arXiv subjects

M. Z. Sheikh

Publications and source records attributed to M. Z. Sheikh.

4 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↗

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↗

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↗