scholarly journals A dissipative random velocity field for fully developed fluid turbulence

2016 ◽  
Vol 794 ◽  
pp. 369-408 ◽  
Author(s):  
Rodrigo M. Pereira ◽  
Christophe Garban ◽  
Laurent Chevillard
Keyword(s):  
Energy Transfer ◽  
Velocity Field ◽  
Turbulent Flows ◽  
Free Parameter ◽  
Structure Functions ◽  
Gradient Tensor ◽  
Fluid Turbulence ◽  
Fully Developed Turbulent Flow ◽  
Dissipative Case ◽  
Velocity Increments

We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field (Chevillardet al.,Europhys. Lett., vol. 89, 2010, 54002) of an incompressible, homogeneous, isotropic and fully developed turbulent flow. A key step in the construction of this model is the introduction of some aspects of the vorticity stretching mechanism that governs the dynamics of fluid particles along their trajectories. An additional further phenomenological step aimed at including the long range correlated nature of turbulence makes this model dependent on a single free parameter,${\it\gamma}$, that can be estimated from experimental measurements. We confirm the realism of the model regarding the geometry of the velocity gradient tensor, the power-law behaviour of the moments of velocity increments (i.e. the structure functions) including the intermittent corrections and the existence of energy transfer across scales. We quantify the dependence of these basic properties of turbulent flows on the free parameter${\it\gamma}$and derive analytically the spectrum of exponents of the structure functions in a simplified non-dissipative case. A perturbative expansion in power of${\it\gamma}$shows that energy transfer, at leading order, indeed take place, justifying the dissipative nature of this random field.

scholarly journals Scale-dependent anisotropy, energy transfer and intermittency in bubble-laden turbulent flows

2021 ◽  
Vol 927 ◽  
Author(s):  
Tian Ma ◽  
Bernhard Ott ◽  
Jochen Fröhlich ◽  
Andrew D. Bragg
Keyword(s):  
Energy Transfer ◽  
Turbulent Flows ◽  
Single Phase ◽  
Nonlinear Term ◽  
Vertical Channel ◽  
Order Structure ◽  
Mixing Properties ◽  
Dissipation Scale ◽  
Velocity Increments ◽  
Small Bubbles

Data from direct numerical simulations of disperse bubbly flows in a vertical channel are used to study the effect of the bubbles on the carrier-phase turbulence. We developed a new method, based on an extension of the barycentric map approach, that allows us to quantify and visualize the anisotropy and componentiality of the flow at any scale. Using this we found that the bubbles significantly enhance anisotropy in the flow at all scales compared with the unladen case, and that for some bubble cases, very strong anisotropy persists down to the smallest scales of the flow. The strongest anisotropy observed was for the cases involving small bubbles. Concerning the energy transfer among the scales of the flow, our results indicate that for the bubble-laden cases, the energy transfer is from large to small scales, just as for the unladen case. However, there is evidence of an upscale transfer when considering the transfer of energy associated with particular components of the velocity field. Although the direction of the energy transfer is the same with and without the bubbles, the behaviour of the energy transfer is significantly modified by the bubbles, suggesting that the bubbles play a strong role in altering the activity of the nonlinear term in the flow. The skewness of the velocity increments also reveals a strong effect of the bubbles on the flow, changing both its sign and magnitude compared with the single-phase case. We also consider the normalized forms of the fourth-order structure functions, and the results reveal that the introduction of bubbles into the flow strongly enhances intermittency in the dissipation range, but suppresses it at larger scales. This strong enhancement of the dissipation-scale intermittency has significant implications for understanding how the bubbles might modify the mixing properties of turbulent flows.

Comments on the reconnexion rate of magnetic fields

1973 ◽  
Vol 9 (1) ◽  
pp. 49-63 ◽  
Author(s):  
E. N. Parker
Keyword(s):  
Velocity Field ◽  
Magnetic Fields ◽  
Turbulent Flows ◽  
Similarity Solutions ◽  
Neutral Point ◽  
Solar Photosphere ◽  
Complete Field ◽  
Fluid Equations ◽  
The Galaxy

The reconnexion rate of magnetic fields is crucial in understanding the fields found in turbulent flows in the solar photosphere and in the galaxy, and in flare phenomena. This paper examines the behaviour of magnetic fields in the neighbourhood of an X-type neutral point. The treatment is kinematical, specifying the velocity field v and constructing solutions to the hydromagnetic equation for B. The calculations demonstrate that the reconnexion rate is controlled by the diffusion in the near neighbourhood of the neutral point, and is not arbitrarily large, as has been suggested by similarity solutions of the complete field and fluid equations for vanishing diffusion

Structure functions in homogeneous and non-homogeneous turbulent flows

1999 ◽  
pp. 319-327 ◽  
Author(s):  
P. Orlandi ◽  
R. A. Antonia ◽  
P. G. Esposito
Keyword(s):  
Turbulent Flows ◽  
Structure Functions

The importance of non-normal contributions to velocity gradient tensor dynamics for spatially developing, inhomogeneous, turbulent flows

2019 ◽  
Vol 20 (9) ◽  
pp. 577-598 ◽  
Author(s):  
P. Beaumard ◽  
O. R. H. Buxton ◽  
C. J. Keylock
Keyword(s):  
Turbulent Flows ◽  
Velocity Gradient ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor

scholarly journals Structure function measurements of the intermittent MHD turbulent cascade

1997 ◽  
Vol 4 (3) ◽  
pp. 185-199 ◽  
Author(s):  
T. S. Horbury ◽  
A. Balogh
Keyword(s):  
Energy Transfer ◽  
High Speed ◽  
Solar Wind Plasma ◽  
Turbulent Energy ◽  
Structure Functions ◽  
Order Structure ◽  
Data Sets ◽  
Magnetic Field Data ◽  
Spacecraft Data ◽  
Turbulent Cascade

Abstract. The intertmittent nature of turbulence within solar wind plasma has been demonstrated by several studies of spacecraft data. Using magnetic field data taken in high speed flows at high heliographic latitudes by the Ulysses probe, the character of fluctuations within the inertia] range is discussed. Structure functions are used extensively. A simple consideration of errors associated with calculations of high moment structure functions is shown to be useful as a practical estimate of the reliability of such calculations. For data sets of around 300 000 points, structure functions of moments above 5 are rarely reliable on the basis of this test, highlighting the importance of considering uncertainties in such calculations. When unreliable results are excluded, it is shown that inertial range polar fluctuations are well described by a multifractal model of turbulent energy transfer. Detailed consideration of the scaling of high order structure functions suggests energy transfer consistent with a "Kolmogorov" cascade.

Two-Fluid Large-Eddy Simulation Approach for Gas-Particle Turbulent Flows Using Equilibrium Assumption

2006 ◽  
Author(s):  
Babak Shotorban ◽  
S. Balachandar
Keyword(s):  
Velocity Field ◽  
Gas Phase ◽  
Turbulent Flows ◽  
Particle Concentration ◽  
Particle Flux ◽  
Subgrid Scale ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Scale Particle ◽  
Two Fluid

This article illustrates a two-fluid large-eddy simulation (LES) approach for gas-particle turbulent flows. The equilibrium assumption in which the velocity of particles is approximated in terms of the velocity and acceleration of the gas phase, is made for the development of gas-particle LES formulation in this study. A filtered Eulerian velocity field is defined for particles and expressed in terms of the temporal and spatial derivatives of the gas-phase filtered velocity field. Also, filtered particle concentration defined in the Eulerian framework is governed by a transport equation with a closure problem resulted from filtering the particle concentration nonlinear convection term and in the form of subgrid-scale particle flux. A Smagorinsky kind of formulation is used to model the subgrid-scale particle flux and close the transport equation of the filtered particle concentration. The developed gas-particle LES formulation is implemented in a homogeneous shear turbulence configuration and results are discussed. It is shown that the equilibrium assumption is valid for sufficiently small particle time constants through conducting the direct numerical simulation of the same configuration.

scholarly journals Experimental and Analytical Study of Axial Turbulent Flows in an Interior Subchannel of a Bare Rod Bundle

1976 ◽  
Vol 98 (2) ◽  
pp. 262-268 ◽  
Author(s):  
P. Carajilescov ◽  
N. E. Todreas
Keyword(s):  
Velocity Field ◽  
Turbulent Flows ◽  
Length Distribution ◽  
Secondary Flows ◽  
Reynolds Stresses ◽  
Rod Bundle ◽  
Aspect Ratios ◽  
Fuel Elements ◽  
Velocity Turbulence ◽  
Rod Array

Reactor fuel elements generally consist of rod bundles with the coolant flowing axially through the bundles in the space between the rods. Heat transfer calculations form an important part in the design of such elements, which can only be carried out if information of the velocity field is available. A one-equation statistical model of turbulence is applied to compute the detailed description of velocity field (axial and secondary flows) and the wall shear stress distribution of steady, fully developed turbulent flows with incompressible, temperature-independent fluid, flowing through triangular arrays of rods with different aspect ratios (P/D). Also experimental measurements of the distributions of the axial velocity, turbulence kinetic energy, and Reynolds stresses were performed using a laser Doppler anemometer (LDA), operating in a “fringe” mode with forward scattering, in a simulated interior subchannel of a triangular rod array with P/D = 1.123 and L/DH = 77. From the experimental results, a new mixing length distribution is proposed. Comparisons between the analytical results and the results of this experiment as well as other experimental data available in the literature are presented. The results are in good agreement.

scholarly journals On universal features of the turbulent cascade in terms of non-equilibrium thermodynamics

2018 ◽  
Vol 848 ◽  
pp. 117-153 ◽  
Author(s):  
Nico Reinke ◽  
André Fuchs ◽  
Daniel Nickelsen ◽  
Joachim Peinke
Keyword(s):  
Probability Density ◽  
Entropy Production ◽  
Turbulent Flows ◽  
Planck Equation ◽  
Small Scale ◽  
Equilibrium Thermodynamics ◽  
Fokker Planck Equation ◽  
Velocity Increments ◽  
Turbulent Cascade ◽  
Fokker Planck

Features of the turbulent cascade are investigated for various datasets from three different turbulent flows, namely free jets as well as wake flows of a regular grid and a cylinder. The analysis is focused on the question as to whether fully developed turbulent flows show universal small-scale features. Two approaches are used to answer this question. First, two-point statistics, namely structure functions of longitudinal velocity increments, and, second, joint multiscale statistics of these velocity increments are analysed. The joint multiscale characterisation encompasses the whole cascade in one joint probability density function. On the basis of the datasets, evidence of the Markov property for the turbulent cascade is shown, which corresponds to a three-point closure that reduces the joint multiscale statistics to simple conditional probability density functions (cPDFs). The cPDFs are described by the Fokker–Planck equation in scale and its Kramers–Moyal coefficients (KMCs). The KMCs are obtained by a self-consistent optimisation procedure from the measured data and result in a Fokker–Planck equation for each dataset. Knowledge of these stochastic cascade equations enables one to make use of the concepts of non-equilibrium thermodynamics and thus to determine the entropy production along individual cascade trajectories. In addition to this new concept, it is shown that the local entropy production is nearly perfectly balanced for all datasets by the integral fluctuation theorem (IFT). Thus, the validity of the IFT can be taken as a new law of the turbulent cascade and at the same time independently confirms that the physics of the turbulent cascade is a memoryless Markov process in scale. The IFT is taken as a new tool to prove the optimal functional form of the Fokker–Planck equations and subsequently to investigate the question of universality of small-scale turbulence in the datasets. The results of our analysis show that the turbulent cascade contains universal and non-universal features. We identify small-scale intermittency as a universality breaking feature. We conclude that specific turbulent flows have their own particular multiscale cascades, in other words, their own stochastic fingerprints.

Centroid Velocity Increments as a Probe of the Turbulent Velocity Field in Interstellar Molecular Clouds

1999 ◽  
pp. 203-207
Author(s):  
D. C. Lis ◽  
T. G. Phillips ◽  
M. Gerin ◽  
J. Keene ◽  
Y. Li ◽  
...  
Keyword(s):  
Velocity Field ◽  
Molecular Clouds ◽  
Turbulent Velocity ◽  
Velocity Increments ◽  
Interstellar Molecular Clouds ◽  
Turbulent Velocity Field

Structure functions and invariants of the anisotropic Reynolds stress tensor in turbulent flows on water-worked gravel beds

2020 ◽  
Vol 32 (5) ◽  
pp. 055106 ◽  
Author(s):  
Nadia Penna ◽  
Ellora Padhi ◽  
Subhasish Dey ◽  
Roberto Gaudio
Keyword(s):  
Stress Tensor ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Structure Functions ◽  
Reynolds Stress Tensor ◽  
Gravel Beds
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