arXiv subjects

François Pétrélis

Publications and source records attributed to François Pétrélis.

14 recordsLinked to original sources

arXiv2026

Magnetic reversals in a geodynamo model with a stably-stratified layer

We study the process of magnetic reversals in the presence of a stably-stratified layer below the core-mantle boundary using direct numerical simulations of the incompressible magnetohydrodynamics equations under the Boussinesq approximation in a spherical shell. We show that the dipolar-multipolar transition shifts to larger Rayleigh numbers in the presence of a stably-stratified layer, and that the dipolar strength of the magnetic field at the core-mantle boundary increases due to the skin effect. By imposing an heterogeneous heat flux at the outer boundary, we break the equatorial symmetry of the flow, and show that different heat flux patterns can trigger different dynamo solutions, such as hemispheric dynamos and polarity reversals. Using kinematic dynamo simulations, we show that the stably-stratified layer leads to similar growth rates of the dipole and quadrupole components of the magnetic field, playing the role of a conducting boundary layer, favouring magnetic reversals, and a dynamics predicted by low-dimensional models.

physics.flu-dyn↗

arXiv2025

Non-local random deposition models for earthquakes and energy propagation

We investigate a new class of non-local random deposition models, initially introduced by physicists to study the field of mechanical constraints (stress) applied along a line or on a given area located in a seismic zone. The non-local features are twofold. First, the falling objects have random and heavy-tailed dimensions. Second, the locations where the objects are falling are at least for some of the models that we consider, depending on the shape of the surface before deposition. We consider $(h_N)_{N\in \N}$ a sequence of random $(d+1)$-dimensional surfaces defined on $[0,D]^d$ for $d\in \{1,2\}$. Thus, the process $h_{N}$ is obtained by adding to $h_{N-1}$ an object $$\s\in [0,D]^d \mapsto Z_{N}^{α-1} ψ\Big(\frac{v_{Y_N}(\s)}{Z_N}\Big),$$ where $Z=(Z_i)_{i\in \N}$ is an i.i.d. sequence of Pareto random variables, where $ψ:[0,\infty)\mapsto \mathbb{R}^+$ determines the global shape of the object, where $v_{\y}(\x)$ is the distance between $\x$ and $\y$ on the torus and where $Y=(Y_i)_{i\in \N}$ are random variables in $[0,D]^d$ that provide the location of each falling object. In the present paper we focus on three variations of this model. First, the rand-model for which $Y$ is an i.i.d. sequence of uniform random variables. Then, the min-model, that introduces an important property of the physics of earthquakes but is also harder to tract since a strong correlation appears between the $N$-th falling object and the shape of the profile $h_{N-1}$. Finally we consider a variant of the rand-model: the stellar model, which allows us to study the intensity of the microwaves emitted by stellar clouds and measured at the Earth surface. For those three models, our results identify the limit in law of $(h_N)_{N\in \N}$ viewed as a sequence of continuous random functions rescaled properly. We also determine the limit in law of the fluctuations of $(h_N)_{N\in \N}$.

math.PR↗

arXiv2025

Rayleigh-B{é}nard Convection with Phase Change Close to the Critical Point

Rayleigh-B{é}nard convection is investigated with sulfur hexafluoride (SF$_6$) in the vicinity of its critical point. In the supercritical domain, direct measurements of the heat flux $Q$ as a function of the temperature difference $ΔT$ are consistent with the usual scaling laws of single-phase turbulent convection. Along the liquid-vapor coexistence curve, heat fluxes are dramatically enhanced by condensation and boiling. Optical measurements are performed to document the size and velocity of the bubbles. We report $Q(ΔT, ε)$ in both domains, with $ε$ the dimensionless distance to the critical point. Critical scaling laws are observed that can guide the development of theoretical models. In addition, this documents a system of diverging heat transfer coefficient, i.e., in which a significant heat flux can be achieved with an arbitrarily small temperature difference as $ε\to 0$.

physics.flu-dyn↗

arXiv2023

Earthquake magnitude distribution and aftershocks: a statistical geometry explanation

The emergence of a power-law distribution for the energy released during an earthquake is investigated in several models. Generic features are identified which are based on the self-affine behavior of the stress field prior to an event. This field behaves at large scale as a random trajectory in 1 dimension of space and a random surface in 2 dimensions. Using concepts of statistical mechanics and results on the properties of these random objects, several predictions are obtained and verified, in particular the value of the power-law exponent of the earthquake energy distribution (the Gutenberg-Richter law) as well as a mechanism for the existence of aftershocks after a large earthquake (the Omori law).

physics.geo-ph↗

arXiv2022

1/f noise and anomalous scaling in Lévy noise-driven on-off intermittency

On-off intermittency occurs in nonequilibrium physical systems close to bifurcation points and is characterised by an aperiodic switching between a large-amplitude "on" state and a small-amplitude "off" state. Lévy on-off intermittency is a recently introduced generalisation of on-off intermittency to multiplicative Lévy noise, which depends on a stability parameter $α$ and a skewness parameter $β$. Here, we derive two novel results on Lévy on-off intermittency by leveraging known exact results on the first-passage time statistics of Lévy flights. First, we compute anomalous critical exponents explicitly as a function of arbitrary Lévy noise parameters $(α,β)$ for the first time, by a heuristic method, complementing previous results. The predictions are verified using numerical solutions of the fractional Fokker-Planck equation. Second, we derive the power spectrum $S(f)$ of Lévy on-off intermittency and show that it displays a power law $S(f)\propto f^κ$ at low frequencies $f$, where $κ\in (-1,0)$ depends on the noise parameters $α,β$. An explicit expression for $κ$ is obtained in terms of $(α,β)$. The predictions are verified using long time series realisations of Lévy on-off intermittency. Our findings help shed light on instabilities subject to non-equilibrium, power-law-distributed fluctuations, emphasizing that their properties can differ starkly from the case of Gaussian fluctuations.

physics.flu-dyn↗

arXiv2021

Symmetry breaking in a turbulent environment

In this work we investigate symmetry breaking in the presence of a turbulent environment. The transition from a symmetric state to a symmetry-breaking state is demonstrated using two examples: (i) the transition of a two-dimensional flow to a three dimensional flow as the fluid layer thickness is varied and (ii) the dynamo instability in a thin layer flow as the magnetic Reynolds number is varied. We show that these examples have similar critical exponents that differ from the mean-field predictions. The critical behavior can be related to the multiplicative nature of the fluctuations and can be predicted in certain limits using results from the statistical properties of random interfaces. Our results indicate the possibility of existence of a new class of out-of-equilibrium phase transition controlled by the multiplicative noise.

physics.flu-dyn↗

arXiv2016

Bifurcations of a large scale circulation in a quasi-bidimensional turbulent flow

We report the experimental study of the bifurcations of a large-scale circulation that is formed over a turbulent flow generated by a spatially periodic forcing. After shortly describing how the flow becomes turbulent through a sequence of symmetry breaking bifurcations, we focus our study on the transitions that occur within the turbulent regime. They are related to changes in the shape of the probability density function (PDF) of the amplitude of the large scale flow. We discuss the nature of these bifurcations and how to model the shape of the PDF.

physics.flu-dyn↗

arXiv2016

Experimental observation of 1/f noise in quasi-bidimensionnal turbulent flows

We report the experimental observation of $1/f^α$ noise in quasi-bidimensionnal turbulence of an electromagnetically forced flow. The large scale velocity $U_L$ exhibits this power-law spectrum with $α\simeq 0.7$ over a range of frequencies smaller than both the characteristic turn-over frequency and the damping rate of the flow. By studying the statistical properties of sojourn time in each polarity of $U_L$, we demonstrate that the $1/f^α$ noise is generated by a renewal process, defined by a two-state model given by the polarities of the large scale circulation. The statistical properties of this renewal process are shown to control the value of the exponent $α$.

physics.flu-dyn↗

arXiv2016

1/f noise in turbulent flows

We report the experimental observation of $1/f$ fluctuations in three different turbulent flow configurations: the large scale velocity driven by a two-dimensional turbulent flow, the magnetic field generated by a turbulent swirling flow of liquid sodium and the pressure fluctuations due to vorticity filaments in a swirling flow. For these three systems, $1/f$ noise is shown to result from the dynamics of coherent structures that display transitions between a small number of states. The interevent duration is distributed as a power-law. The exponent of this power-law and the nature of the dynamics (transition between symmetric states or asymmetric ones) select the exponent of the $1/f$ fluctuations.

physics.flu-dyn↗

arXiv2014

Decay rates of magnetic modes below the threshold of a turbulent dynamo

We measure the decay rates of magnetic field modes in a turbulent flow of liquid sodium below the dynamo threshold.We observe that turbulent fluctuations induce energy transfers between modes with different symmetries (dipolar and quadrupolar). Using symmetry properties, we show how to measure the decay rate of each mode without being restricted to the one with the smallest damping rate.We observe that the respective values of the decay rates of these modes depend on the shape of the propellers driving the flow. Dynamical regimes, including field reversals, are observed onlywhen the modes are both nearly marginal. This is in linewith a recently proposed model.

physics.flu-dyn↗

arXiv2014

Optimum reduction of the dynamo threshold by a ferromagnetic layer located in the flow

We consider a fluid dynamo model generated by the flow on both sides of a moving layer. The magnetic permeability of the layer is larger than that of the flow. We show that there exists an optimum value of magnetic permeability for which the critical magnetic Reynolds number for dynamo onset is smaller than for a nonmagnetic material and also smaller than for a layer of infinite magnetic permeability. We present a mechanism that provides an explanation for recent experimental results. A similar effect occurs when the electrical conductivity of the layer is large.

physics.flu-dyn↗

arXiv2012

Critical exponents in zero dimensions

In the vicinity of the onset of an instability, we investigate the effect of colored multiplicative noise on the scaling of the moments of the unstable mode amplitude. We introduce a family of zero dimensional models for which we can calculate the exact value of the critical exponents $β_m$ for all the moments. The results are obtained through asymptotic expansions that use the distance to onset as a small parameter. The examined family displays a variety of behaviors of the critical exponents that includes anomalous exponents: exponents that differ from the deterministic (mean-field) prediction, and multiscaling: non-linear dependence of the exponents on the order of the moment.

cond-mat.stat-mech↗

arXiv2011

Reversals of a large scale field generated over a turbulent background

We present a study of several systems in which a large scale field is generated over a turbulent background. These large scale fields usually break a symmetry of the forcing by selecting a direction. Under certain conditions, the large scale field displays reversals so that the symmetry of the forcing is recovered statistically. We present examples of such dynamics in the context of the dynamo instability, of two dimensional turbulent Kolmogorov flows and of turbulent Rayleigh-Bénard convection. In these systems reversals occur respectively for the dynamo magnetic field, for the large scale circulation generated by a periodic forcing in space and for the large scale roll generated by turbulent thermal convection. We compare the mechanisms involved and show that their properties depend on some symmetries of the system and on the way they are broken.

physics.flu-dyn↗

arXiv2009

From reversing to hemispherical dynamos

We show that hemispherical dynamos can result from weak equatorial symmetry breaking of the flow in the interior of planets and stars. Using a model of spherical dynamo, we observe that the interaction between a dipolar and a quadrupolar mode can localize the magnetic field in only one hemisphere when the equatorial symmetry is broken. This process is shown to be related to the one that is responsible for reversals of the magnetic field. These seemingly very different behaviors are thus understood in a unified framework.

astro-ph.EP↗