arXiv subjects

Kristian Gustavsson

Publications and source records attributed to Kristian Gustavsson.

17 recordsLinked to original sources

arXiv2026

Guided navigation in turbulence

Navigation in turbulence is challenging because local flow measurements provide limited information about favorable paths beyond the flow correlation scales. We investigate vertical navigation by swimmers in homogeneous isotropic turbulence and compare strategies using local flow information with strategies guided by high-performing trajectories. Compared with naive upward swimming, local strategies enhance the mean vertical velocity by about 10% of the root-mean-square flow velocity, while guidance by precalculated trajectories reaches enhancements of about 40%. This gain is limited by the time required to intercept favorable trajectories, particularly for slow swimmers. We then show that precalculated trajectories are unnecessary: swimmers can dynamically identify high-performing members of a swarm and use them as targets. For sufficiently fast swimmers, this collective strategy keeps much of the benefit of precalculated guidance using only the instantaneous swarm state. Our results demonstrate how distributed trajectory information can be used to overcome limitations of local sensing for navigation in turbulence.

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arXiv2026

Adaptive shape control for microswimmer navigation in turbulence

Navigation in turbulent environments is a fundamental challenge for biological and artificial microswimmers. While most existing studies focus on adapting motility or steering, the role of active morphological changes in navigation remains poorly explored. Here, we investigate a shape-changing spheroidal microswimmer tasked with maximising its displacement from an initial position in two-dimensional stochastic and turbulent flows. Using reinforcement learning (RL), the microswimmer learns to adapt its aspect ratio based on its orientation and local velocity-gradient signals. The learned strategies outperform fixed-shape and short-time-optimal baselines across different flow regimes and remain effective when transferred from stochastic flows to fully resolved turbulence. Guided by the learned policies, we propose a minimal analytical model that captures the essential navigation mechanisms and reproduces the performance across flow regimes. These results show that adaptive morphology provides a robust and physically interpretable control paradigm for microswimmer navigation in complex flows.

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arXiv2025

Short term vs. long term: optimization of microswimmer navigation on different time horizons

We use reinforcement learning to find strategies that allow microswimmers in turbulence to avoid regions of large strain. This question is motivated by the hypothesis that swimming microorganisms tend to avoid such regions to minimise the risk of predation. We ask which local cues a microswimmer must measure to efficiently avoid such straining regions. We find that it can succeed without directional information, merely by measuring the magnitude of the local strain. However, the swimmer avoids straining regions more efficiently if it can measure the sign of local strain gradients. We compare our results with those of an earlier study [Mousavi {\em et al.} Phys. Rev. Res. {\bf 6}, L022034 (2024)] where a short-time expansion was used to find optimal strategies. We find that the short-time strategies work well in some cases but not in others. We derive a new theory that explains when the time-horizon matters for our optimisation problem, and when it does not. We find the strategy with best performance when the time-horizon coincides with the correlation time of the turbulent fluctuations. We also explain how the update frequency (the frequency at which the swimmer updates its strategy) affects the found strategies. We find that higher update frequencies yield better performance.

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arXiv2024

Efficient survival strategy for zooplankton in turbulence

Zooplankton in a quiescent environment can detect predators by hydrodynamic sensing, triggering powerful escape responses. Since turbulent strain tends to mask the hydrodynamic signal, the organisms should avoid such regions, but it is not known how they accomplish this. We found a simple, robust, and highly efficient strategy, that relies on measuring the sign of gradients of squared strain. Plankton following this strategy show very strong spatial clustering, and align against the local flow velocity, facilitating mate finding and feeding. The strategy has the potential to reconcile competing fitness pressures.

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arXiv2023

Caustics in turbulent aerosols form along the Vieillefosse line at weak particle inertia

Caustic singularities of the spatial distribution of particles in turbulent aerosols enhance collision rates and accelerate coagulation. Here we investigate how and where caustics form at weak particle inertia, by analysing a three-dimensional Gaussian statistical model for turbulent aerosols in the persistent limit, where the flow varies slowly compared with the particle relaxation time. In this case, correlations between particle- and fluid-velocity gradients are strong, and caustics are induced by large, strain-dominated excursions of the fluid-velocity gradients. These excursions must cross a characteristic threshold in the plane spanned by the invariants $Q$ and $R$ of the fluid-velocity gradients. Our method predicts that the most likely way to reach this threshold is by a unique ``optimal fluctuation'' that propagates along the Vieillefosse line, $27R^2/4 +Q^3=0$. We determine the shape of the optimal fluctuation as a function of time and show that it is dominant in numerical statistical-model simulations even for moderate particle inertia.

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arXiv2021

Active gyrotactic stability of microswimmers using hydromechanical signals

Many plankton species undergo daily vertical migration to large depths in the turbulent ocean. To do this efficiently, the plankton can use a gyrotactic mechanism, aligning them with gravity to swim downwards, or against gravity to swim upwards. Many species show passive mechanisms for gyrotactic stability. For example, bottom-heavy plankton tend to align upwards. This is efficient for upward migration in quiescent flows, but it is often sensitive to turbulence which upsets the alignment. Here we suggest a simple, robust active mechanism for gyrotactic stability, which is only lightly affected by turbulence and allows alignment both along and against gravity. We use a model for a plankton that swims with a constant speed and can actively steer in response to hydrodynamic signals encountered in simulations of a turbulent flow. Using reinforcement learning, we identify the optimal steering strategy. By using its setae to sense its settling velocity transversal to its swimming direction, the swimmer can deduce information about the direction of gravity, allowing it to actively align upwards. The mechanism leads to a rate of upward migration in a turbulent flow that is of the same order as in quiescent flows, unless the turbulence is very vigorous. In contrast, passive swimmers with typical parameters of copepods show much smaller upward velocity in turbulence. Settling may even cause them to migrate downwards in vigorous turbulence.

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arXiv2021

Lord Kelvin's isotropic helicoid

Nearly 150 years ago, Lord Kelvin proposed the isotropic helicoid, a particle with isotropic yet chiral interactions with a fluid, so that translation couples to rotation. An implementation of his design fabricated with a three-dimensional printer is found experimentally to have no detectable translation-rotation coupling, although the particle point-group symmetry allows this coupling. We explain these results by demonstrating that in Stokes flow, the chiral coupling of such isotropic helicoids made out of non-chiral vanes is due only to hydrodynamic interactions between these vanes. Therefore it is small. In summary, Kelvin's predicted isotropic helicoid exists, but only as a weak breaking of a symmetry of non-interacting vanes in Stokes flow.

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arXiv2021

Paths to caustic formation in turbulent aerosols

The dynamics of small, yet heavy, identical particles in turbulence exhibits singularities, called caustics, that lead to large fluctuations in the spatial particle-number density, and in collision velocities. For large particle, inertia the fluid velocity at the particle position is essentially a white-noise signal and caustic formation is analogous to Kramers escape. Here we show that caustic formation at small particle inertia is different. Caustics tend to form in the vicinity of particle trajectories that experience a specific history of fluid-velocity gradients, characterised by low vorticity and a violent strain exceeding a large threshold. We develop a theory that explains our findings in terms of an optimal path to caustic formation that is approached in the small inertia limit.

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arXiv2021

Optimal control of point-to-point navigation in turbulent time-dependent flows using Reinforcement Learning

We present theoretical and numerical results concerning the problem to find the path that minimizes the time to navigate between two given points in a complex fluid under realistic navigation constraints. We contrast deterministic Optimal Navigation (ON) control with stochastic policies obtained by Reinforcement Learning (RL) algorithms. We show that Actor-Critic RL algorithms are able to find quasi-optimal solutions in the presence of either time-independent or chaotically evolving flow configurations. For our application, ON solutions develop unstable behavior within the typical duration of the navigation process, and are therefore not useful in practice. We first explore navigation of turbulent flow using a constant propulsion speed. Based on a discretized phase-space, the propulsion direction is adjusted with the aim to minimize the time spent to reach the target. Further, we explore a case where additional control is obtained by allowing the engine to power off. Exploiting advection of the underlying flow, allows the target to be reached with less energy consumption. In this case, we optimize a linear combination between the total navigation time and the total time the engine is switched off. Our approach can be generalized to other setups, for example, navigation under imperfect environmental forecast or with different models for the moving vessel.

eess.SY↗

arXiv2019

Zermelo's problem: Optimal point-to-point navigation in 2D turbulent flows using Reinforcement Learning

To find the path that minimizes the time to navigate between two given points in a fluid flow is known as Zermelo's problem. Here, we investigate it by using a Reinforcement Learning (RL) approach for the case of a vessel which has a slip velocity with fixed intensity, Vs , but variable direction and navigating in a 2D turbulent sea. We show that an Actor-Critic RL algorithm is able to find quasi-optimal solutions for both time-independent and chaotically evolving flow configurations. For the frozen case, we also compared the results with strategies obtained analytically from continuous Optimal Navigation (ON) protocols. We show that for our application, ON solutions are unstable for the typical duration of the navigation process, and are therefore not useful in practice. On the other hand, RL solutions are much more robust with respect to small changes in the initial conditions and to external noise, even when V s is much smaller than the maximum flow velocity. Furthermore, we show how the RL approach is able to take advantage of the flow properties in order to reach the target, especially when the steering speed is small.

nlin.CD↗

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.

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arXiv2019

Helicoidal particles in turbulent flows with multi-scale helical injection

We present numerical and theoretical results concerning the properties of turbulent flows with strong multi-scale helical injection. We perform direct numerical simulations of the Navier-Stokes equations under a random helical stirring with power-law spectrum and with different intensities of energy and helicity injections. We show that there exists three different regimes where the forward energy and helicity inertial transfers are: (i) both leading with respect to the external injections, (ii) energy transfer is leading and helicity transfer is sub-leading and (iii) both are sub-leading and helicity is maximal at all scales. As a result, the cases (ii-iii) give flows with Kolmogorov-like inertial energy cascade and tuneable helicity transfers/contents. We further explore regime (iii) by studying its effect on the kinetics of point-like isotropic helicoids, particles whose dynamics is isotropic but breaks parity invariance. We investigate small-scale fractal clustering and preferential sampling of intense helical flow structures. Depending on their structural parameters, the isotropic helicoids either preferentially sample co-chiral or anti-chiral flow structures. We explain these findings in limiting cases in terms of what is known for spherical particles of different densities and degrees of inertia. Furthermore, we present theoretical and numerical results for a stochastic model where dynamical properties can be calculated using analytical perturbation theory. Our study shows that a suitable tuning of the stirring mechanism can strongly modify the small-scale turbulent helical properties and demonstrates that isotropic helicoids are the simplest particles able to preferentially sense helical properties in turbulence.

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arXiv2018

Smart Inertial Particles

We performed a numerical study to train smart inertial particles to target specific flow regions with high vorticity through the use of reinforcement learning algorithms. The particles are able to actively change their size to modify their inertia and density. In short, using local measurements of the flow vorticity, the smart particle explores the interplay between its choices of size and its dynamical behaviour in the flow environment. This allows it to accumulate experience and learn approximately optimal strategies of how to modulate its size in order to reach the target high-vorticity regions. We consider flows with different complexities: a two-dimensional stationary Taylor-Green like configuration, a two-dimensional time-dependent flow, and finally a three-dimensional flow given by the stationary Arnold-Beltrami-Childress helical flow. We show that smart particles are able to learn how to reach extremely intense vortical structures in all the tackled cases.

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arXiv2017

Flow Navigation by Smart Microswimmers via Reinforcement Learning

Smart active particles can acquire some limited knowledge of the fluid environment from simple mechanical cues and exert a control on their preferred steering direction. Their goal is to learn the best way to navigate by exploiting the underlying flow whenever possible. As an example, we focus our attention on smart gravitactic swimmers. These are active particles whose task is to reach the highest altitude within some time horizon, given the constraints enforced by fluid mechanics. By means of numerical experiments, we show that swimmers indeed learn nearly optimal strategies just by experience. A reinforcement learning algorithm allows particles to learn effective strategies even in difficult situations when, in the absence of control, they would end up being trapped by flow structures. These strategies are highly nontrivial and cannot be easily guessed in advance. This Letter illustrates the potential of reinforcement learning algorithms to model adaptive behavior in complex flows and paves the way towards the engineering of smart microswimmers that solve difficult navigation problems.

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arXiv2016

Preferential sampling of helicity by isotropic helicoids

We present a theoretical and numerical study on the motion of isotropic helicoids in complex flows. These are particles whose motion is invariant under rotations but not under mirror reflections of the particle. This is the simplest, yet unexplored, extension of the much studied case of small spherical particles. We show that heavy isotropic helicoids, due to the coupling between translational and rotational degrees of freedom, preferentially sample different helical regions in laminar or chaotic advecting flows. This opens the way to control and engineer particles able to track complex flow structures with potential applications to microfluidics and turbulence.

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arXiv2015

Analysis of the Correlation Dimension for Inertial Particles

We obtain an implicit equation for the correlation dimension which describes clustering of inertial particles in a complex flow onto a fractal measure. Our general equation involves a propagator of a nonlinear stochastic process in which the velocity gradient of the fluid appears as additive noise. When the long-time limit of the propagator is considered our equation reduces to an existing large-deviation formalism, from which it is difficult to extract concrete results. In the short-time limit, however, our equation reduces to a solvability condition on a partial differential equation. We show how this approach leads to a perturbative expansion of the correlation dimension, for which the coefficients can be obtained exactly and in principle to any order. We derive the perturbation series for the correlation dimension of inertial particles suspended in three-dimensional spatially smooth random flows with white-noise time correlations, obtaining the first 33 non-zero coefficients exactly.

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arXiv2009

Correlation Dimension of Inertial Particles in Random Flows

We obtain an implicit equation for the correlation dimension of dynamical systems in terms of an integral over a propagator. We illustrate the utility of this approach by evaluating the correlation dimension for inertial particles suspended in a random flow. In the limit where the correlation time of the flow field approaches zero, taking the short-time limit of the propagator enables the correlation dimension to be determined from the solution of a partial differential equation. We develop the solution as a power series in a dimensionless parameter which represents the strength of inertial effects.

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