arXiv subjects

Francois Daviaud

Publications and source records attributed to Francois Daviaud.

13 recordsLinked to original sources

arXiv2022

A novel concept of fractal dimension in deterministic and stochastic Lorenz-63 systems

Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively by studying the properties of the underlying attractor, the compact object asymptotically hosting the trajectories of the system with their invariant density in the phase-space. This multi-scale nature of natural systems makes it practically impossible to get a clear picture of the attracting set as it spans over a wide range of spatial scales and may even change in time due to non-stationary forcing. Here we combine an adaptive decomposition method with extreme value theory to study the properties of the instantaneous scale-dependent dimension, which has been recently introduced to characterize such temporal and spatial scale-dependent attractors in turbulence and astrophysics. To provide a quantitative analysis of the properties of this metric, we test it on the well-known low-dimensional deterministic Lorenz-63 system perturbed with additive or multiplicative noise. We demonstrate that the properties of the invariant set depend on the scale we are focusing on and that the scale-dependent dimensions can discriminate between additive and multiplicative noise, despite the fact that the two cases exhibit very similar stochastic attractors at large scales. The proposed formalism can be generally helpful to investigate the role of multi-scale fluctuations within complex systems, allowing us to deal with the problem of characterizing the role of stochastic fluctuations across a wide range of physical systems.

nlin.CD↗

arXiv2021

Chameleon attractors in a turbulent flow

Turbulent flows present rich dynamics originating from non-trivial energy fluxes across scales, non-stationary forcings and geometrical constraints. This complexity manifests in non-hyperbolic chaos, randomness, state-dependent persistence and unpredictability. All these features have prevented a full characterization of the underlying turbulent (stochastic) attractor, which will be the key object to unpin this complexity. Here we propose a novel formalism to trace the evolution of the structural characteristics of phase-space trajectories across scales, providing a full characterization of the attractor. We demonstrate that the properties of the dynamically invariant objects depend on the scale we are focusing on. In the case of laboratory experiments on fluids we observe the emergence of an intrinsic timescale, solely determined by nonlinear interactions, controlling the geometrical and topological properties of phase-space trajectories. Given the changing nature of such attractors in time and scales we term them chameleon attractors.

nlin.CD↗

arXiv2019

Universality and Thermodynamics of Turbulence

We investigate universality of the Eulerian velocity structure functions using velocity fields obtained from the stereoscopic particle image velocimetry (SPIV) technique in experiments and the direct numerical simulations (DNS) of the Navier-Stokes equations. We show that the numerical and experimental velocity structure functions up to order 9 follow a log-universality; we find that they collapse on a universal curve, if we use units that include logarithmic dependence on the Reynolds number. We then investigate the meaning and consequences of such log-universality, and show that it is connected with the properties of a "multifractal free energy", based on an analogy between multifractal and themodynamics. We show that in such a framework, the existence of a fluctuating dissipation scale is associated with a phase transition describing the relaminarisation of rough velocity fields with different Holder exponents. Such a phase transition has been already observed using the Lagrangian velocity structure functions, but was so far believed to be out of reach for the Eulerian data.

physics.flu-dyn↗

arXiv2016

Stochastic chaos in a turbulent swirling flow

We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can first reconstruct the associated turbulent attractor and then follow its route towards chaos. We further show that the experimental attractor can be modeled by stochastic Duffing equations, that match the quantitative properties of the experimental flow, namely the number of quasi-stationary states and transition rates among them, the effective dimensions, and the continuity of the first Lyapunov exponents. Such properties can neither be recovered using deterministic models nor using stochastic differential equations based on effective potentials obtained by inverting the probability distributions of the experimental global observables. Our findings open the way to low dimensional modeling of systems featuring a large number of degrees of freedom and multiple quasi-stationary states.

physics.flu-dyn↗

arXiv2014

Probing turbulence intermittency via Auto-Regressive Moving-Average models

We suggest a new approach to probing intermittency corrections to the Kolmogorov law in turbulent flows based on the Auto-Regressive Moving-Average modeling of turbulent time series. We introduce a new index $Υ$ that measures the distance from a Kolmogorov-Obukhov model in the Auto-Regressive Moving-Average models space. Applying our analysis to Particle Image Velocimetry and Laser Doppler Velocimetry measurements in a von Kármán swirling flow, we show that $Υ$ is proportional to the traditional intermittency correction computed from the structure function. Therefore it provides the same information, using much shorter time series. We conclude that $Υ$ is a suitable index to reconstruct the spatial intermittency of the dissipation in both numerical and experimental turbulent fields.

physics.flu-dyn↗

arXiv2009

French Roadmap for complex Systems 2008-2009

This second issue of the French Complex Systems Roadmap is the outcome of the Entretiens de Cargese 2008, an interdisciplinary brainstorming session organized over one week in 2008, jointly by RNSC, ISC-PIF and IXXI. It capitalizes on the first roadmap and gathers contributions of more than 70 scientists from major French institutions. The aim of this roadmap is to foster the coordination of the complex systems community on focused topics and questions, as well as to present contributions and challenges in the complex systems sciences and complexity science to the public, political and industrial spheres.

nlin.AO↗

arXiv2008

Characterization of turbulence in inhomogeneous anisotropic flows

We introduce a global quantity $δ$ that characterizes turbulent fluctuations in inhomogeneous anisotropic flows. This time-dependent quantity is based on spatial averages of global velocity fields rather than classical temporal averages of local velocities. $δ(t)$ provides a useful quantitative characterization of any turbulent flow through generally only two parameters, its time average $\bar δ$ and its variance $δ_2$. Properties of $\bar δ$ and $δ_2$ are experimentally studied in the typical case of the von Kármán flow and used to characterize the scale by scale energy budget as a function of the forcing mode as well as the transition between two flow topologies.

physics.flu-dyn↗

arXiv2008

Supercritical transition to turbulence in an inertially-driven von Karman closed flow

We study the transition from laminar flow to fully developed turbulence for an inertially-driven von Karman flow between two counter-rotating large impellers fitted with curved blades over a wide range of Reynolds number (100 - 1 000 000). The transition is driven by the destabilisation of the azimuthal shear-layer, i.e., Kelvin-Helmholtz instability which exhibits travelling/drifting waves, modulated travelling waves and chaos below the emergence of a turbulent spectrum. A local quantity -the energy of the velocity fluctuations at a given point- and a global quantity -the applied torque- are used to monitor the dynamics. The local quantity defines a critical Reynolds number Rec for the onset of time-dependence in the flow, and an upper threshold/crossover Ret for the saturation of the energy cascade. The dimensionless drag coefficient, i.e., the turbulent dissipation, reaches a plateau above this finite Ret, as expected for a "Kolmogorov"-like turbulence for Re -> infinity. Our observations suggest that the transition to turbulence in this closed flow is globally supercritical: the energy of the velocity fluctuations can be considered as an order parameter characterizing the dynamics from the first laminar time-dependence up to the fully developed turbulence. Spectral analysis in temporal domain moreover reveals that almost all of the fluctuations energy is stored in time-scales one or two orders of magnitude slower than the time-scale based on impeller frequency.

physics.flu-dyn↗

arXiv2004

Multistability and memory effect in a highly turbulent flow: experimental evidence for a global bifurcation

We report an experimental evidence of a global bifurcation on a highly turbulent von Karman flow. The mean flow presents multiple solutions: the canonical symmetric solution becomes marginally unstable towards a flow which breaks the basic symmetry of the driving apparatus even at very large Reynolds number. The global bifurcation between these states is highly subcritical and the system thus keeps a memory of its history. The transition recalls low-dimension dynamical systems transitions and exhibits a very peculiar statistics. We discuss the role of turbulence in two ways: the multiplicity of hydrodynamical solutions and the effect of fluctuations on the nature of transitions.

physics.flu-dyn↗

arXiv2002

Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. I: General presentation and periodic solutions

We present experimental results on hydrothermal traveling-waves dynamics in long and narrow 1D channels. The onset of primary traveling-wave patterns is briefly presented for different fluid heights and for annular or bounded channels, i.e., within periodic or non-periodic boundary conditions. For periodic boundary conditions, by increasing the control parameter or changing the discrete mean-wavenumber of the waves, we produce modulated waves patterns. These patterns range from stable periodic phase-solutions, due to supercritical Eckhaus instability, to spatio-temporal defect-chaos involving traveling holes and/or counter-propagating-waves competition, i.e., traveling sources and sinks. The transition from non-linearly saturated Eckhaus modulations to transient pattern-breaks by traveling holes and spatio-temporal defects is documented. Our observations are presented in the framework of coupled complex Ginzburg-Landau equations with additional fourth and fifth order terms which account for the reflection symmetry breaking at high wave-amplitude far from onset. The second part of this paper (nlin.PS/0208030) extends this study to spatially non-periodic patterns observed in both annular and bounded channel.

nlin.PS↗

arXiv2002

Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II: Convective/absolute transitions

We present experimental results on hydrothermal waves in long and narrow 1D channels. In a bounded channel, we describe the primary and secondary instabilities leading to waves and modulated waves in terms of convective/absolute transitions. Because of on the combined effect of finite group velocity and of the presence of boundaries, the wave-patterns are non-uniform in space. We also investigate non-uniform wave-patterns observed in an annular channel in the presence of sources and sinks of hydrothermal waves. We connect our observations with the complex Ginzburg-Landau model equation in the very same way as in the first part of the paper (nlin.PS/0208029).

nlin.PS↗

arXiv2002

Convective and absolute Eckhaus instability leading to modulated waves in a finite box

We report experimental study of the secondary modulational instability of a one-dimensional non-linear traveling wave in a long bounded channel. Two qualitatively different instability regimes involving fronts of spatio-temporal defects are linked to the convective and absolute nature of the instability. Both transitions appear to be subcritical. The spatio-temporal defects control the global mode structure.

nlin.PS↗

arXiv1999

Bekki-Nozaki Amplitude Holes in Hydrothermal Nonlinear Waves

We present and analyze experimental results on the dynamics of hydrothermal waves occuring in a laterally-heated fluid layer. We argue that the large-scale modulations of the waves are governed by a one-dimensional complex Ginzburg-Landau equation (CGLE). We determine quantitatively all the coefficients of this amplitude equation using the localized amplitude holes observed in the experiment, which we show to be well described as Bekki-Nozaki hole solutions of the CGLE.

patt-sol↗