arXiv subjects

Maurizio Carbone

Publications and source records attributed to Maurizio Carbone.

17 recordsLinked to original sources

arXiv2026

Learning Backward Transport for Source Localization

We address the problem of locating a chemical source in a flow. Based on the duality between the concentration field and Lagrangian tracer trajectories, we interpret concentration detections as evidence of paths connecting the source to the detection points. This Schr\"odinger bridge formulation between plausible emission positions and detection points leverages the backward propagator of passive tracers to frame source localization as the sampling of candidate emission locations via Langevin dynamics. The associated drift reveals classical chemotaxis and cast-and-surge as complementary behaviors emerging from a single transport-based principle. Applied to olfactory search in two-dimensional turbulence, the proposed backtracking framework outperforms classical strategies across varying wind regimes using a single, Galilean-invariant learned propagator.

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arXiv2026

Smart strategies to navigate turbulent odor plumes reorienting to local wind

Olfactory search in turbulent environments is a sensorimotor problem that many animals solve with remarkable efficiency, yet replicating this ability in artificial systems is an enduring challenge because detections are intermittent and wind direction fluctuates strongly, rendering standard search strategies unreliable. We introduce a wind-relative reinforcement-learning framework in which an agent navigates a turbulent plume with a single internal variable --- the elapsed time since the last odor detection --- and selects actions relative to a locally estimated wind direction filtered through an exponential memory kernel. Policies are trained and evaluated in direct numerical simulations of turbulence, capturing the multi-scale characteristics of velocity and odor fields in natural environments, both in the presence and absence of a mean wind. In a mild mean wind, the learned policy outperforms well-known biomimetic policies such as cast-and-surge regardless of the wind memory time, yet adapts its movement pattern to wind-estimation quality. In isotropic turbulence, performance peaks at an intermediate wind memory time, identifying temporal wind integration as a regime-dependent resource. Our results highlight the importance of developing and validating olfactory-navigation strategies under realistic turbulent conditions, and offer a compact design principle for minimal robotic olfactory navigation and testable predictions for biological search behavior.

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arXiv2026

Olfactory pursuit: catching a moving odor source in complex flows

Locating and intercepting a moving target from possibly delayed, intermittent sensory signals is a paradigmatic problem in decision-making under uncertainty, and a fundamental challenge for, e.g., animals seeking prey or mates and autonomous robotic systems. Odor signals are intermittent, strongly mixed by turbulent-like transport, and typically lag behind the true target position, thereby complicating localization. Here, we formulate olfactory pursuit as a partially observable Markov decision process in which an agent maintains a joint belief over the target's position and velocity. Using a discrete run-and-tumble model, we compute quasi-optimal policies by numerically solving the Bellman equation and benchmark them against well-established information-theoretic strategies such as Infotaxis. We show that purely exploratory policies are near-optimal when the target frequently reorients, but fail dramatically when the target exhibits persistent motion. We thus introduce a computationally efficient hybrid policy that combines the information-gain drive of Infotaxis with a "greedy" value function derived from an associated fully observable control problem. Our heuristic achieves near-optimal performance across all persistence times and substantially outperforms purely exploratory approaches. Moreover, our proposal demonstrates strong robustness even in more complex search scenarios, including continuous run-and-tumble prey motion with moderate persistence time, model mismatch, and more accurate plume dynamics representation. Our results identify predictive inference of target motion as the key ingredient for effective olfactory pursuit and provide a general framework for search in information-poor, dynamically evolving environments.

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arXiv2025

Policy heterogeneity improves collective olfactory search in 3-D turbulence

We investigate the role of policy heterogeneity in enhancing the olfactory search capabilities of cooperative agent swarms operating in complex, real-world turbulent environments. Using odor fields from direct numerical simulations of the Navier-Stokes equations, we demonstrate that heterogeneous groups, with exploratory and exploitative agents, consistently outperform homogeneous swarms where the exploration-exploitation tradeoff is managed at the individual level. Our results reveal that policy diversity enables the group to reach the odor source more efficiently by mitigating the detrimental effects of spatial correlations in the signal. These findings provide new insights into collective search behavior in biological systems and offer promising strategies for the design of robust, bioinspired search algorithms in engineered systems.

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arXiv2024

Communities for the Lagrangian Dynamics of the Turbulent Velocity Gradient Tensor: A Network Participation Approach

Complex network analysis methods have been widely applied to nonlinear systems, but applications within fluid mechanics are relatively few. In this paper, we use a network for the Lagrangian dynamics of the velocity gradient tensor (VGT), where each node is a flow state, and the probability of transitioning between states follows from a direct numerical simulation of statistically steady and isotropic turbulence. The network representation of the VGT dynamics is much more compact than the continuous, joint distribution of a set of invariants for the tensor. We focus on choosing optimal variables to discretize and classify the VGT states. To this end, we test several classifications based on topology and various properties of the background flow coherent structures. We do this using the notion of "community" or "module", namely clusters of nodes that are optimally distinct while also containing diverse nodal functions. The best classification based upon VGT invariants often adopted in the literature combines the sign of the principal invariants, $Q$ and $R$, and the sign of the discriminant function, $Δ$, separating regions where the VGT eigenvalues are real and complex. We further improve this classification by including the relative magnitude of the non-normal contribution to the dynamics of the enstrophy and straining stemming from a Schur decomposition of the VGT. The traditional focus on the second VGT principal invariant, $Q$, implies consideration of the difference between the enstrophy and strain-rate magnitude without the non-normal parts. The fact that including the non-normality leads to a better VGT classification highlights the importance of unclosed and complex terms contributing to the VGT dynamics, namely the pressure Hessian and viscous terms, to which the VGT non-normality is intrinsically related.

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arXiv2024

Complex network approach to the turbulent velocity gradient dynamics: High- and low-probability Lagrangian paths

Understanding the dynamics of the turbulent velocity gradient tensor (VGT) is essential to gain insights into the Navier-Stokes equations and improve small-scale turbulence modeling. However, characterizing the VGT dynamics conditional on all its relevant invariants in a continuous fashion is extremely difficult. In this paper, we represent the VGT Lagrangian dynamics using a network where each node represents a unique flow state. This approach enables us to discern how the VGT transitions from one state to another in a simplified fashion. Our analysis reveals intriguing features of the resulting network, such as the clustering of the commonly visited nodes where the eigenvalues of the VGT are real, in the proximity of the Vieillefosse tail. We then relate our complex network approach to the well-established VGT discretization based on the sign of its principal invariants, $Q$ and $R$, and its discriminant, $Δ$. To this end, we separate the shortest paths on the network (geodesics) based on the $Q$-$R$ region to which their starting and arrival nodes belong. The distribution of the length of intra-region geodesics, with starting and arrival nodes belonging to the same $Q$-$R$ region, exhibits a distinct bimodality in two regions of the $Q$-$R$ plane, those in which the deviatoric part of the pressure Hessian introduces complexity to the VGT dynamics. Such bimodality is associated with infrequently visited nodes having to follow a long, low probability path to drastically change the state of the VGT compared to other flow states that can acquire the necessary characteristics without changing their sign for $Q$ or $R$. We complement the geodesics approach by examining random walks on the network, showing how the VGT non-normality and the associated production terms distinguish the shortest commuting paths between different $Q$-$R$ regions.

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arXiv2024

Tailor-designed models for the turbulent velocity gradient through normalizing flow

Small-scale turbulence can be comprehensively described in terms of velocity gradients, which makes them an appealing starting point for low-dimensional modeling. Typical models consist of stochastic equations based on closures for non-local pressure and viscous contributions. The fidelity of the resulting models depends on the accuracy of the underlying modeling assumptions. Here, we discuss an alternative data-driven approach leveraging machine learning to derive a velocity gradient model which captures its statistics by construction. We use a normalizing flow to learn the velocity gradient probability density function (PDF) from direct numerical simulation (DNS) of incompressible turbulence. Then, by using the equation for the single-time PDF of the velocity gradient, we construct a deterministic, yet chaotic, dynamical system featuring the learned steady-state PDF by design. Finally, utilizing gauge terms for the velocity gradient single-time statistics, we optimize the time correlations as obtained from our model against the DNS data. As a result, the model time realizations statistically closely resemble the time series from DNS.

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arXiv2024

Carrier-phase DNS of ignition and combustion of iron particles in a turbulent mixing layer

Three-dimensional CP-DNS of reacting iron particle dust clouds in a turbulent mixing layer are conducted. The simulation approach considers the Eulerian transport equations for the reacting gas phase and resolves all scales of turbulence, whereas the particle boundary layers are modelled employing the Lagrangian point-particle framework for the dispersed phase. The CP-DNS employs an existing sub-model for iron particle combustion that considers the oxidation of iron to FeO and that accounts for both diffusion- and kinetically-limited combustion. At first, the particle sub-model is validated against experimental results for single iron particle combustion considering various particle diameters and ambient oxygen concentrations. Subsequently, the CP-DNS approach is employed to predict iron particle cloud ignition and combustion in a turbulent mixing layer. The upper stream of the mixing layer is initialised with cold particles in air, while the lower stream consists of hot air flowing in the opposite direction. Simulation results show that turbulent mixing induces heating, ignition and combustion of the iron particles. Significant increases in gas temperature and oxygen consumption occur mainly in regions where clusters of iron particles are formed. Over the course of the oxidation, the particles are subjected to different rate-limiting processes. While initially particle oxidation is kinetically-limited it becomes diffusion-limited for higher particle temperatures and peak particle temperatures are observed near the fully-oxidised particle state. Comparing the present non-volatile iron dust flames to general trends in volatile-containing solid fuel flames, non-vanishing particles at late simulation times and a stronger limiting effect of the local oxygen concentration on particle conversion is found for the present iron dust flames in shear-driven turbulence.

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arXiv2023

Investigating the parametric dependence of the impact of two-way coupling on inertial particle settling in turbulence

Tom et al.\ (J.\ Fluid Mech.\ 947, A7, 2022) investigated the impact of two-way coupling (2WC) on particle settling in turbulence. For the limited parameter choices explored, it was found that 2WC substantially enhances particle settling compared to the one-way coupled (1WC) case, even at low mass loading $Φ_m$. Moreover, contrary to previous claims, it was demonstrated that preferential sweeping remains the mechanism responsible for the particles settling faster than the Stokes settling velocity in 2WC flows. However, crucial questions remain: 1) how small must $Φ_m$ be for the effects of 2WC on particle settling to be negligible? 2) does the preferential sweeping mechanism remain relevant in 2WC flows as $Φ_m$ is increased? To answer these, we explore a much broader portion of the parameter space, and our simulations cover cases where the impact of 2WC on the global fluid statistics ranges from negligible to strong. We find that even for $Φ_m=7.5\times 10^{-3}$, 2WC can noticeably increase the settling for some choices of the Stokes and Froude numbers. We also demonstrate that even when $Φ_m$ is large enough for the global fluid statistics to be strongly affected by the particles, preferential sweeping is still the mechanism responsible for the enhanced particle settling. The difference between the 1WC and 2WC cases is that, in the latter the particles are not merely swept around the downward-moving side of vortices, but they also drag the fluid with them as they move down.

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arXiv2023

Asymptotic predictions on the velocity gradient statistics in low-Reynolds number random flows: Onset of skewness, intermittency and alignments

Stirring a fluid through a Gaussian forcing at a vanishingly small Reynolds number produces a Gaussian random field, while flows at higher Reynolds numbers exhibit non-Gaussianity, cascades, anomalous scaling and preferential alignments. Recent works (Yakhot and Donzis, Phys. Rev. Lett., vol. 119, 2017, pp. 044501; Gotoh and Yang, Philos. Trans. Royal Soc. A, vol. 380, 2022, pp. 20210097) investigated the onset of these turbulent hallmarks in low-Reynolds number flows by focusing on the scaling of the velocity increments. They showed that the scalings in random flows at low-Reynolds and in high-Reynolds number turbulence are surprisingly similar. In this work, we address the onset of turbulent signatures in low-Reynolds number flows from the viewpoint of the velocity gradient dynamics, giving insights into its rich statistical geometry. We combine a perturbation theory of the full Navier-Stokes equations with velocity gradient modeling. This procedure results in a stochastic model for the velocity gradient in which the model coefficients follow directly from the Navier-Stokes equations and statistical homogeneity constraints. The Fokker-Planck equation associated with our stochastic model admits an analytic solution which shows the onset of turbulent hallmarks at low Reynolds numbers: skewness, intermittency and preferential alignments arise in the velocity gradient statistics as the Reynolds number increases. The model predictions are in excellent agreement with direct numerical simulations of low-Reynolds number flows.

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arXiv2022

Lagrangian model for passive scalar gradients in turbulence

The equation for the fluid velocity gradient along a Lagrangian trajectory immediately follows from the Navier-Stokes equation. However, such an equation involves two terms that cannot be determined from the velocity gradient along the chosen Lagrangian path: the pressure Hessian and the viscous Laplacian. A recent model handles these unclosed terms using a multi-level version of the recent deformation of Gaussian fields (RDGF) closure (Johnson \& Meneveau, Phys.~Rev.~Fluids, 2017). This model is in remarkable agreement with DNS data and works for arbitrary Taylor Reynolds numbers $\Rey_λ$. Inspired by this, we develop a Lagrangian model for passive scalar gradients in isotropic turbulence. The equation for passive scalar gradients also involves an unclosed term in the Lagrangian frame, namely the scalar gradient diffusion term, which we model using the RDGF approach. However, comparisons of the statistics obtained from this model with direct numerical simulation (DNS) data reveal substantial errors due to erroneously large fluctuations generated by the model. We address this defect by incorporating into the closure approximation information regarding the scalar gradient production along the local trajectory history of the particle. This modified model makes predictions for the scalar gradients, their production rates, and alignments with the strain-rate eigenvectors that are in very good agreement with DNS data. However, while the model yields valid predictions up to around $\Rey_λ\approx 500$, beyond this, the model breaks down.

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arXiv2022

How two-way coupling modifies the multiscale preferential sweeping mechanism

For one-way coupled (1WC) flows, Tom & Bragg (J. Fluid Mech., 871, pp. 244-270, 2019) advanced the analysis of Maxey (J. Fluid Mech., 174, pp. 441-465, 1987), which applied to weakly inertial particles, to particles of arbitrary inertia, and the new theoretical result revealed the role that different scales play in the preferential sweeping mechanism that leads to enhanced particle settling in turbulent flows. Monchaux & Dejoan (Phys. Rev. Fluids, 2, 104302, 2017) showed using direct numerical simulations (DNS) that while for low particle loading the effect of two-way coupling (2WC) on the global flow statistics is weak, 2WC enables the particles to drag the fluid in their vicinity down with them, significantly enhancing their settling, and they argued that 2WC suppresses the preferential sweeping mechanism. We explore this further by considering the impact of 2WC on the contribution made by eddies of different sizes on the particle settling. In agreement with Monchaux & Dejoan, we show that even for low loading, 2WC strongly enhances particle settling, and we show how 2WC modifies the contribution from different flow scales. However, contrary to their study, we show that preferential sweeping remains important in 2WC flows. In particular, for both 1WC and 2WC flows, the settling enhancement due to turbulence is dominated by contributions from particles in straining regions of the flow, but for the 2WC case, the particles in these regions also drag the fluid down with them, leading to an enhancement of their settling compared to the 1WC case.

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arXiv2021

Are there higher-order Betchov homogeneity constraints for incompressible isotropic turbulence?

Incompressible and statistically homogeneous flows obey exact kinematic relations. The Betchov homogeneity constraints (Betchov, J. Fluid Mech., vol. 1, 1956, pp. 497-504) for the average principal invariants of the velocity gradient are among the most well known and extensively employed homogeneity relations. These homogeneity relations have far-reaching implications for the coupled dynamics of strain and vorticity, as well as for the turbulent energy cascade. Whether the Betchov homogeneity constraints are the only possible ones or whether additional homogeneity relations exist has not been proven yet. Here we show that the Betchov homogeneity constraints are the only homogeneity constraints for incompressible and statistically isotropic velocity gradient fields. We also extend our results to derive homogeneity relations involving the velocity gradient and other dynamically relevant quantities, such as the pressure Hessian.

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arXiv2020

Exploring the turbulent velocity gradients at different scales from the perspective of the strain-rate eigenframe

Expressing the evolution equations for the filtered velocity gradient tensor (FVGT) in the strain-rate eigenframe provides an insightful way to disentangle and understand various processes such as strain self-amplification, vortex stretching and tilting, and to consider their properties at different scales in the flow. Using data from Direct Numerical Simulation (DNS) of the forced Navier-Stokes equation, we consider the relative importance of local and non-local terms in the FVGT eigenframe equations across the scales using statistical analysis. The analysis of the eigenframe rotation-rate, that drives vorticity tilting, shows that the anisotropic pressure Hessian plays a key role, with the sub-grid stress making an important contribution outside the dissipation range, and the local spinning due to vorticity making a much smaller contribution. The results also show the striking behavior that the vorticity tilting term remains highly intermittent even at relatively large scales. We derive a generalization of the Lumley triangle that allows us to show that the pressure Hessian has a preference for two-component axisymmetric configurations at small scales, with a transition to a more isotropic state at larger scales. Correlations between the sub-grid stress and other terms in the eigenframe equations are considered, highlighting the coupling between the sub-grid and nonlinear amplification terms, with the sub-grid term playing an important role in regularizing the system. These results provide useful guidelines for improving Lagrangian models of the FVGT, since current models fail to capture a number of subtle features observed in our results.

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arXiv2019

Gauge symmetry and dimensionality reduction of the anisotropic pressure Hessian

Analyzing the fluid velocity gradients in a Lagrangian reference frame provides an insightful way to study the small-scale dynamics of turbulent flows, and further insight is provided by considering the equations in the eigenframe of the strain-rate tensor. The dynamics of the velocity gradient tensor is governed in part by the anisotropic pressure Hessian, which is a non-local functional of the velocity gradient field. This anisotropic pressure Hessian plays a key role in the velocity gradient dynamics, for example in preventing finite-time singularities, but it is difficult to understand and model due to its non-locality and complexity. In this work a gauge symmetry for the pressure Hessian is introduced to the eigenframe equations of the velocity gradient, such that when the gauge is added to the original pressure Hessian, the dynamics of the eigenframe variables remain unchanged. We then exploit this gauge symmetry to perform a rank reduction on the three-dimensional anisotropic pressure Hessian, which, remarkably, is possible everywhere in the flow. The dynamical activity of the newly introduced rank-reduced anisotropic pressure Hessian is confined to two dimensional manifolds in the three dimensional flow, and exhibits striking alignment properties with respect to the strain-rate eigenframe and the vorticity vector. The dimensionality reduction, together with the strong preferential alignment properties, leads to new dynamical insights for understanding and modelling the role of the anisotropic pressure Hessian in three-dimensional flows.

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arXiv2019

Is vortex stretching the main cause of the turbulent energy cascade?

In three dimensional turbulence there is on average a cascade of kinetic energy from the largest to the smallest scales of the flow. While the dominant idea is that the cascade occurs through the physical process of vortex stretching, evidence for this is debated. In the framework of the Karman-Howarth equation for the two point turbulent kinetic energy, we derive a new result for the average flux of kinetic energy between two points in the flow that reveals the role of vortex stretching. However, the result shows that vortex stretching is in fact not the main contributor to the average energy cascade; the main contributor is the self-amplification of the strain-rate field. We emphasize the need to correctly distinguish and not conflate the roles of vortex stretching and strain-self amplification in order to correctly understand the physics of the cascade, and also resolve a paradox regarding the differing role of vortex stretching on the mechanisms of the energy cascade and energy dissipation rate. Direct numerical simulations are used to confirm the results, as well as provide further results and insights on vortex stretching and strain-self amplification at different scales in the flow. Interestingly, the results imply that while vortex stretching plays a sub-leading role in the average cascade, it may play a leading order role during large fluctuations of the energy cascade about its average behavior.

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arXiv2018

Multiscale fluid--particle thermal interaction in isotropic turbulence

We use direct numerical simulations to investigate the interaction between the temperature field of a fluid and the temperature of small particles suspended in the flow, employing both one and two-way thermal coupling, in a statistically stationary, isotropic turbulent flow. Using statistical analysis, we investigate this variegated interaction at the different scales of the flow. We find that the variance of the fluid temperature gradients decreases as the thermal response time of the suspended particles is increased. The probability density function (PDF) of the fluid temperature gradients scales with its variance, while the PDF of the rate of change of the particle temperature, whose variance is associated with the thermal dissipation due to the particles, does not scale in such a self-similar way. The modification of the fluid temperature field due to the particles is examined by computing the particle concentration and particle heat fluxes conditioned on the magnitude of the local fluid temperature gradient. These statistics highlight that the particles cluster on the fluid temperature fronts, and the important role played by the alignments of the particle velocity and the local fluid temperature gradient. The temperature structure functions, which characterize the temperature fluctuations across the scales of the flow, clearly show that the fluctuations of the fluid temperature increments are monotonically suppressed in the two-way coupled regime as the particle thermal response time is increased. Thermal caustics dominate the particle temperature increments at small scales, that is, particles that come into contact are likely to have very large differences in their temperature. This is caused by the nonlocal thermal dynamics of the particles...

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