arXiv subjects

Patricio Clark di Leoni

Publications and source records attributed to Patricio Clark di Leoni.

8 recordsLinked to original sources

arXiv2026

Characterizing periodic orbits in two-dimensional Rayleigh-Bénard flows

Unstable periodic orbits and steady states are believed to form the backbone of spatiotemporal chaos and turbulence, yet their computation in thermally driven flows remains scarce for transitional regimes. In this work we compute and characterize a steady state and three families of periodic orbits in two-dimensional Rayleigh-Bénard at $\mathrm{Pr}=1$, near the transition to chaos. We find that in its route to chaos, the flow hops between several sets of orbits after becoming quasiperiodic. We use Floquet analysis to study the stability of the orbits obtained and characterize their bifurcations, showing how the appearance of primary and secondary frequencies, as well as phase-locking mechanisms, are all related to the dynamics of the orbits. We study in detail how the flow shadows the orbits found and determine in which regimes each orbit is dynamically relevant or not. Our analysis also reveals two important insights: (1) all symmetries are broken before the onset of chaos, and (2) this onset does not alter the behavior of the heat transport.

physics.flu-dyn↗

arXiv2026

Dimensional regimes in Kolmogorov Flow

We study the dimensionality of two-dimensional Kolmogorov flows over a wide range of Reynolds numbers and forcing wavenumbers $k_f=\{2,4,8\}$ using two complementary approaches: convolutional autoencoders and a Kaplan-Yorke estimation based on Lyapunov analysis. As the Reynolds number increases, two distinct transitions are observed: the first corresponds to the destabilization of a periodic orbit, while the second marks the saturation of the large-scale motions. When expressed in terms of the forcing Reynolds number, these transitions occur at nearly the same value for all forcing wavenumbers, suggesting a universal scaling with respect to the forcing scale. By filtering the data to retain only the large-scale range ($k < k_f$), we show that the dimensionality estimated by the autoencoders also saturates at the second transition, implying that once the large scales are fully developed, the subsequent increase in dynamical activity occurs predominantly at smaller scales. At higher Reynolds numbers, the Kaplan-Yorke dimension ceases to grow, revealing its limited sensitivity to the nonlinear interactions that dominate in this regime. Both the Kaplan-Yorke saturation dimension and the filtered large-scale dimensionalities exhibit a linear dependence on $k_f$, indicating that the number of active degrees of freedom scales with the forcing scale rather than with the total number of available Fourier modes.

physics.flu-dyn↗

arXiv2024

Active grid turbulence anomalies through the lens of physics informed neural networks

Active grids operated with random protocols are a standard way to generate large Reynolds number turbulence in wind and water tunnels. But anomalies in the decay and third-order scaling of active-grid turbulence have been reported. We combine Laser Doppler Velocimetry and hot-wire anemometry measurements in a wind tunnel, with machine learning techniques and numerical simulations, to gain further understanding on the reasons behind these anomalies. Numerical simulations that incorporate the statistical anomalies observed in the experimental velocity field near the active grid can reproduce the experimental anomalies observed later in the decay. The results indicate that anomalies in experiments near the active grid introduce correlations in the flow that can persist for long times.

physics.flu-dyn↗

arXiv2024

Reduced Representations of Rayleigh-Bénard Flows via Autoencoders

We analyzed the performance of Convolutional Autoencoders in generating reduced-order representations the temperature field of 2D Rayleigh-Bénard flows at $Pr=1$ and Rayleigh numbers extending from $10^6$ to $10^8$, capturing the range where the flow transitions to turbulence. We present a way of estimating the minimum number of dimensions needed by the Autoencoders to capture all the relevant physical scales of the data that is more apt for highly multiscale flows than previous criteria applied to lower dimensional systems. We compare our architecture with two regularized variants as well as with linear methods, and find that manually fixing the dimension of the latent space produces the best results. We show how the estimated minimum dimension presents a sharp increase around $Ra \sim 10^7$, when the flow starts to transition to turbulence. Furthermore, we show how this dimension does not follow the same scaling as the physically relevant scales, such as the dissipation lengthscale and the thermal boundary layer.

physics.flu-dyn↗

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↗

arXiv2018

Quantitative estimation of effective viscosity in quantum turbulence

We study freely decaying quantum turbulence by performing high resolution numerical simulations of the Gross-Pitaevskii equation (GPE) in the Taylor-Green geometry. We use resolutions ranging from $1024^3$ to $4096^3$ grid points. The energy spectrum confirms the presence of both a Kolmogorov scaling range for scales larger than the intervortex scale $\ell$, and a second inertial range for scales smaller than $\ell$. Vortex line visualizations show the existence of substructures formed by a myriad of small-scale knotted vortices. Next, we study finite temperature effects in the decay of quantum turbulence by using the stochastic Ginzburg-Landau equation to generate thermal states, and then by evolving a combination of these thermal states with the Taylor-Green initial conditions using the GPE. We extract the mean free path out of these simulations by measuring the spectral broadening in the Bogoliubov dispersion relation obtained from spatio-temporal spectra, and use it to quantify the effective viscosity as a function of the temperature. Finally, in order to compare the decay of high temperature quantum and that of classical flows, and to further calibrate the estimations of viscosity from the mean free path in the GPE simulations, we perform low Reynolds number simulations of the Navier-Stokes equations.

cond-mat.quant-gas↗

arXiv2018

Interplay between Alfvén and magnetosonic waves in compressible magnetohydrodynamics turbulence

Using spatio-temporal spectra we show direct evidence of excitation of magnetosonic and Alfvén waves in three-dimensional compressible magnetohydrodynamic turbulence at small Mach numbers. For the plasma pressure dominated regime, or high $β$ regime (with $β$ the ratio between fluid and magnetic pressure), and for the magnetic pressure dominated regime, or low $β$ regime, we study magnetic field fluctuations parallel and perpendicular to a guide magnetic field $\textbf{B}_0$. In the low $β$ case we find excitation of compressible and incompressible fluctuations, with a transfer of energy towards Alfvénic modes and to a lesser extent towards magnetosonic modes. In particular, we find signatures of the presence of fast magnetosonic waves in a scenario compatible with that of weak turbulence. In the high $β$ case, fast and slow magnetosonic waves are present, with no clear trace of Alfvén waves, and a significant part of the energy is carried by two-dimensional turbulent eddies.

physics.plasm-ph↗

arXiv2015

Spatio-temporal detection of Kelvin waves in quantum turbulence simulations

We present evidence of Kelvin excitations in space-time resolved spectra of numerical simulations of quantum turbulence. Kelvin waves are transverse and circularly polarized waves that propagate along quantized vortices, for which the restitutive force is the tension of the vortex line, and which play an important role in theories of superfluid turbulence. We use the Gross-Pitaevskii equation to model quantum flows, letting an initial array of well-organized vortices develop into a turbulent bundle of intertwined vortex filaments. By achieving high spatial and temporal resolution we are able to calculate space-time resolved mass density and kinetic energy spectra. Evidence of Kelvin and sound waves is clear in both spectra. Identification of the waves allows us to extract the spatial spectrum of Kelvin waves, clarifying their role in the transfer of energy

physics.flu-dyn↗