A phenomenological theory of Eulerian and Lagrangian velocity fluctuations in turbulent flows

AbstractMarusic et al. (J. Fluid Mech., vol. 716, 2013, R3) show the first clear evidence of universal logarithmic scaling emerging naturally (and simultaneously) in the mean velocity and the intensity of the streamwise velocity fluctuations about that mean in canonical turbulent flows near walls. These observations represent a significant advance in understanding of the behaviour of wall turbulence at high Reynolds number, but perhaps the most exciting implication of the experimental results lies in the agreement with the predictions of such scaling from a model introduced by Townsend (J. Fluid Mech., vol. 11, 1961, pp. 97–120), commonly termed the attached eddy hypothesis. The elegantly simple, yet powerful, study by Marusic et al. should spark further investigation of the behaviour of all fluctuating velocity components at high Reynolds numbers and the outstanding predictions of the attached eddy hypothesis.

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Simulation of Artificial Turbulence by the Vortex Method

Computational Technologies for Fluid/Thermal/Structural/Chemical Systems With Industrial Applications, Volume 1 ◽

10.1115/pvp2002-1536 ◽

2002 ◽

Author(s):

Yoshifumi Ogami ◽

Kazuie Nishiwaki ◽

Yoshinobu Yoshihara

Keyword(s):

Turbulent Flows ◽

Three Dimensional ◽

Vortex Method ◽

Energy Spectra ◽

System Of Nonlinear Equations ◽

Vortex Methods ◽

Velocity Fluctuations ◽

Integral Scales ◽

Relative Errors ◽

Les Model

First, a simple and accurate numerical method is presented to produce velocity fluctuations that are determined by the prescribed physical quantities and qualities of turbulence such as longitudinal and lateral spectra, and integral scales. The fluctuations are obtained by solving a system of nonlinear equations that are derived from the equations of energy spectra and of root mean square of the fluctuations. This method requires as many computer memories and computations as one-dimensional case even for the three dimensional calculations. It is shown that there is a strong resemblance of the simulated velocity fluctuations and experimental data. The energy spectra of these velocity fluctuations are quite accurate with less than 0.01% relative errors to the prescribed spectra. Secondly, these solutions are used to examine the capability of the vortex methods to produce turbulent flows with the prescribed parameters. It is found that although the energy spectra by the vortex method scatter to some extent, they are distributed along the prescribed spectra. It can be said that the vortex methods are able to simulate the target turbulence fairly well. Also it is found that the solutions with the LES model increase and deviate from the target spectrum at the higher frequency regions. This may suggest the nonessentiality of the LES model for the vortex method.

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Lagrangian Velocity Statistics in Turbulent Flows: Effects of Dissipation

Physical Review Letters ◽

10.1103/physrevlett.91.214502 ◽

2003 ◽

Vol 91 (21) ◽

Cited By ~ 69

Author(s):

L. Chevillard ◽

S. G. Roux ◽

E. Levêque ◽

N. Mordant ◽

J.-F. Pinton ◽

...

Keyword(s):

Turbulent Flows ◽

Velocity Statistics ◽

Lagrangian Velocity

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On a New Theory of free Turbulence

Journal of the Royal Aeronautical Society ◽

10.1017/s0368393100106613 ◽

1943 ◽

Vol 47 (390) ◽

pp. 167-176 ◽

Cited By ~ 37

Author(s):

H. Reichardt

Keyword(s):

Differential Equation ◽

Turbulent Flows ◽

Turbulent Mixing ◽

Thermal Conduction ◽

Phenomenological Theory ◽

Rational Application ◽

Turbulent Momentum ◽

Molecular Balance

Measurements of momentum in regions of turbulent mixing show that an analogy exists between the processes of turbulent and molecular balance which enables a rational application of the differential equation of thermal conduction to the propagation of turbulent momentum to be made. This fact forms the basis of a new phenomenological theory of free turbulent flows.

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Coherence of Velocity Fluctuations in Turbulent Flows

Physical Review Letters ◽

10.1103/physrevlett.128.014501 ◽

2022 ◽

Vol 128 (1) ◽

Author(s):

G. Prabhudesai ◽

S. Perrard ◽

F. Pétrélis ◽

S. Fauve

Keyword(s):

Turbulent Flows ◽

Velocity Fluctuations

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Single inertial particle statistics in turbulent flows from Lagrangian velocity models

Physical Review Fluids ◽

10.1103/physrevfluids.7.014303 ◽

2022 ◽

Vol 7 (1) ◽

Author(s):

Jan Friedrich ◽

Bianca Viggiano ◽

Mickael Bourgoin ◽

Raúl Bayoán Cal ◽

Laurent Chevillard

Keyword(s):

Turbulent Flows ◽

Inertial Particle ◽

Velocity Models ◽

Lagrangian Velocity ◽

Particle Statistics

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Improved Discrete Random Walk Stochastic Model for Simulating Particle Dispersion and Deposition in Inhomogeneous Turbulent Flows

Journal of Fluids Engineering ◽

10.1115/1.4047538 ◽

2020 ◽

Vol 142 (10) ◽

Author(s):

Amir A. Mofakham ◽

Goodarz Ahmadi

Keyword(s):

Random Walk ◽

Turbulent Flows ◽

Particle Deposition ◽

Finite Size ◽

Particle Dispersion ◽

Concentration Profiles ◽

Velocity Fluctuations ◽

Point Particles ◽

Deposition Velocities ◽

Gradient Drift

Abstract The performance of different versions of the discrete random walk models in turbulent flows with nonuniform normal root-mean-square (RMS) velocity fluctuations and turbulence time scales were carefully investigated. The OpenFOAM v2−f low Reynolds number turbulence model was used for evaluating the fully developed streamwise velocity and the wall-normal RMS velocity fluctuations profiles in a turbulent channel flow. The results were then used in an in-house matlab particle tracking code, including the drag and Brownian forces, and the trajectories of randomly injected point-particles with diameters ranging from 10 nm to 30 μm were evaluated under the one-way coupling assumption. The distributions and deposition velocities of fluid-tracer and finite-size particles were evaluated using the conventional-discrete random walk (DRW) model, the modified-DRW model including the velocity gradient drift correction, and the new improved-DRW model including the velocity and time gradient drift terms. It was shown that the conventional-DRW model leads to superfluous migration of fluid-point particles toward the wall and erroneous particle deposition rate. The concentration profiles of tracer particles obtained by using the modified-DRW model still are not uniform. However, it was shown that the new improved-DRW model with the velocity and time scale drift corrections leads to uniform distributions for fluid-point particles and reasonable concentration profiles for finite-size heavy particles. In addition, good agreement was found between the estimated deposition velocities of different size particles by the new improved-DRW model with the available data.

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TURBULENCE DRIVEN BY FARADAY SURFACE WAVES

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194514603792 ◽

2014 ◽

Vol 34 ◽

pp. 1460379 ◽

Cited By ~ 1

Author(s):

MICHAEL SHATS ◽

NICOLAS FRANCOIS ◽

HUA XIA ◽

HORST PUNZMANN

Keyword(s):

Turbulent Flows ◽

Fluid Motion ◽

Three Dimensional ◽

Spectral Energy ◽

Vertical Acceleration ◽

Faraday Waves ◽

Frequency Spectra ◽

Inverse Energy Cascade ◽

Lagrangian Velocity ◽

Measuring Frequency

We report experimental results which show that the particle motion on the surface perturbed by Faraday waves is similar to the fluid motion in 2D turbulence. It supports the inverse energy cascade or the spectral energy transfer from smaller to larger scales. The vertical acceleration ranges from the Faraday instability threshold up to the droplet nucleation threshold where the ripples are a couple of millimeters high. Such a configuration rules out any 2D assumption on the fluid motion. The motion of floaters on the surface of the Faraday waves is essentially three dimensional but its horizontal component shows unexpected analogy with two-dimensional turbulence. The presence of the inverse cascade is detected by measuring frequency spectra of the Lagrangian velocity and confirmed by computing the third moment of the horizontal Eulerian velocity fluctuations. This is a robust phenomenon observed in deep water in a broad range of flow energies and wavelengths. The emergence of such a phenomenology in Faraday waves broadens the applicability of features common to 2D turbulent flows to the context of surface wave phenomena which is prevalent in many systems.

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Extreme events and non-Kolmogorov spectra in turbulent flows behind two side-by-side square cylinders

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.456 ◽

2019 ◽

Vol 874 ◽

pp. 677-698 ◽

Cited By ~ 2

Author(s):

Yi Zhou ◽

Koji Nagata ◽

Yasuhiko Sakai ◽

Tomoaki Watanabe

Keyword(s):

Flow Regime ◽

Turbulent Flows ◽

Power Law ◽

Extreme Events ◽

Upstream Region ◽

Velocity Fluctuations ◽

Square Cylinders ◽

Gap Flow ◽

Power Law Exponent ◽

Non Gaussian

Turbulent flows behind two side-by-side square cylinders with three different gap ratios, namely, $L_{d}/T_{0}=4,$ 6 and 8 ($L_{d}$ is the separation distance between two cylinders and $T_{0}$ is the cylinder thickness) are investigated by using direct numerical simulations. Depending on the strength of the gap flow, the three cases can generally be characterized into two regimes, one being the weak gap flow regime and the other being the robust gap flow regime. The wake-interaction length scale can only be applied to characterize the spatial evolution of the dual-wake flow in the robust gap flow regime. And only in this regime can the so-called ‘extreme events’ (i.e. non-Gaussian velocity fluctuations with large flatness) be identified. For the case with $L_{d}/T_{0}=6$, two downstream locations, i.e. $X/T_{0}=6$ and 26, at which the turbulent flows are highly non-Gaussian distributed and approximately Gaussian distributed, respectively, are analysed in detail. A well-defined $-5/3$ energy spectrum can be found in the near-field region (i.e. $X/T_{0}=6$), where the turbulent flow is still developing and highly intermittent and Kolmogorov’s universal equilibrium hypothesis does not hold. We confirm that the approximate $-5/3$ power law in the high-frequency range is closely related to the occurrences of the extreme events. As the downstream distance increases, the velocity fluctuations gradually adopt a Gaussian distribution, corresponding to a decrease in the strength of the extreme events. Consequently, the range of the $-5/3$ power law narrows. In the upstream region (i.e. $X/T_{0}=6$), the second-order structure function exhibits a power-law exponent close to $1$, whereas in the far downstream region (i.e. $X/T_{0}=26$) the expected $2/3$ power-law exponent appears. The larger exponent at $X/T_{0}=6$ is related to the fact that fluid motions in the intermediate range can directly ‘feel’ the large-scale vortex shedding.

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ANALYSIS OF ENERGY SPECTRA BY THE VORTEX METHOD WITH ARTIFICIAL TURBULENCE

Revista de Engenharia Térmica ◽

10.5380/reterm.v3i2.3528 ◽

2004 ◽

Vol 3 (2) ◽

pp. 143

Author(s):

Y. Ogami ◽

K. Nishiwaki ◽

Y. Yoshihara

Keyword(s):

Turbulent Flows ◽

Kinematic Viscosity ◽

Vortex Method ◽

Energy Spectra ◽

Mean Square ◽

Characteristic Parameters ◽

Mean Velocity ◽

Velocity Fluctuations ◽

Inlet Condition ◽

The Given

First, in order to use as an inlet condition for turbulent simulation, a method is presented which produces numerically an artificial turbulence, namely, a series of velocity fluctuations of which frequency is Gaussian, and energy spectrum and root mean square correspond to the given ones. Besides, the fluctuation data are determined by the characteristic parameters of turbulent flows such as the inlet mean velocity, the kinematic viscosity, the Kolmogorov scale and the integral time scale. Our examples show excellent accuracy and flexibility of the method. Secondly, the vortex method has been studied to see the ability of the method to deal with turbulent flows. It is found that the energy spectra produced by this agree well with the ones given as the inlet condition, and that the vortex method is able to produce turbulent flows with the given parameters described above.

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