before developing instabilities and falling below the detection limit. Systematic vortex pairing was found for the Bo105 but not for the EC135. The remnants of the tip vortices were identified further downstream in the wake by means of rotor-harmonic velocity signals, but they play a minor role in comparison to broad-banded turbulent fluctuations with a Kolmogorov-like spectrum. For vertical takeoff cases, the rotor wake had a hover-like structure until breaking down into low-frequency oscillations when exceeding a hub height of approximately 1.4 rotor radii. In forward flight, different types of wake velocity footprints were categorized on the basis of the normalized advance ratio. Blade–vortex interactions were found in the frontal area of the main rotor planes and between the main rotor tip vortices and the Bo105's tail rotor. The interactions prevent a further evolution of the tip vortices.

Continuously heated granular gas of elongated particles

Some years ago, Harth et al. experimentally explored the steady state dynamics of a heated granular gas of rod-like particles in microgravity [K. Harth et al. Phys. Rev. Lett. 110, 144102 (2013)]. Here, we report numerical results that quantitatively reproduce their experimental findings and provide additional insight into the process. A system of sphero-cylinders is heated by the vibration of three flat side walls, resulting in one symmetrically heated direction, one non-symmetrically heated direction, and one non-heated direction. In the non-heated direction, the speed distribution follows a stretched exponential distribution $$p(\upsilon )\, \propto \,{\rm{exp}}\left( { - {{\left( {{{\left| \upsilon \right|} \mathord{\left/ {\vphantom {{\left| \upsilon \right|} C}} \right. \kern-\nulldelimiterspace} C}} \right)}^{1.5}}} \right)$$. In the symmetrically heated direction, the velocity statistics at low speeds is similar but it develops pronounced exponential tails at high speeds. In the non-symmetrically heated direction (not accessed experimentally), the distribution also follows $$p(\upsilon )\, \propto \,{\rm{exp}}\left( { - {{\left( {{{\left| \upsilon \right|} \mathord{\left/ {\vphantom {{\left| \upsilon \right|} C}} \right. \kern-\nulldelimiterspace} C}} \right)}^{1.5}}} \right)$$ , but the velocity statistics of rods moving toward the vibrating wall resembles the indirectly excited direction, whereas the velocity statistics of those moving away from the wall resembles the direct excited direction.

Imprint of baryons and massive neutrinos on velocity statistics

We explored the impact of baryonic effects (namely stellar and active galactic nuclei feedback) on the moments of pairwise velocity using the Illustris-TNG, EAGLE, cosmo-OWLS, and BAHAMAS suites of cosmological hydrodynamical simulations. The assumption that the mean pairwise velocity of the gas component follows that of the dark matter is studied here at small separations, and we find that even at pair separations of 10–20 h−1Mpc, there is a 4–5% velocity bias. At smaller separations, it gets larger with varying strength depending on the sub-grid prescription. By isolating different physical processes, our findings suggest that the large-scale velocity bias is mainly driven by stellar rather than active galactic nuclei feedback. If unaccounted for, this velocity offset could possibly bias cosmological constraints from the kinetic Sunyaev-Zel’dovich effect in future cosmic microwave background (CMB) surveys. Furthermore, we examined how the first and the second moment of the pairwise velocity are affected by both the baryonic and the neutrino free-streaming effects for both the matter and gas components. For both moments, we were able to disentangle the effects of baryonic processes from those of massive neutrinos; and for pair separations below 20 h−1Mpc, we find that these moments of the pairwise velocity decrease with increasing neutrino mass. Our work thus sets out a way in which the pairwise velocity statistics can be utilised to constrain the summed mass of neutrinos from future CMB surveys and peculiar velocity surveys.