arXiv subjects

K. Gustavsson

Publications and source records attributed to K. Gustavsson.

At least 19 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↗

arXiv2025

Fluid-inertia torques from particle-shape symmetry

Numerical simulation of particle motion in fluids at low particle Reynolds numbers is often based on empirical force and torque models obtained by fitting force and torque from ab-initio computations for simple particle shapes such as spheres, spheroids, or cylindrical disks and fibres. To do the same for more complex particles shapes, one needs to first know how particle shape constrains the dependence of force and torque on flow velocity, its gradient, and on particle orientation. Here we use symmetry analysis and perturbation theory to determine the form of the hydrodynamic torque on a particle settling in a quiescent fluid at low but non-zero particle Reynolds numbers, for particle shapes with different point-group symmetries. The symmetry conclusions are verified by comparing with explicit calculations for nearly spherical particles.

physics.flu-dyn↗

arXiv2025

Smart navigation of a gravity-driven glider with adjustable centre-of-mass

Artificial gliders are designed to disperse as they settle through a fluid, requiring precise navigation to reach target locations. We show that a compact glider settling in a viscous fluid can navigate by dynamically adjusting its centre-of-mass. Using fully resolved direct numerical simulations (DNS) and reinforcement learning, we find two optimal navigation strategies that allow the glider to reach its target location accurately. These strategies depend sensitively on how the glider interacts with the surrounding fluid. The nature of this interaction changes as the particle Reynolds number Re$_p$ changes. Our results explain how the optimal strategy depends on Re$_p$. At large Re$_p$, the glider learns to tumble rapidly by moving its centre-of-mass as its orientation changes. This generates a large horizontal inertial lift force, which allows the glider to travel far. At small Re$_p$, by contrast, high viscosity hinders tumbling. In this case, the glider learns to adjust its centre-of-mass so that it settles with a steady, inclined orientation that results in a horizontal viscous force. The horizontal range is much smaller than for large Re$_p$, because this viscous force is much smaller than the inertial lift force at large Re$_p$. *These authors contributed equally.

physics.flu-dyn↗

arXiv2025

Transport barriers for microswimmers in unsteady flow

Certain flow structures trap active microorganisms over extended periods, impacting mortality and growth by inhibiting foraging, exploration, and predator evasion. We show that transport barriers and trapping of a microswimmer in unsteady vortex flow can be understood in terms of Lagrangian coherent structures (LCS) in phase space, taking into account both flow and swimming dynamics. These phase-space LCS constrain when and how artificial microswimmers can be trained by reinforcement learning to escape traps. Our results suggest that phase-space LCS can explain training failure and success in a broad class of navigation problems.

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

Statistical models for the dynamics of heavy particles in turbulence

When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy particles, with mass densities larger than that of the carrying fluid, can detach from the flow. This results in preferential sampling, small-scale fractal clustering, and large collision velocities. To describe these effects of particle inertia, it is necessary to consider both particle positions and velocities in phase space. In recent years, statistical phase-space models have significantly contributed to our understanding of inertial-particle dynamics in turbulence. These models help to identify the key mechanisms and non-dimensional parameters governing the particle dynamics, and have made qualitative, and in some cases quantitative predictions. This article reviews statistical phase-space models for the dynamics of small, yet heavy, spherical particles in turbulence. We evaluate their effectiveness by comparing their predictions with results from numerical simulations and laboratory experiments, and summarise their successes and failures. Annu. Rev. Fluid Mech. 56: In press. DOI: 10.1146/annurev-fluid-032822-014140.

physics.flu-dyn↗

arXiv2023

Caustic formation in a non-Gaussian model for turbulent aerosols

Caustics in the dynamics of heavy particles in turbulence accelerate particle collisions. The rate $\mathscr{J}$ at which these singularities form depends sensitively on the Stokes number St, the non-dimensional inertia parameter. Exact results for this sensitive dependence have been obtained using Gaussian statistical models for turbulent aerosols. However, direct numerical simulations of heavy particles in turbulence yield much larger caustic-formation rates than predicted by the Gaussian theory. In order to understand possible mechanisms explaining this difference, we analyse a non-Gaussian statistical model for caustic formation in the limit of small St. We show that at small St, $\mathscr{J}$ depends sensitively on the tails of the distribution of Lagrangian fluid-velocity gradients. This explains why different authors obtained different St-dependencies of $\mathscr{J}$ in numerical-simulation studies. The most-likely gradient fluctuation that induces caustics at small St, by contrast, is the same in the non-Gaussian and Gaussian models. Direct-numerical simulation results for particles in turbulence show that the optimal fluctuation is similar, but not identical, to that obtained by the model calculations.

physics.flu-dyn↗

arXiv2023

Finite-time Lyapunov exponents of deep neural networks

We compute how small input perturbations affect the output of deep neural networks, exploring an analogy between deep networks and dynamical systems, where the growth or decay of local perturbations is characterised by finite-time Lyapunov exponents. We show that the maximal exponent forms geometrical structures in input space, akin to coherent structures in dynamical systems. Ridges of large positive exponents divide input space into different regions that the network associates with different classes. These ridges visualise the geometry that deep networks construct in input space, shedding light on the fundamental mechanisms underlying their learning capabilities.

cond-mat.dis-nn↗

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↗

arXiv2022

Critical charges for droplet collisions

The collision efficiency of uncharged micron-sized water droplets in air is determined by the breakdown of hydrodynamics at droplet separations of the order of the mean-free path, by van-der-Waals forces, or a combination of the two. In contrast, electrostatic forces determine the collision efficiency of charged droplets if the charge is large enough. To find the charge for which the transition to charge-dominated collisions occurs, we computed the collision efficiency of charged, hydrodynamically-interacting droplets settling in quiescent air, including the breakdown of hydrodynamics at small interfacial distances. For oppositely charged droplets, the transition occurs when a saddle point of the relative droplet-dynamics exits the region where the hydrodynamics breaks down. For droplets with radii $16\,\mu$m and $20\,\mu$m, this occurs at $\sim 10^3$ elementary charges $e$. For smaller charges, the collision efficiency depends upon the Kn number (defined as the ratio of the mean-free-path of air to the mean droplet radius), whereas for larger charges it does not. For droplets charged with the same polarity, the critical charge is $\sim 10^4\,e$ for the above radii.

physics.flu-dyn↗

arXiv2022

Alignment of elongated swimmers in a laminar and turbulent Kolmogorov flow

Many aquatic microorganisms are able to swim. In natural environments they typically do so in the presence of flows. In recent years it has been shown that the interplay of swimming and flows can give rise to interesting and biologically relevant phenomena, such as accumulation of microorganisms in specific flow regions and local alignment with the flow properties. Here, we consider a mechanical model for elongated microswimmers in a Kolmogorov flow, a prototypic shear flow, both in steady and in turbulent conditions. By means of direct numerical simulations, supported by analytical calculation in a simplified stochastic setting, we find that the alignment of the swimming direction with the local velocity is a general phenomenon. We also explore how the accumulation of microorganisms, typically observed in steady flows, is modified by the presence of unsteady fluctuations.

physics.flu-dyn↗

arXiv2022

Constraints on parameter choices for successful reservoir computing

Echo-state networks are simple models of discrete dynamical systems driven by a time series. By selecting network parameters such that the dynamics of the network is contractive, characterized by a negative maximal Lyapunov exponent, the network may synchronize with the driving signal. Exploiting this synchronization, the echo-state network may be trained to autonomously reproduce the input dynamics, enabling time-series prediction. However, while synchronization is a necessary condition for prediction, it is not sufficient. Here, we study what other conditions are necessary for successful time-series prediction. We identify two key parameters for prediction performance, and conduct a parameter sweep to find regions where prediction is successful. These regions differ significantly depending on whether full or partial phase space information about the input is provided to the network during training. We explain how these regions emerge.

cs.LG↗

arXiv2022

Bifurcations in droplet collisions

Saffman and Turner (1957) argued that the collision rate for droplets in turbulence increases as the turbulent strain rate increases. But the numerical simulations of Dhanasekaran et al. (2021) in a steady straining flow show that the Saffman-Turner model is oversimplified because it neglects droplet-droplet interactions. These result in a complex dependence of the collision rate on the strain rate and on the differential settling speed. Here we show that this dependence is explained by a sequence of bifurcations in the collision dynamics. We compute the bifurcation diagram when strain is aligned with gravity, and show that it yields important insights into the collision dynamics. First, the steady-state collision rate remains non-zero in the limit Kn $\to0$, contrary to the common assumption that the collision rate tends to zero in this limit (Kn is a non-dimensional measure of the mean free path of air). Second, the non-monotonic dependence of the collision rate on the differential settling speed is explained by a grazing bifurcation. Third, the bifurcation analysis explains why so-called "closed trajectories" appear and disappear. Fourth, our analysis predicts strong spatial clustering near certain saddle points, where the effects of strain and differential settling cancel

physics.flu-dyn↗

arXiv2021

Navigation of micro-swimmers in steady flow: the importance of symmetries

Marine microorganisms must cope with complex flow patterns and even turbulence as they navigate the ocean. To survive they must avoid predation and find efficient energy sources. A major difficulty in analysing possible survival strategies is that the time series of environmental cues in non-linear flow is complex, and that it depends on the decisions taken by the organism. One way of determining and evaluating optimal strategies is reinforcement learning. In a proof-of-principle study, Colabrese et al. [Phys. Rev. Lett. (2017)] used this method to find out how a micro-swimmer in a vortex flow can navigate towards the surface as quickly as possible, given a fixed swimming speed. The swimmer measured its instantaneous swimming direction and the local flow vorticity in the laboratory frame, and reacted to these cues by swimming either left, right, up, or down. However, usually a motile microorganism measures the local flow rather than global information, and it can only react in relation to the local flow, because in general it cannot access global information (such as up or down in the laboratory frame). Here we analyse optimal strategies with local signals and actions that do not refer to the laboratory frame. We demonstrate that symmetry-breaking is required in order to learn vertical migration in a meaningful way. Using reinforcement learning we analyse the emerging strategies for different sets of environmental cues that microorganisms are known to measure.

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↗

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

Fractal catastrophes

We analyse the spatial inhomogeneities ('spatial clustering') in the distribution of particles accelerated by a force that changes randomly in space and time. To quantify spatial clustering, the phase-space dynamics of the particles must be projected to configuration space. Folds of a smooth phase-space manifold give rise to catastrophes ('caustics') in this projection. When the inertial particle dynamics is damped by friction, however, the phase-space manifold converges towards a fractal attractor. It is believed that caustics increase spatial clustering also in this case, but a quantitative theory is missing. We solve this problem by determining how projection affects the distribution of finite-time Lyapunov exponents. Applying our method in one spatial dimension we find that caustics arising from the projection of a dynamical fractal attractor ('fractal catastrophes') make a distinct and universal contribution to the distribution of spatial finite-time Lyapunov exponents. Our results explain a projection formula for the spatial fractal correlation dimension, and how a fluctuation relation for the distribution of finite-time Lyapunov exponents for white-in-time Gaussian force fields breaks upon projection. We explore the implications of our results for heavy particles in turbulence, and for wave propagation in random media.

cond-mat.stat-mech↗

arXiv2019

Alignment of non-spherical active particles in chaotic flows

We study the orientation statistics of spheroidal, axisymmetric microswimmers, with shapes ranging from disks to rods, swimming in chaotic, moderately turbulent flows. Numerical simulations show that rod-like active particles preferentially align with the flow velocity. To explain the underlying mechanism we solve a statistical model via perturbation theory. We show that such alignment is caused by correlations of fluid velocity and its gradients along particle paths combined with fore-aft symmetry breaking due to both swimming and particle nonsphericity. Remarkably, the discovered alignment is found to be a robust kinematical effect, independent of the underlying flow evolution. We discuss its possible relevance for aquatic ecology.

physics.flu-dyn↗