arXiv subjects

Alain Pumir

Publications and source records attributed to Alain Pumir.

At least 19 recordsLinked to original sources

arXiv2026

Scaling laws and local enhancements of buoyancy flux in stratified turbulent flows

In the presence of stratification, turbulent flows exhibit intermittency not only at small scales but also at large scales, comparable to the mean flow, as observed in the atmosphere and oceans. We study such flows through a large parametric exploration using direct numerical simulations of the Boussinesq equations with different forcing types. We examine two Prandtl numbers (1 and 6) and vary the Froude number ($Fr$) over a range of geophysical interest values, $0.01\le Fr \le 1$, corresponding to a variation in terms of the buoyancy Reynolds number ($R_{IB}$) of $0.06\le R_{IB} \le 2300$. We analyze the dependence on $R_{IB}$ of the buoyancy flux ($B_f$), the mixing efficiency, the shear parameters, and the vertical momentum flux. Strongly non-Gaussian tails in the spatio-temporal distribution of the $B_f$ are observed, with kurtosis reaching $\approx 10^2$, indicating the potential for stratified geophysical flows to be characterized by highly variable transport properties along the direction of gravity even under stable stratification. This is associated with long-time intermittent behavior of vertical velocity and temperature at large scale, which produces local turbulence and enhances dissipation and transport. We present evidence that the skewness of $B_f$ increases with $R_{IB}$ as a power-law and saturates in the passive-scalar limit. We also show that the domain-averaged $B_f$ exhibits two distinct trends: logarithmic growth with $R_{IB}$ and approach to a small offset as stratification strengthens. A simple model for the temporal evolution of energy and $B_f$ indicates that the defect between vertical and potential energy drives strong $B_f$ events. This trend directly leads to convective instabilities, the formation of two-dimensional and three-dimensional eddies, and rapid dissipation on a turnover timescale, allowing the energetic cycle to restart-also occurring in bursts.

physics.flu-dyn↗

arXiv2026

Relation between the moments of longitudinal velocity derivatives and of dissipation in turbulence

In homogeneous and isotropic turbulence, measurements of the longitudinal velocity derivative, $\partial_1 u_1$, make it possible to estimate a surrogate of the rate of energy dissipation per unit mass, $\epsilon$: $\epsilon_s = 15 \nu (\partial_1 u_1)^2 $, where $\nu$ is the fluid viscosity, in the sense that the averages of $\epsilon$ and $\epsilon_s$ are equal. We show here that the $n^{th}$ moments of the fluctuations $\epsilon$ and $\epsilon_s$, for $n > 2$, are not exactly proportional to each other, and that the expression for the moment $\langle \epsilon_s^n \rangle$ for $ n \ge 3$ involves in addition to a term proportional to $\langle \epsilon^n \rangle$, other contributions involving the invariant of the strain tensor, $\SSs$: ${\rm tr}( \SSs^3)$. The contribution of this term depends on the distribution of the dimensionless ratio $\mathcal{R} \equiv {\rm tr}(\SSs^3)/{\rm tr}(\SSs^2)^{3/2}$. We find, however, that the relation obtained by assuming that $\mathcal{R}$ is uniformly distributed in the interval $-1/\sqrt{6} \le \mathcal{R} \le 1/\sqrt{6}$, which is obtained when the matrix $\SSs$ has a Gaussian distribution, differs by no more than a few percents from the exact distribution.

physics.flu-dyn↗

arXiv2026

Entrainment of the suprachiasmatic nucleus network by a light-dark cycle

The synchronization of biological activity with the alternation of day and night (circadian rhythm) is performed in the brain by a group of neurons, constituting the suprachiasmatic nucleus (SCN). The SCN is divided into two subgroups of oscillating cells: the ventro-lateral (VL) neurons, which are exposed to light (photic signal) and the dorso-medial (DM) neurons which are coupled to the VL cells. When the coupling between these neurons is strong enough, the system synchronizes with the photic period. Upon increasing the cell coupling, the entrainment of the DM cells has been recently shown to occur via a very sharp (jumping) transition when the period of the photic input is larger than the intrinsic period of the cells. Here, we characterize this transition with a simple realistic model. We show that two bifurcations possibly lead to the disappearance of the endogenous mode. Using a mean field model, we show that the jumping transition results from a supercritical Hopf-like bifurcation. This finding implies that both the period and strength of the stimulating photic signal, and the relative fraction of cells in the VL and DM compartments are crucial in determining the synchronization of the system.

nlin.AO↗

arXiv2025

The contribution of dilatational motion to energy flux in homogeneous compressible turbulence

We analyze the energy flux in compressible turbulence by generalizing the exact decomposition recently proposed by Johnson (Phys. Rev. Lett., vol. 124, 2020. 104501) to study incompressible turbulent flows. This allows us to characterize the effect of dilatational motion on the inter-scale energy transfer in three-dimensional compressible turbulence. Our analysis reveals that the contribution of dilatational motion to energy transfer is due to three different physical mechanisms: the interaction between dilatation and strain, between dilatation and vorticity, and the self-interaction of dilatational motion across scales. By analyzing numerical simulations of flows at moderate turbulent Mach numbers ($Ma_t \lesssim 0.3$), we validate our theoretical derivations and provide a quantitative description of the role of dilatational motion in energy transfer. In particular, we determine the scaling dependence of the dilatational contributions on the turbulent Mach number. Moreover, our findings reveal that the eddy-viscosity assumption often used in large-eddy simulations, in the spirit of the approach used for incompressible flows, effectively neglects the interaction between solenoidal-dilatational energy transfer and overestimate dilatational effects.

physics.flu-dyn↗

arXiv2024

Universality of extreme events in turbulent flows

The universality of small scales, a cornerstone of turbulence, has been nominally confirmed for low-order mean-field statistics, such as the energy spectrum. However, small scales exhibit strong intermittency, exemplified by formation of extreme events which deviate anomalously from a mean-field description. Here, we investigate the universality of small scales by analyzing extreme events of velocity gradients in different turbulent flows, viz. direct numerical simulations (DNS) of homogeneous isotropic turbulence, inhomogeneous channel flow, and laboratory measurements in a von Karman mixing tank. We demonstrate that the scaling exponents of velocity gradient moments, as function of Reynolds number ($Re$), are universal, in agreement with previous studies at lower $Re$, and further show that even proportionality constants are universal when considering one moment order as a function of another. Additionally, by comparing various unconditional and conditional statistics across different flows, we demonstrate that the structure of the velocity gradient tensor is also universal. Overall, our findings provide compelling evidence that even extreme events are universal, with profound implications for turbulence theory and modeling.

physics.flu-dyn↗

arXiv2024

Multi-Particle Dispersion in Rotating-Stratified Turbulent Flows

The transport of matter by turbulent flows plays an important role, in particular in a geophysical context. Here, we study the relative movement of groups of two (pairs) and four (tetrahedra) Lagrangian particles using direct numerical simulations of the stably-stratified Boussinsesq equations, with Brunt-V\"ais\"al\"a frequency $N$ and Coriolis parameter $f$. We cover regimes close to homogeneous isotropic turbulence, to flows dominated by stratification and rotation, keeping fixed the ratio $N/f = 5$. The flows studied are anisotropic, so the relative motion between two particles depends not only on the initial separation between the particles, but also on their orientation with respect to the vertical axis. In all cases considered, we demonstrate that the relative particle motion differs depending on whether dispersion is considered forward or backwards in time, although the asymmetry becomes less pronounced when stratification and rotation increase. On the other hand, the strong fluctuations in the dispersion between two particles become more extreme when $N$ and $f$ increase. We also find evidence for the formation of shear layers, which become more pronounced as $N$ and $f$ become larger. Finally, we show that the irreversibility on the dispersion of a set of particles forming initially a regular tetrahedron becomes weaker when the influence of stratification and rotation increase, a property that we relate to that of the perceived rate-of-strain tensor.

physics.flu-dyn↗

arXiv2024

Lagrangian irreversibility and energy exchanges in rotating-stratified turbulent flows

Turbulence in stratified and rotating turbulent flows is characterized by an interplay between waves and eddies, resulting in continuous exchanges between potential and kinetic energy. Here, we study how these processes affect the turbulent energy cascade from large to small scales, which manifests itself by an irreversible evolution of the relative kinetic energy between two tracer particles. We find that when $r_0$, the separation between particles, is below a characteristic length $\ell_t$, potential energy is on average transferred to kinetic energy, reducing time irreversibility, and conversely when $r_0 > \ell_t$. Our study reveals that the scale $\ell_t$ coincides with the buoyancy length scale $L_B$ over a broad range of configurations until a transitional wave-dominated regime is reached.

physics.flu-dyn↗

arXiv2023

Flux-conserving directed percolation

We discuss a model for directed percolation in which the flux of material along each bond is a dynamical variable. The model includes a physically significant limiting case where the total flux of material is conserved. We show that the distribution of fluxes is asymptotic to a power law at small fluxes. We give an implicit equation for the exponent, in terms of probabilities characterising site occupations. In one dimension the site occupations are exactly independent, and the model is exactly solvable. In two dimensions, the independent-occupation assumption gives a good approximation. We explore the relationship between this model and traditional models for directed percolation.

cond-mat.dis-nn↗

arXiv2023

Role of pressure in generation of intense velocity gradients in turbulent flows

We investigate the role of pressure, via its Hessian tensor $\mathbf{H}$, on amplification of vorticity and strain-rate and contrast it with other inviscid nonlinear mechanisms. Results are obtained from direct numerical simulations of isotropic turbulence with Taylor-scale Reynolds number in the range $140-1300$. Decomposing $\mathbf{H}$ into local isotropic ($\mathbf{H}^{\rm I}$) and nonlocal deviatoric ($\mathbf{H}^{\rm D}$) components reveals that $\mathbf{H}^{\rm I}$ depletes vortex stretching (VS), whereas $\mathbf{H}^{\rm D}$ enables it, with the former slightly stronger. The resulting inhibition is significantly weaker than the nonlinear mechanism which always enables VS. However, in regions of intense vorticity, identified using conditional statistics, contribution from $\mathbf{H}$ dominates over nonlinearity, leading to overall depletion of VS. We also observe near-perfect alignment between vorticity and the eigenvector of $\mathbf{H}$ corresponding to the smallest eigenvalue, which conforms with well-known vortex-tubes. We discuss the connection between this depletion, essentially due to (local) $\mathbf{H}^{\rm I}$, and recently identified self-attenuation mechanism [Buaria et al. {\em Nat. Commun.} 11:5852 (2020)], whereby intense vorticity is locally attenuated through inviscid effects. In contrast, the influence of $\mathbf{H}$ on strain-amplification is weak. It opposes strain self-amplification, together with VS, but its effect is much weaker than VS. Correspondingly, the eigenvectors of strain and $\mathbf{H}$ do not exhibit any strong alignments. For all results, the dependence on Reynolds number is very weak. In addition to the fundamental insights, our work provides useful data and validation benchmarks for future modeling endeavors, for instance in Lagrangian modeling of velocity gradient dynamics, where conditional $\mathbf{H}$ is explicitly modeled.

physics.flu-dyn↗

arXiv2023

Energy transfer and vortex structures: Visualizing the incompressible turbulent energy cascade

The transfer of kinetic energy from large to small scales is a hallmark of turbulent flows. Yet, a precise mechanistic description of this transfer, which is expected to occur via an energy cascade, is still missing. Several conceptually simple configurations with vortex tubes have been proposed as a testing ground to understand the energy cascade. Here, we focus on incompressible flows and compare the energy transfer occurring in a statistically steady homogeneous isotropic turbulent (HIT) flow with the generation of fine-scale motions in configurations involving vortex tubes. We start by filtering the velocity field in bands of wavenumbers distributed logarithmically, which allows us to study energy transfer in Fourier space and also visualize the energy cascade in real space. In the case of a statistically steady HIT flow at a moderate Reynolds number, our numerical results do not reveal any significant correlation between regions of intense energy transfers and vorticity or strain, filtered in corresponding wavenumber bands, nor any simple self-similar process. In comparison, in the transient turbulent flow obtained from the interaction between two antiparallel vortex tubes, we observe a qualitatively simpler organization of the intense structures, as well as of the energy transfer. The process leading to vortex reconnection via flattening of interacting vortex cores in two intense ribbons of vorticity, also appears as qualitatively different from the physics of HIT. Our results indicate that the specific properties of the transient flows affect the way energy is transferred, and may not be representative of HIT.

physics.flu-dyn↗

arXiv2022

Low-order moments of the velocity gradient in homogeneous compressible turbulence

We derive from first principles analytic relations for the second and third order moments of the velocity gradient mij = dui/dxj in compressible turbulence, which generalize known relations in incompressible flows. These relations, although derived for homogeneous flows, hold approximately for a mixing layer. We also discuss how to apply these relations to determine all the second and third moments of the velocity gradient experimentally.

physics.flu-dyn↗

arXiv2022

Turbulence generation by large-scale extreme vertical drafts and the modulation of local energy dissipation in stably stratified geophysical flows

We observe the emergence of strong vertical drafts in direct numerical simulations of the Boussinesq equations in a range of parameters of geophysical interest. These structures, which appear intermittently in space and time, generate turbulence and enhance kinetic and potential energy dissipation, providing a possible explanation for the observed variability of the local energy dissipation in the bulk of oceanic flows, and the modulation of its probability distribution function. We show how, due to the extreme drafts, in runs with Froude numbers observable in geophysical scenarios, roughly 10% of the domain flow can account for up to 50% of the global volume dissipation, reminiscent of estimates based on oceanic models.

physics.flu-dyn↗

arXiv2022

Vorticity-strain rate dynamics and the smallest scales of turbulence

Building upon the intrinsic properties of Navier-Stokes dynamics, namely the prevalence of intense vortical structures and the interrelationship between vorticity and strain rate, we propose a simple framework to quantify the extreme events and the smallest scales of turbulence. We demonstrate that our approach is in excellent agreement with the best available data from direct numerical simulations of isotropic turbulence, with Taylor-scale Reynolds number up to 1300. We additionally highlight a shortcoming of prevailing intermittency models due to their disconnection from observed correlation between vorticity and strain. Our work accentuates the importance of this correlation as a crucial step in developing an accurate understanding of intermittency in turbulence.

physics.flu-dyn↗

arXiv2021

Non-local amplification of intense vorticity in turbulent flows

The nonlinear and nonlocal coupling of vorticity and strain-rate constitutes a major hindrance in understanding the self-amplification of velocity gradients in turbulent fluid flows. Utilizing highly-resolved direct numerical simulations of isotropic turbulence in periodic domains of up to $12288^3$ grid points, and Taylor-scale Reynolds number $R_λ$ in the range $140-1300$, we investigate this non-locality by decomposing the strain-rate tensor into local and non-local contributions obtained through Biot-Savart integration of vorticity in a sphere of radius $R$. We find that vorticity is predominantly amplified by the non-local strain coming beyond a characteristic scale size, which varies as a simple power-law of vorticity magnitude. The underlying dynamics preferentially align vorticity with the most extensive eigenvector of non-local strain. The remaining local strain aligns vorticity with the intermediate eigenvector and does not contribute significantly to amplification; instead it surprisingly attenuates intense vorticity, leading to breakdown of the observed power-law and ultimately also the scale-invariance of vorticity amplification, with important implications for prevailing intermittency theories.

physics.flu-dyn↗

arXiv2021

Instability and disintegration of vortex rings during head-on collisions and wall interactions

The head-on collision of two vortex rings can produce diverse phenomena: a tiara of secondary rings, vortex sheets which flatten and interact iteratively, or the violent disintegration of the rings into a turbulent cloud. The outcome of the interaction is determined by the nature of the instability affecting two impinging vortex rings. Here, we carry out a systematic study to determine the dominant instability as a function of the parameters of the problem. To this end, we numerically simulate the head on collision of vortex rings with circulation Reynolds numbers between $1000$ and $3500$ and varying slenderness ratios $Λ=a/R$ ranging from $Λ=0.1$ to $0.35$, with $a$ the core radius and $R$ the ring radius. By studying the temporal evolution of the energy and viscous dissipation, we elucidate the role azimuthal instabilities play in determining what the outcomes of the collision are. We then compare these collisions to the head-on impact of a vortex ring on a free-slip and a no-slip wall. The free-slip wall imposes a mirror symmetry, which impedes certain instabilities and at sufficiently large Reynolds numbers leads to the formation of a half-tiara of vortices. Impact against a no-slip wall results in the process where a secondary vortex ring is formed after the ejection of the resulting boundary layer. When the Reynolds number is above a certain threshold, which increases with $Λ$, the vortices disintegrate through azimuthal instabilities, resulting in a turbulent cloud.

physics.flu-dyn↗

arXiv2021

Generation of intense dissipation in high Reynolds number turbulence

Intense fluctuations of energy dissipation rate in turbulent flows result from the self-amplification of strain rate via a quadratic nonlinearity, with contributions from vorticity (via the vortex stretching mechanism) and the pressure Hessian tensor, which we analyze here using direct numerical simulations of isotropic turbulence in periodic domains of up to $12288^3$ grid points, and Taylor-scale Reynolds numbers in the range $140-1300$. We extract the statistics of various terms involved in amplification of strain and additionally condition them on the magnitude of strain. We find that strain is overall self-amplified by the quadratic nonlinearity, and depleted via vortex stretching; whereas pressure Hessian acts to redistribute strain fluctuations towards the mean-field and thus depleting intense strain. Analyzing the intense fluctuations of strain in terms of its eigenvalues reveals that the net amplification is solely produced by the third eigenvalue, resulting in strong compressive action. In contrast, the self-amplification terms acts to deplete the other two eigenvalues, whereas vortex stretching acts to amplify them, both effects canceling each other almost perfectly. The effect of the pressure Hessian for each eigenvalue is qualitatively similar to that of vortex stretching, but significantly weaker in magnitude. Our results conform with the familiar notion that intense strain is organized in sheet-like structures, which are in the vicinity of, but never overlap with regions of intense vorticity due to fundamental differences in their amplifying mechanisms.

physics.flu-dyn↗

arXiv2021

Connecting Large-Scale Velocity and Temperature Bursts with Small-Scale Intermittency in Stratified Turbulence

Non-Gaussian statistics of large-scale fields are routinely observed in data from atmospheric and oceanic campaigns and global models. Recent direct numerical simulations (DNSs) showed that large-scale intermittency in stably stratified flows is due to the emergence of sporadic, extreme events in the form of bursts in the vertical velocity and the temperature. This phenomenon results from the interplay between waves and turbulent motions, affecting mixing. We provide evidence of the enhancement of the classical small-scale (or internal) intermittency due to the emergence of large-scale drafts, connecting large- and small-scale bursts. To this aim we analyze a large set of DNSs of the stably stratified Boussinesq equations over a wide range of values of the Froude number ($Fr\approx 0.01-1$). The variation of the buoyancy field kurtosis with $Fr$ is similar to (though with smaller values than) the kurtosis of the vertical velocity, both showing a non-monotonic trend. We present a mechanism for the generation of extreme vertical drafts and vorticity enhancements which follows from the exact equations for field gradients.

physics.flu-dyn↗

arXiv2021

Cascades and Reconnection in Interacting Vortex Filaments

At high Reynolds number, the interaction between two vortex tubes leads to intense velocity gradients, which are at the heart of fluid turbulence. This vorticity amplification comes about through two different instability mechanisms of the initial vortex tubes, assumed anti-parallel and with a mirror plane of symmetry. At moderate Reynolds number, the tubes destabilize via a Crow instability, with the nonlinear development leading to strong flattening of the cores into thin sheets. These sheets then break down into filaments which can repeat the process. At higher Reynolds number, the instability proceeds via the elliptical instability, producing vortex tubes that are perpendicular to the original tube directions. In this work, we demonstrate that these same transition between Crow and Elliptical instability occurs at moderate Reynolds number when we vary the initial angle $β$ between two straight vortex tubes. We demonstrate that when the angle between the two tubes is close to $π/2$, the interaction between tubes leads to the formation of thin vortex sheets. The subsequent breakdown of these sheets involves a twisting of the paired sheets, followed by the appearance of a localized cloud of small scale vortex structures. At smaller values of the angle $β$ between the two tubes, the breakdown mechanism changes to an elliptic cascade-like mechanism. Whereas the interaction of two vortices depends on the initial condition, the rapid formation of fine-scales vortex structures appears to be a robust feature, possibly universal at very high Reynolds numbers.

physics.flu-dyn↗