arXiv subjects

A. Pumir

Publications and source records attributed to A. Pumir.

14 recordsLinked to original sources

arXiv2026

Statistical orientation and distribution of columnar ice crystals in turbulent flows

We study the motion of columnar ice crystals that form in clouds over a range of low temperature. Our focus here is on elongated ice crystals, which are smaller than the size of the smallest eddies in the flow, with a moderate aspect ratio comprised between $3$ and $5$. We determine turbulent solutions of the Navier-Stokes equations over a range of turbulent kinetic energy dissipation characteristic of clouds ($4.41\;{\rm cm}^2/{\rm s}^3 \le \varepsilon \le 1120\;{\rm cm}^2/{\rm s}^3$) by using direct numerical simulations, and we follow the motion of crystals using simplified but realistic models for the motion of non-spherical, elongated particles. The influence of the fluid inertia leads to a preferential alignment of the crystals perpendicular to the direction of gravity, the alignment effect being opposed by the turbulent fluctuations. Along with the strong alignment of the crystal axis perpendicular to gravity, we observe only a weak alignment with the vorticity, much weaker than in the absence of gravity. The settling velocity depends only weakly on the orientation of the crystals, but is strongly enhanced when $\varepsilon$ increases, an effect that we attribute to preferential concentration in the flow. As the inertia of the columnar ice crystals considered here is significant, we observe a strong spatial clustering. Finally, we discuss the relevance of the effects identified here on the collision frequency between ice crystals in cloud conditions.

physics.flu-dyn↗

arXiv2024

Does small-scale turbulence matter for ice growth in mixed-phase clouds?

Representing the glaciation of mixed-phase clouds in terms of the Wegener-Bergeron-Findeisen process is a challenge for many weather and climate models, which tend to overestimate this process because cloud dynamics and microphysics are not accurately represented. As turbulence is essential for the transport of water vapour from evaporating liquid droplets to ice crystals, we developed a statistical model using established closures to assess the role of small-scale turbulence. The model successfully captures results of direct numerical simulations, and we use it to assess the role of small-scale turbulence. We find that small-scale turbulence broadens the droplet-size distribution somewhat, but it does not significantly affect the glaciation time on submetre scales. However, our analysis indicates that turbulence on larger spatial scales is likely to affect ice growth. While the model must be amended to describe larger scales, the present work facilitates a path forward to understanding the role of turbulence in the Wegener-Bergeron-Findeisen process.

physics.flu-dyn↗

arXiv2024

Torques on curved atmospheric fibres

Small particles are transported over long distances in the atmosphere, with significant environmental impact. The transport of symmetric particles is well understood, but atmospheric particles, such as curved microplastic fibres or ash particles, are generally asymmetric. This makes the description of their transport properties uncertain. Here, we derive a model for how planar curved fibres settle in quiescent air. The model explains that fluid-inertia torques may align such fibres at oblique angles with gravity as seen in recent laboratory experiments, and shows that inertial alignment is a general and thus important factor for the transport of atmospheric particles.

physics.flu-dyn↗

arXiv2023

Lagrangian supersaturation fluctuations at the cloud edge

Evaporation of cloud droplets accelerates when turbulence mixes dry air into the cloud, affecting droplet-size distributions in atmospheric clouds, combustion sprays, and jets of exhaled droplets. The challenge is to model local correlations between droplet numbers, sizes, and supersaturation, which determine supersaturation fluctuations along droplet paths (Lagrangian fluctuations). We derived a statistical model that accounts for these correlations. Its predictions are in quantitative agreement with results of direct numerical simulations, and it explains the key mechanisms at play.

physics.flu-dyn↗

arXiv2023

Inertia induces strong orientation fluctuations of non-spherical atmospheric particles

The orientation of non-spherical particles in the atmosphere, such as volcanic ash and ice crystals, influences their residence times, and the radiative properties of the atmosphere. Here, we demonstrate experimentally that the orientation of heavy submillimeter spheroids settling in still air exhibits decaying oscillations, whereas it relaxes monotonically in liquids. Theoretical analysis shows that these oscillations are due to particle inertia, caused by the large particle-fluid mass-density ratio. This effect must be accounted for to model solid particles in the atmosphere.

physics.flu-dyn↗

arXiv2021

Experimental validation of fluid inertia models for a cylinder settling in a quiescent flow

The precise description of the motion of anisotropic particles in a flow rests on the understanding of the force and torque acting on them. Here, we study experimentally small, very elongated particles settling in a fluid at small Reynolds number. In our experiments, we can, to a very good approximation, relate the rate of rotation of cylindrical tungsten rods, of aspect ratios β= 8 and β= 16, settling in pure glycerol to the torque they are experiencing. This allows us to compare the measured torque with expressions obtained either in the slender-rod limit, or in the case of spheroids. Both theories predict a simple angle dependence for the torque, which is found to capture very well the experimental results. Surprisingly, the slender-rod approximation predicts much better the results for β= 8, than for β= 16. In the latter case, the expression obtained for a spheroid provides a better approximation. The translational dynamics is shown to be in qualitative agreement with the slender-rod and spheroid models, the former one being found to represent better the experimental data.

physics.flu-dyn↗

arXiv2021

Explicit construction of joint multipoint statistics in complex systems

Complex systems often involve random fluctuations for which self-similar properties in space and time play an important role. Fractional Brownian motions, characterized by a single scaling exponent, the Hurst exponent $H$, provide a convenient tool to construct synthetic signals that capture the statistical properties of many processes in the physical sciences and beyond. However, in certain strongly interacting systems, e.g., turbulent flows, stock market indices, or cardiac interbeats, multiscale interactions lead to significant deviations from self-similarity and may therefore require a more elaborate description. In the context of turbulence, the Kolmogorov-Oboukhov model (K62) describes anomalous scaling, albeit explicit constructions of a turbulent signal by this model are not available yet. Here, we derive an explicit formula for the joint multipoint probability density function of a multifractal field. To this end, we consider a scale mixture of fractional Ornstein-Uhlenbeck processes and introduce a fluctuating length scale in the corresponding covariance function. In deriving the complete statistical properties of the field, we are able to systematically model synthetic multifractal phenomena. We conclude by giving a brief outlook on potential applications which range from specific tailoring or stochastic interpolation of wind fields to the modeling of financial data or non-Gaussian features in geophysical or geospatial settings.

physics.flu-dyn↗

arXiv2021

Inertial torque on a small spheroid in a stationary uniform flow

How anisotropic particles rotate and orient in a flow depends on the hydrodynamic torque they experience. Here we compute the torque acting on a small spheroid in a uniform flow by numerically solving the Navier-Stokes equations. Particle shape is varied from oblate (aspect ratio $λ= 1/6$) to prolate ($λ= 6$), and we consider low and moderate particle Reynolds numbers (${\rm Re} \le 50$). We demonstrate that the angular dependence of the torque, predicted theoretically for small particle Reynolds numbers remains qualitatively correct for Reynolds numbers up to ${\rm Re} \sim 10$. The amplitude of the torque, however, is smaller than the theoretical prediction, the more so as ${\rm Re}$ increases. For Re larger than $10$, the flow past oblate spheroids acquires a more complicated structure, resulting in systematic deviations from the theoretical predictions. Overall, our numerical results provide a justification of recent theories for the orientation statistics of ice-crystals settling in a turbulent flow.

physics.flu-dyn↗

arXiv2021

Stochastic interpolation of sparsely sampled time series via multi-point fractional Brownian bridges

We propose and test a method to interpolate sparsely sampled signals by a stochastic process with a broad range of spatial and/or temporal scales. To this end, we extend the notion of a fractional Brownian bridge, defined as fractional Brownian motion with a given scaling (Hurst) exponent $H$ and with prescribed start and end points, to a bridge process with an arbitrary number of intermediate and non-equidistant points. Determining the optimal value of the Hurst exponent, $H_{opt}$, appropriate to interpolate the sparse signal, is a very important step of our method. We demonstrate the validity of our method on a signal from fluid turbulence in a high Reynolds number flow and discuss the implications of the non-self-similar character of the signal. The method introduced here could be instrumental in several physical problems, including astrophysics, particle tracking, specific tailoring of surrogate data, as well as in domains of natural and social sciences.

physics.data-an↗

arXiv2020

Effect of particle inertia on the alignment of small ice crystals in turbulent clouds

Small non-spherical particles settling in a quiescent fluid tend to orient so that their broad side faces down, because this is a stable fixed point of their angular dynamics at small particle Reynolds number. Turbulence randomises the orientations to some extent, and this affects the reflection patterns of polarised light from turbulent clouds containing ice crystals. An overdamped theory predicts that turbulence-induced fluctuations of the orientation are very small when the settling number Sv (a dimensionless measure of the settling speed) is large. At small Sv, by contrast, the overdamped theory predicts that turbulence randomises the orientations. This overdamped theory neglects the effect of particle inertia. Therefore we consider here how particle inertia affects the orientation of small crystals settling in turbulent air. We find that it can significantly increase the orientation variance, even when the Stokes number St (a dimensionless measure of particle inertia) is quite small. We identify different asymptotic parameter regimes where the tilt-angle variance is proportional to different inverse powers of Sv. We estimate parameter values for ice crystals in turbulent clouds and show that they cover several of the identified regimes. The theory predicts how the degree of alignment depends on particle size, shape and turbulence intensity, and that the strong horizontal alignment of small crystals is only possible when the turbulent energy dissipation is weak, of the order of $1\,$cm$^2$/s$^3$ or less.

physics.flu-dyn↗

arXiv2019

Theory for the effect of fluid inertia on the orientation of a small particle settling in turbulence

Ice crystals settling through a turbulent cloud are rotated by turbulent velocity gradients. In the same way, turbulence affects the orientation of aggregates of organic matter settling in the ocean. In fact most solid particles encountered in Nature are not spherical, and their orientation affects their settling speed, as well as collision rates between particles. Therefore it is important to understand the distribution of orientations of non-spherical particles settling in turbulence. Here we study the angular dynamics of small prolate spheroids settling in homogeneous isotropic turbulence. We consider a limit of the problem where the fluid torque due to convective inertia dominates, so that rods settle essentially horizontally. Turbulence causes the orientation of the settling particles to fluctuate, and we calculate their orientation distribution for prolate spheroids with arbitrary aspect ratios for large settling number Sv (a dimensionless measure of the settling speed), assuming small Stokes number St (a dimensionless measure of particle inertia). This overdamped theory predicts that the orientation distribution is very narrow at large Sv, with a variance proportional to ${\rm Sv}^{-4}$. By considering the role of particle inertia, we analyse the limitations of the overdamped theory, and determine its range of applicability. Our predictions are in excellent agreement with numerical simulations of simplified models of turbulent flows. Finally we contrast our results with those of an alternative theory predicting that the orientation variance scales as ${\rm Sv}^{-2}$ at large Sv.

physics.flu-dyn↗

arXiv2018

Vertical drafts and mixing in stratified turbulence: sharp transition with Froude number

We investigate the large-scale intermittency of vertical velocity and temperature, and the mixing properties of stably stratified turbulent flows using both Lagrangian and Eulerian fields from direct numerical simulations, in a parameter space relevant for the atmosphere and the oceans. Over a range of Froude numbers of geophysical interest ($\approx 0.05-0.3$) we observe very large fluctuations of the vertical components of the velocity and the potential temperature, localized in space and time, with a sharp transition leading to non-Gaussian wings of the probability distribution functions. This behavior is captured by a simple model representing the competition between gravity waves on a fast time-scale and nonlinear steepening on a slower time-scale. The existence of a resonant regime characterized by enhanced large-scale intermittency, as understood within the framework of the proposed model, is then linked to the emergence of structures in the velocity and potential temperature fields, localized overturning and mixing. Finally, in the same regime we observe a linear scaling of the mixing efficiency with the Froude number and an increase of its value of roughly one order of magnitude.

physics.flu-dyn↗

arXiv2017

Statistical model for the orientation of non-spherical particles settling in turbulence

The orientation of small anisotropic particles settling in a turbulent fluid determines some essential properties of the suspension. We show that the orientation distribution of small heavy spheroids settling through turbulence can be accurately predicted by a simple Gaussian statistical model that takes into account particle inertia and provides a quantitative understanding of the orientation distribution on the problem parameters when fluid inertia is negligible. Our results open the way to a parameterisation of the distribution of ice-crystals in clouds, and potentially leads to an improved understanding of radiation reflection, or particle aggregation through collisions in clouds.

physics.flu-dyn↗

arXiv2003

Kinematic simulation of multi point turbulent dispersion

As three particles are advected by a turbulent flow, they separate from each other and develop non trivial geometries, which effectively reflect the structure of the turbulence. We investigate here the geometry, in a statistical sense, of three Lagrangian particles advected, in 2-dimensions, by Kinematic Simulation (KS). KS is a Lagrangian model of turbulent diffusion that makes no use of any delta correlation in time at any level. With this approach, situations with a very large range of inertial scales and varying persistence of spatial flow structure can be studied. We first show numerically that the model flow reproduces recent experimental results at low Reynolds numbers. The statistical properties of the shape distribution at much higher Reynolds number is then considered. Even at the highest available inertial range, of scale, corresponding to a ratio between large and small scales of $L/η\approx 17,000$, we find that the radius of gyration of the three points does not precisely follow Richardson's prediction. The shapes of the triangles have a high probability to be elongated. The corresponding shape distribution is not found to be perfectly self similar, even for our highest ratio of inertial scales. We also discuss how the parameters of the synthetic flow, such as the exponent of the spectrum and the effect of the sweeping affect our results. Our results suggest that a non trivial distribution of shapes will be observed at high Reynolds numbers, although it may not be exactly self similar. Special attention is given to the effects of persistence of spatial flow structure.

nlin.CD↗