scholarly journals On the universality of anomalous scaling exponents of structure functions in turbulent flows

2018 ◽  
Vol 837 ◽  
pp. 657-669 ◽  
Author(s):  
E.-W. Saw ◽  
P. Debue ◽  
D. Kuzzay ◽  
F. Daviaud ◽  
B. Dubrulle
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Velocity Structure ◽  
Swirling Flow ◽  
Spatial Scales ◽  
Structure Functions ◽  
Inertial Subrange ◽  
Scaling Exponents ◽  
Von Karman ◽  
Von Kármán

All previous experiments in open turbulent flows (e.g. downstream of grids, jets and the atmospheric boundary layer) have produced quantitatively consistent values for the scaling exponents of velocity structure functions (Anselmet et al., J. Fluid Mech., vol. 140, 1984, pp. 63–89; Stolovitzky et al., Phys. Rev. E, vol. 48 (5), 1993, R3217; Arneodo et al., Europhys. Lett., vol. 34 (6), 1996, p. 411). The only measurement of scaling exponents at high order (${>}6$) in closed turbulent flow (von Kármán swirling flow) using Taylor’s frozen flow hypothesis, however, produced scaling exponents that are significantly smaller, suggesting that the universality of these exponents is broken with respect to change of large scale geometry of the flow. Here, we report measurements of longitudinal structure functions of velocity in a von Kármán set-up without the use of the Taylor hypothesis. The measurements are made using stereo particle image velocimetry at four different ranges of spatial scales, in order to observe a combined inertial subrange spanning approximately one and a half orders of magnitude. We found scaling exponents (up to ninth order) that are consistent with values from open turbulent flows, suggesting that they might be in fact universal.

Inertial particle relative velocity statistics in homogeneous isotropic turbulence

2012 ◽  
Vol 696 ◽  
pp. 45-66 ◽  
Author(s):  
Juan P. L. C. Salazar ◽  
Lance R. Collins
Keyword(s):  
Structure Function ◽  
Relative Velocity ◽  
Velocity Structure ◽  
Structure Functions ◽  
Inertial Subrange ◽  
Inertial Particles ◽  
Inertial Particle ◽  
Scaling Exponents ◽  
Velocity Statistics ◽  
Dissipation Range

AbstractIn the present study, we investigate the scaling of relative velocity structure functions, of order two and higher, for inertial particles, both in the dissipation range and the inertial subrange using direct numerical simulations (DNS). Within the inertial subrange our findings show that contrary to the well-known attenuation in the tails of the one-point acceleration probability density function (p.d.f.) with increasing inertia (Bec et al., J. Fluid Mech., vol. 550, 2006, pp. 349–358), the opposite occurs with the velocity structure function at sufficiently large Stokes numbers. We observe reduced scaling exponents for the structure function when compared to those of the fluid, and correspondingly broader p.d.f.s, similar to what occurs with a passive scalar. DNS allows us to isolate the two effects of inertia, namely biased sampling of the velocity field, a result of preferential concentration, and filtering, i.e. the tendency for the inertial particle velocity to attenuate the velocity fluctuations in the fluid. By isolating these effects, we show that sampling is playing the dominant role for low-order moments of the structure function, whereas filtering accounts for most of the scaling behaviour observed with the higher-order structure functions in the inertial subrange. In the dissipation range, we see evidence of so-called ‘crossing trajectories’, the ‘sling effect’ or ‘caustics’, and find good agreement with the theory put forth by Wilkinson et al. (Phys. Rev. Lett., vol. 97, 2006, 048501) and Falkovich & Pumir (J. Atmos. Sci., vol. 64, 2007, 4497) for Stokes numbers greater than 0.5. We also look at the scaling exponents within the context of the model proposed by Bec et al. (J. Fluid Mech., vol. 646, 2010, pp. 527–536). Another interesting finding is that inertial particles at low Stokes numbers sample regions of higher kinetic energy than the fluid particle field, the converse occurring at high Stokes numbers. The trend at low Stokes numbers is predicted by the theory of Chun et al. (J. Fluid Mech., vol. 536, 2005, 219–251). This work is relevant to modelling the particle collision rate (Sundaram & Collins, J. Fluid Mech., vol. 335, 1997, pp. 75–109), and highlights the interesting array of phenomena induced by inertia.

Scaling exponents of the velocity structure functions in the interplanetary medium

1994 ◽  
Vol 12 (7) ◽  
pp. 585-590 ◽  
Author(s):  
V. Carbone
Keyword(s):  
Large Scale ◽  
Velocity Structure ◽  
Interplanetary Medium ◽  
Interplanetary Space ◽  
Field Measurements ◽  
Structure Functions ◽  
Scaling Exponents ◽  
Work Related ◽  
Large Scale Magnetic Field ◽  
Velocity Structure Function

Abstract. We analyze the scaling exponents of the velocity structure functions, obtained from the velocity fluctuations measured in the interplanetary space plasma. Using the expression for the energy transfer rate which seems the most relevant in describing the evolution of the pseudo-energy densities in the interplanetary medium, we introduce an energy cascade model derived from a simple fragmentation process, which takes into account the intermittency effect. In the absence and in the presence of the large-scale magnetic field decorrelation effect the model reduces to the fluid and the hydromagnetic p-model, respectively. We show that the scaling exponents of the q-th power of the velocity structure functions, as obtained by the model in the absence of the decorrelation effect, furnishes the best-fit to the data analyzed from the Voyager 2 velocity field measurements at 8.5 AU. Our results allow us to hypothesize a new kind of scale-similarity for magnetohydrodynamic turbulence when the decorrelation effect is at work, related to the fourth-order velocity structure function.

scholarly journals Solar wind low-frequency magnetohydrodynamic turbulence: extended self-similarity and scaling laws

1996 ◽  
Vol 3 (4) ◽  
pp. 247-261 ◽  
Author(s):  
V. Carbone ◽  
P. Veltri ◽  
R. Bruno
Keyword(s):  
Solar Wind ◽  
Scaling Laws ◽  
Velocity Structure ◽  
Fluid Flows ◽  
Structure Functions ◽  
Point Of View ◽  
Self Similarity ◽  
Extended Self ◽  
Scaling Exponents ◽  
Magnetohydrodynamic Turbulence

Abstract. In this paper we review some of the work done in investigating the scaling properties of Magnetohydrodynamic turbulence, by using velocity fluctuations measurements performed in the interplanetary space plasma by the Helios spacecraft. The set of scaling exponents ξq for the q-th order velocity structure functions, have been determined by using the Extended Self-Similarity hypothesis. We have found that the q-th order velocity structure function, when plotted vs. the 4-th order structure function, displays a range of self-similarity which extends over all the lengths covered by measurements, thus allowing for a very good determination of ξq. Moreover the results seem to show that the scaling exponents are the same regardless the various observation periods considered. The obtained scaling exponents have been compared with the results of some intermittency models for Kraichnan's turbulence, derived in the framework of infinitely divisible fragmentation processes, showing the good agreement between these models and our observations. Finally, on the basis of the actually available data sets, we show that scaling laws in Solar Wind turbulence seem to be different from turbulent scaling laws in the ordinary fluid flows. This is true for high-order velocity structure functions, while low-order velocity structure functions show the same scaling laws. Since our measurements involve length scales which extend over many order of magnitude where dissipation is practically absent, our results show that Solar Wind turbulence can be regarded as a testing bench for the investigation of general scaling behaviour in turbulent flows. In particular our results strongly support the point of view which attributes a key role to the inertial range dynamics in determining the intermittency characteristics in fluid flows, in contrast with the point of view which attributes intermittency to a finite Reynolds number effect.

On the survival of strong vortex filaments in ‘model’ turbulence

1999 ◽  
Vol 394 ◽  
pp. 261-279 ◽  
Author(s):  
ROBERTO VERZICCO ◽  
JAVIER JIMÉNEZ
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Spatial Scales ◽  
Axial Strain ◽  
Compact Object ◽  
Mean Value ◽  
Theoretical Explanation ◽  
Small Scale ◽  
Vortex Filaments ◽  
Single Scale

This paper discusses numerical experiments in which an initially uniform columnar vortex is subject to several types of axisymmetric forcing that mimic the strain field of a turbulent flow. The mean value of the strain along the vortex axis is in all cases zero, and the vortex is alternately stretched and compressed. The emphasis is on identifying the parameter range in which the vortex survives indefinitely. This extends previous work in which the effect of steady single-scale non-uniform strains was studied. In a first series of experiments the effect of the unsteadiness of the forcing is analysed, and it is found that the vortex survives as a compact object if the ratio between the oscillation frequency and the strain itself is low enough. A theoretical explanation is given which agrees with the numerical results. The strain is then generalized to include several spatial scales and oscillation frequencies, with characteristics similar to those in turbulent flows. The largest velocities are carried by the large scales, while the highest gradients and faster time scales are associated with the shorter wavelengths. Also in these cases ‘infinitely long’ vortices are obtained which are more or less uniform and compact. Vorticity profiles averaged along their axes are approximately Gaussian. The radii obtained from these profiles are proportional to the Burgers' radius of the r.m.s. (small-scale) axial strain, while the azimuthal velocities are proportional to the maximum (large-scale) axial velocity differences. The study is motivated by previous observations of intense vortex filaments in turbulent flows, and the scalings found in the present experiments are consistent with those found in the turbulent simulations.

scholarly journals Equations relating structure functions of all orders

2001 ◽  
Vol 434 ◽  
pp. 379-388 ◽  
Author(s):  
REGINALD J. HILL
Keyword(s):  
Velocity Structure ◽  
Arbitrary Order ◽  
Structure Functions ◽  
Navier Stokes ◽  
Isotropic Case ◽  
Incompressibility Condition ◽  
Scaling Exponents ◽  
Navier Stokes Equation ◽  
Local Isotropy ◽  
Locally Homogeneous

Exact equations are given that relate velocity structure functions of arbitrary order with other statistics. ‘Exact’ means that no approximations are used except that the Navier–Stokes equation and incompressibility condition are assumed to be accurate. The exact equations are used to determine the structure function equations of all orders for locally homogeneous but anisotropic turbulence as well as for the locally isotropic case. The uses of these equations for investigating the approach to local homogeneity as well as to local isotropy and the balance of the equations and identification of scaling ranges are discussed. The implications for scaling exponents and investigation of intermittency are briefly discussed.

scholarly journals A note on the non-inertial similarity solution for von Kármán swirling flow

2020 ◽  
pp. 2150030
Author(s):  
Madeleine L. Combrinck
Keyword(s):  
Boundary Layer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Similarity Solution ◽  
Shooting Method ◽  
Swirling Flow ◽  
Boundary Layer Equations ◽  
Von Karman ◽  
Von Kármán

This note proposes a non-inertial similarity solution for the classic von Kármán swirling flow as perceived from the rotational frame. The solution is obtained by implementing non-inertial similarity parameters in the non-inertial boundary layer equations. This reduces the partial differential equations to a set of ordinary differential equations that is solved through an integration routine and shooting method.

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