282 research outputs found
Estimating intermittency in three-dimensional Navier-Stokes turbulence
The issue of why computational resolution in Navier-Stokes turbulence is so
hard to achieve is addressed. It is shown that Navier-Stokes solutions can
potentially behave differently in two distinct regions of space-time
where is comprised of a union of disjoint
space-time `anomalies'. Large values of |\nabla\bom| dominate
, which is consistent with the formation of vortex sheets or
tightly-coiled filaments. The local number of degrees of freedom
needed to resolve the regions in
satisfies \mathcal{N}^{\pm}(\bx, t)\lessgtr c_{\pm}\mathcal{R}_{u}^{3}
where is a Reynolds number dependent on the local
velocity field u(\bx, t)
Small scale aspects of flows in proximity of the turbulent/non-turbulent interface
The work reported below is a first of its kind study of the properties of
turbulent flow without strong mean shear in a Newtonian fluid in proximity of
the turbulent/non-turbulent interface, with emphasis on the small scale
aspects. The main tools used are a three-dimensional particle tracking system
(3D-PTV) allowing to measure and follow in a Lagrangian manner the field of
velocity derivatives and direct numerical simulations (DNS). The comparison of
flow properties in the turbulent (A), intermediate (B) and non-turbulent (C)
regions in the proximity of the interface allows for direct observation of the
key physical processes underlying the entrainment phenomenon. The differences
between small scale strain and enstrophy are striking and point to the definite
scenario of turbulent entrainment via the viscous forces originating in strain.Comment: 4 pages, 4 figures, Phys. Fluid
On an alternative explanation of anomalous scaling and how well-defined is the concept of inertial range
The main point of this communication is that there is a small non-negligible
amount of eddies-outliers/very strong events (comprising a significant subset
of the tails of the PDF of velocity increments in the nominally-defined
inertial range) for which viscosity/dissipation is of utmost importance at
whatever high Reynolds number. These events contribute significantly to the
values of higher-order structure functions and their anomalous scaling. Thus
the anomalous scaling is not an attribute of the conventionally-defined
inertial range, and the latter is not a well-defined concept. The claim above
is supported by an analysis of high-Reynolds-number flows in which among other
things it was possible to evaluate the instantaneous rate of energy
dissipation.Comment: 7 pages, 6 figure
Viscous tilting and production of vorticity in homogeneous turbulence
Viscous depletion of vorticity is an essential and well known property of turbulent flows, balancing, in the mean, the net vorticity production associated with the vortex stretching mechanism. In this letter, we, however, demonstrate that viscous effects are not restricted to a mere destruction process, but play a more complex role in vorticity dynamics that is as important as vortex stretching. Based on the results from three dimensional particle tracking velocimetry experiments and direct numerical simulation of homogeneous and quasi-isotropic turbulence, we show that the viscous term in the vorticity equation can also locally induce production of vorticity and changes of the orientation of the vorticity vector (viscous tilting)
On the evolution of flow topology in turbulent Rayleigh-Bénard convection
Copyright 2016 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.Small-scale dynamics is the spirit of turbulence physics. It implicates many attributes of flow topology evolution, coherent structures, hairpin vorticity dynamics, and mechanism of the kinetic energy cascade. In this work, several dynamical aspects of the small-scale motions have been numerically studied in a framework of Rayleigh-Benard convection (RBC). To do so, direct numerical simulations have been carried out at two Rayleigh numbers Ra = 10(8) and 10(10), inside an air-filled rectangular cell of aspect ratio unity and pi span-wise open-ended distance. As a main feature, the average rate of the invariants of the velocity gradient tensor (Q(G), R-G) has displayed the so-calledPeer ReviewedPostprint (author's final draft
Expanding the Q-R space to three dimensions
The two-dimensional space spanned by the velocity gradient invariants Q and R is expanded to three dimensions by the decomposition of R into its strain production −1/3sijsjkski and enstrophy production 1/4ωiωjsij terms. The {Q; R} space is a planar projection of the new three-dimensional representation. In the {Q; −sss; ωωs} space the Lagrangian evolution of the velocity gradient tensor Aij is studied via conditional mean trajectories (CMTs) as introduced by Martín et al. (Phys. Fluids, vol. 10, 1998, p. 2012). From an analysis of a numerical data set for isotropic turbulence of Reλ ~ 434, taken from the Johns Hopkins University (JHU) turbulence database, we observe a pronounced cyclic evolution that is almost perpendicular to the Q-R plane. The relatively weak cyclic evolution in the Q-R space is thus only a projection of a much stronger cycle in the {Q; −sss; ωωs} space. Further, we find that the restricted Euler (RE) dynamics are primarily counteracted by the deviatoric non-local part of the pressure Hessian and not by the viscous term. The contribution of the Laplacian of Aij, on the other hand, seems the main responsible for intermittently alternating between low and high intensity Aij state
Large scale flow effects, energy transfer, and self-similarity on turbulence
The effect of large scales on the statistics and dynamics of turbulent
fluctuations is studied using data from high resolution direct numerical
simulations. Three different kinds of forcing, and spatial resolutions ranging
from 256^3 to 1024^3, are being used. The study is carried out by investigating
the nonlinear triadic interactions in Fourier space, transfer functions,
structure functions, and probability density functions. Our results show that
the large scale flow plays an important role in the development and the
statistical properties of the small scale turbulence. The role of helicity is
also investigated. We discuss the link between these findings and
intermittency, deviations from universality, and possible origins of the
bottleneck effect. Finally, we briefly describe the consequences of our results
for the subgrid modeling of turbulent flows
Log-Poisson Cascade Description of Turbulent Velocity Gradient Statistics
The Log-Poisson phenomenological description of the turbulent energy cascade
is evoked to discuss high-order statistics of velocity derivatives and the
mapping between their probability distribution functions at different Reynolds
numbers. The striking confirmation of theoretical predictions suggests that
numerical solutions of the flow, obtained at low/moderate Reynolds numbers can
play an important quantitative role in the analysis of experimental high
Reynolds number phenomena, where small scales fluctuations are in general
inaccessible from direct numerical simulations
Geometrical statistics of the vorticity vector and the strain rate tensor in rotating turbulence
We report results on the geometrical statistics of the vorticity vector
obtained from experiments in electromagnetically forced rotating turbulence. A
range of rotation rates is considered, from non-rotating to rapidly
rotating turbulence with a maximum background rotation rate of rad/s
(with Rossby number much smaller than unity). Typically, in our experiments
. The measurement volume is located in the
centre of the fluid container above the bottom boundary layer, where the
turbulent flow can be considered locally statistically isotropic and
horizontally homogeneous for the non-rotating case, see van Bokhoven et al.,
Phys. Fluids 21, 096601 (2009). Based on the full set of velocity derivatives,
measured in a Lagrangian way by 3D Particle Tracking Velocimetry, we have been
able to quantify statistically the effect of system rotation on several flow
properties. The experimental results show how the turbulence evolves from
almost isotropic 3D turbulence ( rad/s) to quasi-2D
turbulence ( rad/s) and how this is reflected by several
statistical quantities. In particular, we have studied the orientation of the
vorticity vector with respect to the three eigenvectors of the local strain
rate tensor and with respect to the vortex stretching vector. Additionally, we
have quantified the role of system rotation on the self-amplification terms of
the enstrophy and strain rate equations and the direct contribution of the
background rotation on these evolution equations. The main effect is the strong
reduction of extreme events and related (strong) reduction of the skewness of
PDFs of several quantities such as, for example, the intermediate eigenvalue of
the strain rate tensor and the enstrophy self-amplification term.Comment: 17 pages, 6 figures, 3 table
Acceleration, pressure and related quantities in the proximity of the turbulent/non-turbulent interface
This paper presents an analysis of flow properties in the proximity of the turbulent/non-turbulent interface (TNTI), with particular focus on the acceleration of fluid particles, pressure and related small scale quantities such as enstrophy, ω2 = ωiωi, and strain, s2 = sijsij. The emphasis is on the qualitative differences between turbulent, intermediate and non-turbulent flow regions, emanating from the solenoidal nature of the turbulent region, the irrotational character of the non-turbulent region and the mixed nature of the intermediate region in between. The results are obtained from a particle tracking experiment and direct numerical simulations (DNS) of a temporally developing flow without mean shear. The analysis reveals that turbulence influences its neighbouring ambient flow in three different ways depending on the distance to the TNTI: (i) pressure has the longest range of influence into the ambient region and in the far region non-local effects dominate. This is felt on the level of velocity as irrotational fluctuations, on the level of acceleration as local change of velocity due to pressure gradients, Du/Dt ∂u/∂t − p/ρ, and, finally, on the level of strain due to pressure-Hessian/strain interaction, (D/Dt)(s2/2) (∂/∂t)(s2/2) −sijp,ij > 0; (ii) at intermediate distances convective terms (both for acceleration and strain) as well as strain production −sijsjkski > 0 start to set in. Comparison of the results at Taylor-based Reynolds numbers Reλ = 50 and Reλ = 110 suggests that the distances to the far or intermediate regions scale with the Taylor microscale λ or the Kolmogorov length scale η of the flow, rather than with an integral length scale; (iii) in the close proximity of the TNTI the velocity field loses its purely irrotational character as viscous effects lead to a sharp increase of enstrophy and enstrophy-related terms. Convective terms show a positive peak reflecting previous findings that in the laboratory frame of reference the interface moves locally with a velocity comparable to the fluid velocity fluctuation
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