Session A22: Turbulence: General I

Optimizing turbulent flow in an octagonal tank driven by synthetic jet arrays

We investigate turbulent flow in the octagonal tank stirred by four-quadrant planar jet arrays. The zero-net-mass flux jets are individually controlled by the Sunbathing algorithm in which the On / Off times are selected from two Gaussian distributions with different means but the same coefficient of variation. In order to create the optimal turbulent flow, a large volume of homogeneous isotropic turbulence with negligible mean flow, we vary the experimental conditions including jet-array configuration (jet-to-jet distance and the number of jets in horizontal and vertical direction), with or without screens in front of arrays, and the algorithmic parameters (mean On / Off time ratio and period of a single On-Off cycle). The quantitative measurement is performed by two-dimensional particle image velocimetry (PIV). The merit of the octagonal tank is to allow orthogonal field-of-views to be aligned without additional optics, such as a liquid-filled prism used for the stereoscopic PIV in the box-shaped tank. Velocity statistics, two-point correlations, energy spectra, and turbulence metrics are acquired from the velocity data and applied to compare the performance of the experimental conditions.   

The Turbulent Dissipation Range is Not Described by (Deterministic) Navier-Stokes

Incompressible Navier-Stokes is generally believed to model low-Mach turbulent fluid flows down to almost the mean-free-path, ignoring effects of molecular noise. Estimating this noise using Landau-Lifschitz fluctuating hydrodynamics, we find that the turbulent energy spectrum is modified around the Kolmogorov scale, with expected exponential decay in the far dissipation range replaced by thermal equipartition, in agreement with predictions of Betchov 60 years ago. The far dissipation-range intermittency predicted by Kraichnan is replaced by Gaussian equilibrium statistics. We verify our arguments by simulations of a shell model of turbulence, finding also that inertial-range statistics are unaltered by thermal noise. Our results imply that turbulent processes which involve sub-Kolmogorov scale eddies, such as high-Schmidt mixing, combustion, condensation, etc. are not correctly modelled by deterministic Navier-Stokes. Instead, the Landau-Lifschitz stochastic equations must be employed, requiring fundamentally different numerical algorithms. New theoretical questions arise, because molecular viscosities are renormalized by thermal noise and become dependent upon numerical grid size. Novel experimental methods that can resolve sub-Kolmogorov scales are also urgently required.    

Clustering of vector nulls in homogeneous isotropic turbulence

The study of geometrical properties of the velocity, the Lagrangian acceleration, and the vorticity fields in turbulent flows has received considerable attention in the past decades. The geometrical properties of these fields can be useful to model important phenomena in turbulent flows such as superdifusivity, preferential concentration of particles, vortex reconnection, among many others. In this work, we analyze the vector nulls of such vector fields, coming from direct numerical simulations of forced homogeneous isotropic turbulence at $Re_\lambda \in O([40-600])$.  We show that the clustering of velocity nulls is much stronger than those of acceleration and vorticity nulls. These acceleration and vorticity nulls, however, are denser than the velocity nulls. We study the scaling of clusters of these null points with $Re_\lambda$ and with characteristic turbulence lengthscales. We also analyze datasets of point inertial particles with Stokes numbers $St = 0.5$, 3, and 6, at $Re_\lambda = 240$. Inertial particles display preferential concentration with a degree of clustering that resembles some properties of the clustering of the Lagrangian acceleration nulls, in agreement with the proposed sweep-stick mechanism of clustering formation.   

Not Participating

In this work we investigate the capability of Artificial Neural networks to build Subgrid Closure for a Shell Model of turbulence. Shell Models are dynamical systems of Ordinary Differential Equations that have been shown to rather faithfully mimic the phenomenology of the energy cascade of the Naver Stokes Equations in Fourier space. Our method employs a novel custom-made Neural Network architecture comprising a classical integrator (Runge-Kutta 4^th order) for the large scales of turbulence, augmented with LSTM cells to obtain the values of the fluxes to the small scales. We are able to reproduce, within statistical error bars, the intermittent behavior found in the full model, obtaining the correct scaling laws for Eulerian and Lagrangian structure functions and outperforming classical physics based methods. This work demonstrates the capability of Machine Learning to capture complex multiscale dynamics and reproduce complex multi-scale and multi-time non-gaussian behaviors, opening up the possibility to tackle turbulence modelling in Navier-Stokes Equations.   

Probing the large scale velocity statistics in turbulence

Turbulent flows in three dimensions of space involve a direct cascade of energy from a large scale $l_0$ to a much smaller Kolmogorov length scale $\eta$. In the limit of large Reynolds number, the statistical properties of the inertial range $1 \ll k l_0 \ll l_0/\eta$ have been well studied, starting from the analytical predictions given by Kolmogorov in 1941, and much refined since then. The dynamics of large scales ($k l_{0} \ll 1$) in the absence of bidimensionalization (rotation and/or stratification), however, have been much less studied experimentally. Two analytical predictions for the mean wavenumber energy spectrum ($E(k)$) have been proposed over the years, one by Saffman with $E(k) \propto k^{2}$ and one by Batchelor with $E(k) \propto k^{4}$. Up to date, both the Saffman and Batchelor spectra lack direct experimental evidence. We present a novel experiment that achieves a significant scale separation between the forcing scale and the experiment size to exhibit large scale statistics. Using index matching technique, we also obtain full optical access to measure in the bulk, the statistics of the large scales in a turbulent flow. As a result, we are able to test the theoretical predictions by Saffman and Batchelor.   

Experimental measurement of large scale velocity fluctuations in a turbulent flow

We design an experiment to study the large scale velocity fluctuations of a three dimensional turbulent flow to test the two existing theoretical predictions; one by Saffman and the other by Batchelor, for the mean wavenumber energy spectrum. Using an innovative modification of the 3D scanning PIV technique, we achieve a measure of the three dimensional two point velocity correlation function in a turbulent flow. We report the observation of the Saffman spectrum over a wide range of Reynolds numbers studied in the experiment. Our observation implies a thermalization of the large scale fluctuations in a turbulent flow. These experimental results show that the large scale fluctuations may be described by equilibrium statistical mechanics, contrary to the direct cascade of energy. We will eventually discuss how our experimental observation may open the door for the statistical description of the large scale dynamics of turbulence.   

How turbulence develops from a randomly spinning active grid

We present results from time-resolved PIV measurements taken directly downstream of a turbulence-generating active grid installed in a water channel with Re_λ ≈ 10³. Grid-generated turbulence is typically studied at locations downstream of the grid, where it is developed and homogeneous, isotropic turbulence. The turbulence at these locations finds its origin farther upstream, in the region of inhomogeneous turbulence directly downstream of the active grid, that has remained relatively unexplored. To unravel the mystery of the interaction between the active grid and the flow passing through, we compare three fully-random active grid operation modes of different mean wing-rotation frequencies, and a static grid reference case of minimum blockage, at locations between 2 and 4 mesh sizes (0.1 and 0.2 channel-widths) downstream of the grid. With increasing wing rotation frequencies, we find a decrease in the mean turbulence intensity. This indicates that the rotation of the wings does not introduce vorticity to the flow directly, as this would show the opposite relation, but that perhaps another production mechanism is involved. We explore this idea and compare results obtained close to the grid to positions farther downstream to gain insight in the evolution of grid-generated turbulence.   

Not Participating

Intermediate to large scale structures in atmospheric turbulence can often cause sudden and unpredictable motions for aircrafts in flight. This has been experienced by almost everyone who has been in an airplane, and is often the first example that people think of when describing turbulence. This study seeks to experimentally investigate a lab-scale model glider subjected to different incoming freestream turbulence generated by an active grid. The experiment is performed in a water channel where the turbulence characteristics are measured with laser diagnostics. The model glider measures 4 cm in length and 5 cm in wing span, and is tethered via fishing lines through its CG to an anchor point upstream. It is allowed free motion within the interrogation volume, and produces sufficient lift such that it "flies" when the flow velocity is approximately 0.4 m/s. The motion of the glider is tracked and correlated to the measured characteristics of the flow field. The goal of the study is to investigate how the turbulence statistics influence the motion of the glider on a global scale, thus providing insight into the interactions between them.   

Features of small-scale vortical structures from a fully resolved experimental dataset of von Kármán mixing flow

Intense vortical structures or ‘worms’ at the small-scales have been studied in a wide range of turbulent flows, mostly using DNS.In the present study, we investigate dynamics/statistics of the worms in a fully resolved three-dimensional experimental dataset of a turbulent mixing flow measured at the center of a large von Kármán mixing tank at a Re_λ=179. To avoid arbitrariness in the detection method, an objective detection method proposed by Haller et al. is implemented. In total, 1003 snapshots (volumes) of the flow acquired at random times with the spatial resolution of 1η, where η is the Kolmogorov length scale, have been studied. As a result, about 12500 structures were detected having an average radius of 5.1η, which is in a good agreement with previous findings. Different features of the turbulent flow were studied and compared relative to the whole volume and locally within the structures. Comparison of the joint probability density functions (J-PDFs) of the enstrophy and dissipation shows that within the structures, high vorticity and low shear are dominant. Alignment of the vorticity-eigenvectors inside the structures shows that the vorticity vector is well aligned with the intermediate eigenvector and is normal to the compressive and extensional eigenvectors demonstrating that the structures are quasi one-dimensional.The intermediate eigenvalue was found to be positive on average.This shows that enstrophy production inside the structures results from vortex stretching.We then consider the entrainment/detrainment at the boundary of the structures. This shows that the structures are entraining ambient fluid on average and that this entrainment is a result of the competing effects of non-viscous and viscous phenomena consistent with Burgers’ vortices.