10:45
Intermittency and Scaling 1
10:45
15 mins
#218
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Experimental Study of the Bottleneck in fully developed Turbulence
Eberhard Bodenschatz, Christian Küchler, Gregory Bewley
Abstract: The shape of the turbulent energy spectrum at high Taylor-scale Reynolds numbers Rλ has been investigated in numerical, laboratory, and field experiments. It is important for both the fundamental understanding of turbulence and for tests of LES and its numerous applications. Deviations from the K41 theory have been identified in the past, most prominently corrections to the spectral slope in the inertial range due to intermittency. At the transition to the dissipation range, an excess of energy is frequently observed and has been coined the bottleneck effect. It has been subject to various theories (e.g. [4, 11, 8, 10]) and studied in DNS [3]. We can quantify for the first time (to the best of our knowledge) in a classical wind tunnel experiment how the bottleneck effect gets weaker with increasing Rλ. The data is largely consistent with the results of Donzis & Sreenivasan [3].
The Variable Density Turbulence Tunnel (see Ref. [2]) exploits the capabilities of a unique active grid to produce turbulent flows up to Rλ ∼ 6000 in pressurized sulphur-hexaflouride. We use Nanoscale Thermal Anemometry Probes provided by Princeton University (see e.g. [1, 9, 7, 5]) to acquire two-point statistics of high resolution. As any hot-wire anemometry setup, our system might posess a non-flat frequency response of the system. It has been studied by Hutchins et al. [6] and their results point towards deviations in the range of frequencies where the bottleneck is expected in our experiment. By combining the flexibility of the mosaic-like active grid and different fluid densities we present relative energy spectra almost free of probe biases that allow the measurement of the subtle decay of the bottleneck peak with increasing Rλ.
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11:00
15 mins
#127
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4-D PARTICLE TRACKING VELOCIMETRY MEASUREMENTS IN A VON KARMAN TURBULENCE EXPERIMENT
Yaşar Ostovan, Christophe Cuvier, Paul Debue, Valentina VALORI, Adam cheminet, Tarek Chaabo, Jean-Marc Foucaut, Jean-Philippe Laval, Cécile Wiertel-Gasquet, Vincent Padilla, Bérengère Dubrulle, François Daviaud
Abstract: Measurements resolving dissipative scales are crucial to get a better understanding of extreme events of inertial dissipation in turbulent flows {saw2016}. Targeting this objective, time-resolved Lagrangian Particle Tracking experiments are performed in a Von Karman facility.
The measurements are conducted in a volume of 45×40×6 mm3 in water utilizing four high-speed cameras and a high-speed laser. A schematic of the Von Karman facility and a sample snapshot of Lagrangian trajectories of tracked particles for 21 time-steps are shown in Fig.1. The Von Karman tank has a diameter of 0.2m and a height of 0.18m. Reference coordinate system of the measurement domain is shown in Fig.1a. The measurements are conducted in a wide range of Reynolds numbers from 6,000 to 150,000.
Parameters of "Shake-The-Box" analysis {Schanz2016} are optimized to get not only a maximum number of tracks (to obtain higher spatial resolution), but also a minimum error in tracked particle positions using Lagrangian spectral analysis. For the measurements with Re=6,000, the optimization leads to more than 50,000 tracks in the measurement domain, which results in a mean spacing of particles smaller than 0.6 mm (of the order of Kolmogorov length-scale). Moreover, more than 40% of the tracks are longer than 20 time-steps. In the talk, the optimization process and spectral analysis will be discussed in detail.
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11:15
15 mins
#4
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Inertial range skewness of the longitudinal velocity derivative in locally isotropic turbulence
Semion Sukoriansky, Eliezer Kit, Harindra Fernando
Abstract: Longitudinal velocity-derivative skewness is directly proportional to the rate of enstrophy generation, and hence is a key parameter for characterizing small-scale turbulence. In addition, the skewness is used for qualitative assurance of turbulence measurements, for example, level of noise and unsteadiness. Obtaining of skewness requires accurate measurements at the finest scales in the dissipation subrange, which is an onerous task. We define a derivative skewness of the inertial range scales that is readily accessible experimentally, and derive its value analytically [1]. The results depend on the filtering procedure of small scales. Analytically derived inertial range skewness is compared with those computed by high resolution numerical simulations and obtained in laboratory experiments and in the MATERHORN field campaign. The MATERHORN data were acquired under nocturnal conditions in a mountain terrain. An obvious advantage is that these data belong to high Reynolds numbers typical of environmental turbulence, and the Taylor microscale of the field data used was of the order of 1300. On the other hand, the necessity of using robust high resolution probes in this natural environment required the use of relatively large-sized, multi-sensor-hot-film probes (few millimeters) that limit the measurement resolution at fine scales [2]. To circumvent this limitation, the derivative skewness determined for the inertial range was used. The computed and measured values were very close to the theoretical prediction. An alternative definition of the derivative skewness in the full and the inertial range scales is examined to identify the effects of intermittency.
Real turbulent flows are often affected by external body forces such as buoyancy and Coriolis forces that act differently on different scales. The derivative skewness of the filtered velocity field with moving filtration cut-off may shed light on modification of spectral energy transport and vorticity dynamics by external forces.
References
[1] S. Sukoriansky, E. Kit, E. Zemach, S. Midya and H.J.S. Fernando. Inertial range skewness of the longitudinal velocity derivative in locally isotropic turbulence. Physical Review Fluids 3: 114605, 2018.
[2] E. Kit, C. Hocut, D. Liberzon and H.J.S. Fernando. Fine-scale turbulent bursts in stable atmospheric boundary layer in complex terrain. J. Fluid Mech. 833: 745, 2017.
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11:30
15 mins
#8
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On a new symmetry-induced modeling framework applied to the closure problem of turbulence
Dario Klingenberg, Martin Oberlack, Dominik Pluemacher
Abstract: We present a new and generic framework allowing to formulate model equations based entirely on
physical principles, thereby eliminating the requirement to model specific terms of given unclosed equations.
Lie symmetry theory is employed to encode physical principles such as Galileian or rotational invariance independently of equations.
This novel modeling approach is particularly interesting in the context of turbulence modeling,
as it allows incorporating physical principles relating to important
properties of turbulent statistics, which have been cast in terms of symmetries.
Existing turbulence models generally fail to reflect turbulent statistics correctly,
because in the conventional modeling approaches, unclosed quantities are modeled term by term.
A symmetry is defined as a transformation that, when inserted into an equation, leaves this equation
form invariant.
For any given equation, all symmetries can be calculated algorithmically.
Symmetries are often used as a powerful tool for classifying and solving (partial) differential equations.
In the case of differential equations describing physical systems, such as the Navier-Stokes equations,
there is the additional benefit that their symmetries often correspond to important physical concepts and principles
such as the Galileian group of classical mechanics.
Indeed, many of the Navier-Stokes symmetries have been implicitly used
in natural and engineering sciences including the field of turbulence modeling, which have a clear symmetry representation.
Examples of such implicit use include dimensional analysis and tensor invariant modeling.
The current work is aimed at explicitly using symmetries to generate turbulence models, thus fully exploiting
the mathematical and constructive potential of the theory.
It is an important requirement for a set of effective or semi-empirical model equations to contain the same set of symmetries as the exact equations
in order to ensure that the model correctly encodes the relevant physical principles.
Looking at the history of turbulence models, it is observed that each generation of models contained more Navier-Stokes symmetries
than the previous one, which has led to increasingly accurate and reliable models.
For example, among the existing two-equation models, the vast majority contain all Navier-Stokes symmetries,
though because of the Boussinesq approximation, they do have additional, unphysical symmetries,
which falsely render them insensitive to time-dependent rotation and high streamline curvature.
From the serious shortcomings that these models, including Reynolds stress transport models, still exhibit, it
is however obvious that additional constraints are necessary.
Analysing the exact statistical representation of turbulence given by the
Reynolds-averaged Navier-Stokes (RANS) equations extended by the multi-point moment equations,
it turns out that all classical Navier-Stokes symmetries directly translate to the statistical approach.
Interestingly, additional symmetries without a direct counterpart in the Navier-Stokes equations can be identified
~\cite{oberlack2010,rosteck2011}.
These symmetries, referred to as statistical symmetries in the following, have been shown to encode important
properties of turbulent statistics, namely (i) intermittency and (ii) non-Gaussianity~\cite{waclawczyk2014}.
The statistical symmetries have been found to be the key ingredient for new and highly accurate
turbulent scaling laws including higher moments~\cite{sadeghi2018}, but also classical scaling laws such as the log law~\cite{waclawczyk2014}
rely inherently on the statistical symmetries.
Even though this could greatly increase the predictive quality, existing turbulence models do not contain these
symmetries.
In fact, incorporating the statistical symmetries in a turbulence model using conventional modeling techniques
can be shown to be a basically unfeasible task.
Therefore, an invariant modeling approach is developed that allows algorithmically
generating equations invariant under a given set of symmetries.
Without additional model variables, it can be shown to be impossible to formulate a closed set of equations
that is invariant under all classical and statistical symmetries.
However, by carrying out the invariant modeling algorithm, it becomes clear that introducing
a new velocity-like model variable enables the
formulation of closed model equations with the desired symmetry properties.
We show the resulting form of the model equations both for an eddy-viscosity model and for a Reynolds stress transport model,
which differs significantly from that of conventional model equations.
Future developments will be concerned with implementing these equations into a
numerical solver framework and to further improve and calibrate models founded on the present framework.
Acknoledgement:
The work of Dario Klingenberg is supported by the Excellence Initiative of the
German Federal and State Governments and the Graduate School of Computational
Engineering at Technische Universität Darmstadt.
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11:45
15 mins
#101
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Arrow of time in turbulent flows and its ramifications
Mahendra Verma
Abstract: Fundamental interactions are either fully or nearly symmetric under time reversal. But macroscopic phenomena have a definite arrow of time. Many researchers believe that the direction of time is towards increasing entropy. In this paper, we provide an alternate mechanism that is applicable to turbulent flows. In three-dimensional hydrodynamics forced at large scale, the energy flows from large scales to dissipative scales. This generic and multiscale process breaks the time reversal symmetry and principle of detailed balance, thus can yield an arrow of time. We conjecture that the above picture of time irreversibility could be employed to a more general scenario. We also compare the above perspective with the second law of thermodynamics.
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12:00
15 mins
#391
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Universality of power fluctuations in turbulence
Rémi Zamansky, Wouter Bos
Abstract: To generate or maintain a turbulent flow, one needs to introduce kinetic energy. Whereas the fluctuations of the dissipation rate have been investigated extensively, the fluctuations of the injected power have received much less attention. One of the reasons is that these fluctuations are not expected to be universal, since the different possible forcings of a turbulent flow might lead to very distinct behaviour of the power fluctuations. We show that this assertion is incorrect.
Power fluctuations in a turbulent flow are fairly universal and the reason for this is that they are not merely determined by the forcing, but also by the impedance of the turbulence itself, and this impedance can be fairly universal, in particular in the inertial range of a turbulent flow.
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12:15
15 mins
#322
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Non-locality of strain rate and vortex stretching in turbulent flows
Dhawal Buaria, Alain Pumir, Eberhard Bodenschatz
Abstract: Understanding the formation of extreme events in the velocity gradients, characteristic of small-scale intermittency, remains a central question in fluid turbulence. In absence of any boundaries, gradient amplification occurs through vortex stretching, a non-linear coupling between strain rate and vorticity. This coupling is non-local, in the sense that velocity and its derivatives can be expressed in terms of the vorticity via the Biot-Savart integral. In this regard, a key question arises about what proportion of the stretching acting at a spatial point arises from the local and the non-local contribution to the integral around it. Using direct numerical simulations of isotropic turbulence, on up to 8192^3 grid points and Taylor-scale Reynolds number of 650, we aim to characterize the non-locality of vortex stretching.
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12:30
15 mins
#27
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Eulerian vs Lagrangian irreversibility in an experimental turbulent von Karman flow
Berengere Dubrulle, Paul Debue, Valentina Valori Valentina, Tarek Chaabo, Adam Cheminet, Yasar Ostovan, Christophe Cuvier, Jean-Philippe Laval, Jean-Marc Foucaut, Cecile Wiertel, Vincent Padilla, Francois Daviaud
Abstract: In a viscous fluid, the energy dissipation is the signature of the breaking of the time-reversal symmetry $t\to -t$, ${\bf u}\to -{\bf u}$, where $u$ is the velocity. This symmetry of the Navier-Stokes equations is explicitly broken by viscosity. Yet, in the limit of large Reynolds numbers, when flow becomes turbulent, the non-dimensional energy dissipation per unit mass becomes independent of the viscosity, meaning that the time-reversal symmetry is spontaneously broken\cite{FB,Jucha14,Onsager}. Natural open questions related to such observation are: what is the mechanism of this spontaneous symmetry breaking? Can we associate the resulting time irreversibility to dynamical processes occurring in the flow? Can we devise tools to locally measure this time irreversibility?\
In this talk, I try to answer these questions in a turbulent von Karman experiment. The flow is generated by two counter-rotating impellers fitted with blades. Thanks to a high resolution 4-D PTV technique, we obtain time-resolved Lagrangian and Eulerian velocity measurements, at a resolution of the order of the Kolmogorov scale (see Figure \ref{fig1}). I use these measurements to compare Eulerian and Lagrangian signatures of irreversibility, and link them with peculiar properties of the local velocity field or trajectories.
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