arXiv subjects

F. Pétrélis

Publications and source records attributed to F. Pétrélis.

7 recordsLinked to original sources

arXiv2026

Dynamical and statistical properties of large scales in turbulence

We present a review of results concerning the properties of scales larger than the forcing scale in turbulent flows. In three-dimensional turbulence, when the power driving the flow is injected at a well-defined scale, the injection scale separates the small-scale range, where the Kolmogorov cascade takes place, from the large-scale range across which the mean energy flux is zero, suggesting that these modes are in equilibrium. We show that, in the case of spatially periodic forcing involving only a few modes, an equipartition energy spectrum is generated at large scales, and we discuss the deviations from equipartition observed with more complex forcings. In two-dimensional turbulence, the injection scale separates the direct enstrophy cascade toward small scales from the inverse energy cascade toward large scales. Because of the inverse cascade, one would not expect equilibrium statistical physics tools to be suitable for describing the large-scale structures. Yet this is precisely the situation in which such tools have been most widely used. We indeed show that the bifurcations observed between different largescale regimes of two-dimensional turbulence, both in experiments and in direct numerical simulations, can be qualitatively described by the Truncated Euler equations, whose solutions satisfy statistical equilibrium.

physics.flu-dyn↗

arXiv2025

Coherence of velocity fluctuations in a turbulent round jet

Coherence between the velocity fluctuations measured at two points is investigated in a turbulent jet flow. Coherence is calculated in different regions of the flow by changing the separation between the points, the distance between the points from the exit of the jet and from its central axis, and the injection velocity of the jet. It is observed that coherence scales with the system parameters, the functional form of coherence and the corresponding scaling laws change depending on in which region coherence is measured, and that coherence is self similar in both the regions.

physics.flu-dyn↗

arXiv2024

Random interfaces generated by the addition of structures of variable size

We consider the random deposition of objects of variable width and height over a line. The successive additions of these structures create a random interface. We focus on the regime of heavy tailed distributions of the structure width. When the structure center is chosen at random, the problem is exactly solvable and we prove that the interfaces generically tend towards self-affine random curves. The asymptotic behavior reached after a large number of iterations is universal in the sense that it depends on only three parameters: the shape of the added structure at its maximum, the power-law exponent of the width distribution and the exponent that relates height and width. The parameter space displays several transitions that separate different asymptotic behaviors. In particular for a set of parameters, the interface tends towards a fractional Brownian motion. Our results reveal the existence of a new class of random interfaces which properties appear to be robust. The mechanism that generates correlations at large distance is identified and it explains the appearance of such correlations in several situations of interest such as the physics of earthquakes or the propagation of energy through a diffusive medium.

cond-mat.stat-mech↗

arXiv2021

Coherence of velocity fluctuations in turbulent flows

We investigate the spatio-temporal quantity of coherence for turbulent velocity fluctuations at spatial distances of the order or larger than the integral length scale $l_{0}$. Using controlled laboratory experiments, an exponential decay as a function of distance is observed with a decay rate which depends on the flow properties. The same law is observed in two different flows indicating that it can be a generic property of turbulent flows.

physics.flu-dyn↗

arXiv2017

Observation of thermal equilibrium in capillary wave turbulenc

We consider capillary wave turbulence at scales larger than the forcing one. At such scales, our measurements show that the surface waves dynamics is the one of a thermal equilibrium state in which the effective temperature is related to the injected power. We characterize this evolution with a scaling law and report the statistical properties of the large-scale surface elevation depending on this effective temperature.

physics.flu-dyn↗

arXiv2015

Dynamo regimes and transitions in the VKS experiment

The Von K{á}rm{á}n Sodium experiment yields a variety of dynamo regimes, when asymmetry is imparted to the flow by rotating impellers at different speed F1 and F2. We show that as the intensity of forcing, measured as F1 + F2, is increased, the transition to a self-sustained magnetic field is always observed via a supercritical bifurcation to a stationary state. For some values of the asymmetry parameter $\θ$ = (F1--F2)/(F1+F2), time dependent dynamo regimes develop. They are observed either when the forcing is increased for a given value of asymmetry, or when the amount of asymmetry is varied at sufficiently high forcing. Two qualitatively different transitions between oscillatory and stationary regimes are reported, involving or not a strong divergence of the period of oscillations. These transitions can be interpreted using a low dimensional model based on the interactions of two dynamo modes.

physics.flu-dyn↗

arXiv2011

Anomalous exponents at the onset of an instability

Critical exponents are calculated exactly at the onset of an instability, using asymptotic expansiontechniques. When the unstable mode is subject to multiplicative noise whose spectrum at zero frequency vanishes, we show that the critical behavior can be anomalous, i.e. the mode amplitude X scales with departure from onset μas $ ~ μ^β$ with an exponent $β$ different from its deterministic value. This behavior is observed in a direct numerical simulation of the dynamo instability and our results provide a possible explanation to recent experimental observations.

physics.flu-dyn↗