arXiv subjects

Alain Pumir

Publications and source records attributed to Alain Pumir.

At least 37 records · Page 2Linked to original sources

arXiv2020

Vortex stretching and enstrophy production in high Reynolds number turbulence

An essential ingredient of turbulent flows is the vortex stretching mechanism, which emanates from the non-linear interaction of vorticity and strain-rate tensor and leads to formation of extreme events. We analyze the statistical correlations between vorticity and strain rate by using a massive database generated from very well resolved direct numerical simulations of forced isotropic turbulence in periodic domains. The grid resolution is up to $12288^3$, and the Taylor-scale Reynolds number is in the range $140-1300$. In order to understand the formation and structure of extreme vorticity fluctuations, we obtain statistics conditioned on enstrophy (vorticity-squared). The magnitude of strain, as well as its eigenvalues, is approximately constant when conditioned on weak enstrophy; whereas they grow approximately as power laws for strong enstrophy, which become steeper with increasing $R_λ$. We find that the well-known preferential alignment between vorticity and the intermediate eigenvector of strain tensor is even stronger for large enstrophy, whereas vorticity shows a tendency to be weakly orthogonal to the most extensive eigenvector (for large enstrophy). Yet the dominant contribution to the production of large enstrophy events arises from the most extensive eigendirection, the more so as $R_λ$ increases. Nevertheless, the stretching in intense vorticity regions is significantly depleted, consistent with the kinematic properties of weakly-curved tubes in which they are organized. Further analysis reveals that intense enstrophy is primarily depleted via viscous diffusion, though viscous dissipation is also significant. Implications for modeling are nominally addressed as appropriate.

physics.flu-dyn↗

arXiv2020

Self-attenuation of extreme events in Navier-Stokes turbulence

Turbulent fluid flows are ubiquitous in nature and technology, and are mathematically described by the incompressible Navier-Stokes equations (INSE). A hallmark of turbulence is spontaneous generation of intense whirls, resulting from amplification of the fluid rotation-rate (vorticity) by its deformation-rate (strain). This interaction, encoded in the non-linearity of INSE, is non-local, i.e., depends on the entire state of the flow, constituting a serious hindrance in turbulence theory and in establishing regularity of INSE. Here, we unveil a novel aspect of this interaction, by separating strain into local and non-local contributions utilizing the Biot-Savart integral of vorticity in a sphere of radius R. Analyzing highly-resolved numerical turbulent solutions to INSE, we find that when vorticity becomes very large, the local strain over small R surprisingly counteracts further amplification. This uncovered self-attenuation mechanism is further shown to be connected to local Beltramization of the flow, and could provide a direction in establishing the regularity of INSE.

physics.flu-dyn↗

arXiv2020

Improved Preterm Prediction Based on Optimized Synthetic Sampling of EHG Signal

Preterm labor is the leading cause of neonatal morbidity and mortality and has attracted research efforts from many scientific areas. The inter-relationship between uterine contraction and the underlying electrical activities makes uterine electrohysterogram (EHG) a promising direction for preterm detection and prediction. Due the scarcity of EHG signals, especially those of preterm patients, synthetic algorithms are applied to create artificial samples of preterm type in order to remove prediction bias towards term, at the expense of a reduction of the feature effectiveness in machine-learning based automatic preterm detecting. To address such problem, we quantify the effect of synthetic samples (balance coefficient) on features' effectiveness, and form a general performance metric by utilizing multiple feature scores with relevant weights that describe their contributions to class separation. Combined with the activation/inactivation functions that characterizes the effect of the abundance of training samples in term and preterm prediction precision, we obtain an optimal sample balance coefficient that compromise the effect of synthetic samples in removing bias towards the majority and the side-effect of reducing features' importance. Substantial improvement in prediction precision has been achieved through a set of numerical tests on public available TPEHG database, and it verifies the effectiveness of the proposed method.

cs.LG↗

arXiv2020

Single-particle Lagrangian statistics from direct numerical simulations of rotating-stratified turbulence

Geophysical fluid flows are predominantly turbulent and often strongly affected by the Earth's rotation, as well as by stable density stratification. Using direct numerical simulations of forced Boussinesq equations, we study the influence of these effects on the motion of fluid particles, focusing on cases where the frequencies associated with rotation and stratification (RaS), $N$ and $f$ respectively, are held at a fixed ratio $N/f=5$. As the intensity of RaS increases, a sharp transition is observed between a regime dominated by eddies to a regime dominated by waves, which can also be seemingly described by simply comparing the time scale $1/N$ and $τ_η$ (the Kolmogorov time scale). We perform a detailed study of Lagrangian statistics of acceleration, velocity and related quantities in the two regimes. The flow anisotropy induces a clear difference between particle motion in the horizontal and vertical directions. In the regime $Nτ_η<1$, acceleration statistics in both horizontal and vertical directions, exhibit well known characteristics of isotropic turbulence. In contrast for $Nτ_η>1$, they are directly influenced by imposed RaS. The Lagrangian velocity statistics exhibit visible anisotropy for all runs; nevertheless the degree of anisotropy becomes very strong in the regime $Nτ_η>1$. We find that in the regime $Nτ_η<1$, rotation enhances the mean displacement of particles in horizontal planes at short times, but inhibits them at longer times. This inhibition of horizontal displacement becomes stronger for $Nτ_η>1$, with no clear diffusive behavior. Displacements in the vertical direction are always inhibited. The inhibition becomes extremely strong when $Nτ_η>1$, with the particles almost being trapped horizontally.

physics.flu-dyn↗

arXiv2019

Frequency gradients in heterogeneous oscillatory media can spatially localize self-organized wave sources that coordinate system-wide activity

Rhythmogenesis, which is critical for many biological functions, involves a transition to coherent activity through cell-cell communication. In the absence of centralized coordination by specialized cells (pacemakers), competing oscillating clusters impede this global synchrony. We show that spatial symmetry-breaking through a frequency gradient results in the emergence of localized wave sources driving system-wide activity. Such gradients, arising through heterogeneous inter-cellular coupling, may explain directed rhythmic activity during labor in the uterus despite the absence of pacemakers.

nlin.AO↗

arXiv2019

Turbulence generation through an iterative cascade of the elliptical instability

The essence of turbulent flow is the conveyance of energy through the formation, interaction, and destruction of eddies over a wide range of spatial scales--from the largest scales where energy is injected, down to the smallest scales where it is dissipated through viscosity. Currently, there is no mechanistic framework that captures how the interactions of vortices drive this cascade. We show that iterations of the elliptical instability, arising from the interactions between counter-rotating vortices, lead to the emergence of turbulence. We demonstrate how the nonlinear development of the elliptical instability generates an ordered array of antiparallel secondary filaments. The secondary filaments mutually interact, leading to the formation of even smaller tertiary filaments. In experiments and simulations, we observe two and three iterations of this cascade, respectively. Our observations indicate that the elliptical instability could be one of the fundamental mechanisms by which the turbulent cascade develops.

physics.flu-dyn↗

arXiv2019

Importance of fluid inertia for the orientation of spheroids settling in turbulent flow

How non-spherical particles orient as they settle in a flow has important practical implications in a number of scientific and engineering problems. In a quiescent fluid, a slowly settling particle orients so that it settles with its broad side first. This is an effect of the torque due to convective inertia of the fluid set in motion by the settling particle, which maximises the drag experienced by the particle. Turbulent flows tend to randomise the particle orientation. Recently the settling of non-spherical particles in turbulence was analysed neglecting the effect of convective fluid inertia, but taking into account the effect of the turbulent fluid-velocity gradients on the particle orientation. These studies reached the opposite conclusion, namely that a rod settles preferentially with its tip first, wheras a disk settles with its edge first, therefore minimizing the drag on the particle. Here, we consider both effects, the convective inertial torque as well as the torque due to fluctuating velocity gradients, and ask under which circumstances either one or the other dominate. To this end we estimate the ratio of the magnitudes of the two torques. Our estimates suggest that the fluid-inertia torque prevails in high-Reynolds number flows. In this case non-spherical particles are expected to settle with a maximal drag. But when the Reynolds number is small then the torque due to fluid-velocity gradients may dominate, causing the particle to settle with its broad side first.

physics.flu-dyn↗

arXiv2019

Extreme velocity gradients in turbulent flows

Fully turbulent flows are characterized by intermittent formation of very localized and intense velocity gradients. These gradients can be orders of magnitude larger than their typical value and lead to many unique properties of turbulence. Using direct numerical simulations of the Navier-Stokes equations with unprecedented small-scale resolution, we characterize such extreme events over a significant range of turbulence intensities, parameterized by the Taylor-scale Reynolds number ($R_λ$). Remarkably, we find the strongest velocity gradients to empirically scale as $τ_K^{-1} R_λ^β$, with $β\approx 0.775 \pm 0.025$, where $τ_K$ is the Kolmogorov time scale (with its inverse, $τ_K^{-1}$, being the {r.m.s.} of velocity gradient fluctuations). Additionally, we observe velocity increments across very small distances $r \le η$, where $η$ is the Kolmogorov length scale, to be as large as the {r.m.s.} of the velocity fluctuations. Both observations suggest that the smallest length scale in the flow behaves as $ηR_λ^{-α}$, with $α= β- \frac{1}{2}$, which is at odds with predictions from existing phenomenological theories. We find that extreme gradients are arranged in vortex tubes, such that strain conditioned on vorticity grows on average slower than vorticity, approximately as a power law with an exponent $γ< 1$, which weakly increases with $R_λ$. Using scaling arguments, we get $β=(2-γ)^{-1}$, which suggests that $β$ would also slowly increase with $R_λ$. We conjecture that approaching the limit of infinite $R_λ$, the flow is overall smooth, with intense velocity gradients over scale $ ηR_λ^{-1/2}$, corresponding to $β= 1$.

physics.flu-dyn↗

arXiv2018

A Cascade Leading to the Emergence of Small Structures in Vortex Ring Collisions

When vortex rings collide head-on at high enough Reynolds numbers, they ultimately annihilate through a violent interaction which breaks down their cores into a turbulent cloud. We experimentally show that this very strong interaction, which leads to the production of fluid motion at very fine scales, uncovers direct evidence of a novel iterative cascade of instabilities in a bulk fluid. When the coherent vortex cores approach each other, they deform into tent-like structures, and the mutual strain causes them to locally flatten into extremely thin vortex sheets. These sheets then break down into smaller secondary vortex filaments, which themselves rapidly flatten and break down into even smaller tertiary filaments. By performing numerical simulations of the full Navier-Stokes equations, we also resolve one iteration of this instability and highlight the subtle role that viscosity must play in the rupturing of a vortex sheet. The concurrence of this observed iterative cascade of instabilities over various scales with those of recent theoretical predictions could provide a new mechanistic framework in which the evolution of turbulent flows can be examined in real-time as a series of discrete dynamic instabilities.

physics.flu-dyn↗

arXiv2018

Lacunarity Exponents

Many physical processes result in very uneven, apparently random, distributions of matter, characterized by fluctuations of the local density over orders of magnitude. The density of matter in the sparsest regions can have a power-law distribution, with an exponent that we term the lacunarity exponent. We discuss a mechanism which explains the wide occurrence of these power laws, and give analytical expressions for the exponent in some simple models.

nlin.CD↗

arXiv2017

Phoresis in turbulent flows

Phoresis, the drift of particles induced by scalar gradients in a flow, can result in an effective compressibility, bringing together or repelling particles from each other. Here, we ask whether this effect can affect the transport of particles in a turbulent flow. To this end, we study how the dispersion of a cloud of phoretic particles is modified when injected in the flow, together with a blob of scalar, whose effect is to transiently bring particles together, or push them away from the center of the blob. The resulting phoretic effect can be quantified by a single dimensionless number. Phenomenological considerations lead to simple predictions for the mean separation between particles, which are consistent with results of direct numerical simulations. Using the numerical results presented here, as well as those from previous studies, we discuss quantitatively the experimental consequences of this work and the possible impact of such phoretic mechanisms in natural systems.

physics.flu-dyn↗

arXiv2017

Uniformity Transition for Ray Intensities in Random Media

This paper analyses a model for the intensity of distribution for rays propagating without absorption in a random medium. The random medium is modelled as a dynamical map. After $N$ iterations, the intensity is modelled as a sum $S$ of ${\cal N}$ contributions from different trajectories, each of which is a product of $N$ independent identically distributed random variables $x_k$, representing successive focussing or de-focussing events. The number of ray trajectories reaching a given point is assumed to proliferate exponentially: ${\cal N}=Λ^N$, for some $Λ>1$. We investigate the probability distribution of $S$. We find a phase transition as parameters of the model are varied. There is a phase where the fluctuations of $S$ are suppressed as $N\to \infty$, and a phase where the $S$ has large fluctuations, for which we provide a large deviation analysis.

physics.optics↗

arXiv2017

Stability in Chaos

Intrinsic instability of trajectories characterizes chaotic dynamical systems. We report here that trajectories can exhibit a surprisingly high degree of stability, over a very long time, in a chaotic dynamical system. We provide a detailed quantitative description of this effect for a one-dimensional model of inertial particles in a turbulent flow using large-deviation theory. Specifically, the determination of the entropy function for the distribution of finite-time Lyapunov exponents reduces to the analysis of a Schrödinger equation, which is tackled by semi-classical methods.

nlin.CD↗

arXiv2017

Structure of the velocity gradient tensor in turbulent shear flows

The expected universality of small-scale properties of turbulent flows implies isotropic properties of the velocity gradient tensor in the very large Reynolds number limit. Using direct numerical simulations, we determine the tensors formed by n = 2 and 3 velocity gradients at a single point in turbulent homogeneous shear flows, and in the log-layer of a turbulent channel flow, and we characterize the departure of these tensors from the corresponding isotropic prediction. Specifically, we separate the even components of the tensors, invariant under reflexion with respect to all axes, from the odd ones, which identically vanish in the absence of shear. Our results indicate that the largest deviation from isotropy comes from the odd component of the third velocity gradient correlation function, especially from the third moment of the derivative along the normal direction of the streamwise velocity component. At the Reynolds numbers considered (R_lambda ~ 140), we observe that these second and third order correlation functions are significantly larger in turbulent channel flows than in homogeneous shear flow. Overall, our work demonstrates that a mean shear leads to relatively simple structure of the velocity gradient tensor. How isotropy is restored in the very large Reynolds limit remains to be understood.

physics.flu-dyn↗

arXiv2017

Can hail and rain nucleate cloud droplets?

We present results from moist convection in a mixture of pressurized sulfur hexa-flouride (liquid and vapor) and helium (gas) to model the wet and dry components of the earth's atmosphere. To allow for homogeneous nucleation, we operate the experiment close to critical conditions. We report on the nucleation of microdroplets in the wake of large cold liquid drops falling through the supersaturated atmosphere and show that the homogeneous nucleation is caused by isobaric cooling of the saturated sulfur hexaflouride vapor. Our results carry over to atmospheric clouds: falling hail and cold rain drops may enhance the heterogeneous nucleation of microdroplets in their wake under supersaturated atmospheric conditions. We also observed that under appropriate conditions settling microdroplets form a rather stable horizontal cloud layer, which separates regions of super and sub critical saturation.

physics.ao-ph↗

arXiv2017

Aggregation-fragmentation-diffusion model for trail dynamics

We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a larger one and also, one trail may split into two. In addition, trails move diffusively. The model is defined by two parameters which quantify the fragmentation rate and the fragment size. In the long-time limit, the system reaches a steady state, and our focus is the limiting distribution of trail weights. We find that the density of trail weight has power-law tail $P(w) \sim w^{-γ}$ for small weight $w$. We obtain the exponent $γ$ analytically, and find that it varies continuously with the two model parameters. The exponent $γ$ can be positive or negative, so that in one range of parameters small-weight tails are abundant, and in the complementary range, they are rare.

cond-mat.stat-mech↗

arXiv2017

Convergent Chaos

Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion should be refined. Despite their overall intrinsic instability, trajectories may be very strongly convergent in phase space over extremely long periods, as revealed by our investigation of a simple chaotic system (a realistic model for small bodies in a turbulent flow). We establish that this strong convergence is a multi-facetted phenomenon, in which the clustering is intense, widespread and balanced by lacunarity of other regions. Power laws, indicative of scale-free features, characterise the distribution of particles in the system. We use large-deviation and extreme-value statistics to explain the effect. Our results show that the interpretation of the 'butterfly effect' needs to be carefully qualified. We argue that the combination of mixing and clustering processes makes our specific model relevant to understanding the evolution of simple organisms. Lastly, this notion of 'convergent chaos', which implies the existence of conditions for which uncertainties are unexpectedly small, may also be relevant to the valuation of insurance and futures contracts.

nlin.CD↗

arXiv2016

Non-Thermal Einstein Relations

We consider a particle moving with equation of motion $\dot x=f(t)$, where $f(t)$ is a random function with statistics which are independent of $x$ and $t$, with a finite drift velocity $v=\langle f\rangle$ and in the presence of a reflecting wall. Far away from the wall, translational invariance implies that the stationary probability distribution is $P(x)\sim \exp(αx)$. A classical example of a problem of this type is sedimentation equilibrium, where $α$ is determined by temperature. In this work we do not introduce a thermal reservoir and $α$ is determined from the equation of motion. We consider a general approach to determining $α$ which is not always in agreement with Einstein's relation between the mean velocity and the diffusion coefficient. We illustrate our results with a model inspired by the Boltzmann equation.

nlin.CD↗