1,217 research outputs found
Inertial particles distribute in turbulence as Poissonian points with random intensity inducing clustering and supervoiding
This work considers the distribution of inertial particles in turbulence
using the point-particle approximation. We demonstrate that the random point
process formed by the positions of particles in space is a Poisson point
process with log-normal random intensity ("log Gaussian Cox process" or LGCP).
The probability of having a finite number of particles in a small volume is
given in terms of the characteristic function of a log-normal distribution.
Corrections due to discreteness of the number of particles to the previously
derived statistics of particle concentration in the continuum limit are
provided. These are relevant for dealing with experimental or numerical data.
The probability of having regions without particles, i.e. voids, is larger for
inertial particles than for tracer particles where voids are distributed
according to Poisson processes. Further, the probability of having large voids
decays only log-normally with size. This shows that particles cluster, leaving
voids behind. At scales where there is no clustering there can still be an
increase of the void probability so that turbulent voiding is stronger than
clustering. The demonstrated double stochasticity of the distribution
originates in the two-step formation of fluctuations. First, turbulence brings
the particles randomly close together which happens with Poisson-type
probability. Then, turbulence compresses the particles' volume in the
observation volume. We confirm the theory of the statistics of the number of
particles in small volumes by numerical observations of inertial particle
motion in a chaotic ABC flow. The improved understanding of clustering
processes can be applied to predict the long-time survival probability of
reacting particles. Our work implies that the particle distribution in weakly
compressible flow with finite time correlations is a LGCP, independently of the
details of the flow statistics
The turbulence boundary of a temporal jet
We examine the structure of the turbulence boundary of a temporal plane jet at using statistics conditioned on the enstrophy. The data is obtained by direct numerical simulation and threshold values span 24 orders of magnitude, ranging from essentially irrotational fluid outside the jet to fully turbulent fluid in the jet core. We use two independent estimators for the local entrainment velocity based on the enstrophy budget. The data show clear evidence for the existence of a viscous superlayer (VSL) that envelopes the turbulence. The VSL is a nearly one-dimensional layer with low surface curvature. We find that both its area and viscous transport velocity adjust to the imposed rate of entrainment so that the integral entrainment flux is independent of threshold, although low-Reynolds-number effects play a role for the case under consideration. This threshold independence is consistent with the inviscid nature of the integral rate of entrainment. A theoretical model of the VSL is developed that is in reasonably good agreement with the data and predicts that the contribution of viscous transport and dissipation to interface propagation have magnitude and , respectively. We further identify a turbulent core region (TC) and a buffer region (BR) connecting the VSL and the TC. The BR grows in time and inviscid enstrophy production is important in this region. The BR shows many similarities with the turbulent-non-turbulent interface (TNTI), although the TNTI seems to extend into the TC. The average distance between the TC and the VSL, i.e.the BR thickness is about 10 Kolmogorov length scales or half a Taylor length scale, indicating that intense turbulent flow regions and viscosity-dominated regions are in close proximit
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
Elasto-inertial turbulence
Turbulence is ubiquitous in nature yet even for the case of ordinary
Newtonian fluids like water our understanding of this phenomenon is limited.
Many liquids of practical importance however are more complicated (e.g. blood,
polymer melts or paints), they exhibit elastic as well as viscous
characteristics and the relation between stress and strain is nonlinear. We
here demonstrate for a model system of such complex fluids that at high shear
rates turbulence is not simply modified as previously believed but it is
suppressed and replaced by a new type of disordered motion, elasto-inertial
turbulence (EIT). EIT is found to occur at much lower Reynolds numbers than
Newtonian turbulence and the dynamical properties differ significantly. In
particular the drag is strongly reduced and the observed friction scaling
resolves a longstanding puzzle in non-Newtonian fluid mechanics regarding the
nature of the so-called maximum drag reduction asymptote. Theoretical
considerations imply that EIT will arise in complex fluids if the extensional
viscosity is sufficiently large
Numerically accurate computation of the conditional trajectories of the topological invariants in turbulent flows
AbstractThe computation of the topological invariants of the velocity gradient tensor and of their conditional mean trajectories in incompressible turbulent flows is revisited. It is argued that probability conservation requires that the conditional mean trajectories should be closed when a statistically stationary wall-bounded or periodic domain is considered, and this is confirmed numerically for a turbulent channel. It is argued that previous reports of inward spiraling of the conditional trajectories are either due to incomplete statistics in inhomogeneous flows or to numerical errors
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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