Reversible Navier-Stokes equation on logarithmic lattices.

The three-dimensional reversible Navier-Stokes (RNS) equations are a modification of the dissipative Navier-Stokes (NS) equations, first introduced by Gallavotti [Phys. Lett. A 223, 91 (1996)0375-960110.

Scale dependence 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 deterministic 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.

Dynamical footprints of hurricanes in the tropical dynamics.

Hurricanes-and more broadly tropical cyclones-are high-impact weather phenomena whose adverse socio-economic and ecosystem impacts affect a considerable part of the global population. Despite our reasonably robust meteorological understanding of tropical cyclones, we still face outstanding challenges for their numerical simulations. Consequently, future changes in the frequency of occurrence and intensity of tropical cyclones are still debated.

Eulerian vs Lagrangian Irreversibility in an Experimental Turbulent Swirling Flow.

In a turbulent fluid, the time-reversal symmetry is explicitly broken by viscosity, and spontaneously broken in the inviscid limit. Recently, Drivas [J. Nonlinear Sci.

A Model of Interacting Navier-Stokes Singularities.

We introduce a model of interacting singularities of Navier-Stokes equations, named pinçons. They follow non-equilibrium dynamics, obtained by the condition that the velocity field around these singularities obeys locally Navier-Stokes equations. This model can be seen as a generalization of the vorton model of Novikov that was derived for the Euler equations.

A correspondence between the multifractal model of turbulence and the Navier-Stokes equations.

The multifractal model of turbulence (MFM) and the three-dimensional Navier-Stokes equations are blended together by applying the probabilistic scaling arguments of the former to a hierarchy of weak solutions of the latter. This process imposes a lower bound on both the multifractal spectrum [Formula: see text], which appears naturally in the Large Deviation formulation of the MFM, and on [Formula: see text] the standard scaling parameter. These bounds respectively take the form: (i) [Formula: see text], which is consistent with Kolmogorov's four-fifths law ; and (ii) [Formula: see text].

Characterizing most irregular small-scale structures in turbulence using local Hölder exponents.

Two scalar fields characterizing respectively pseudo-Hölder exponents and local energy transfers are used to capture the topology and the dynamics of the velocity fields in areas of lesser regularity. The present analysis is conducted using velocity fields from two direct numerical simulations of the Navier-Stokes equations in a triply periodic domain. A typical irregular structure is obtained by averaging over the 213 most irregular events.

A Maximum Entropy Production Hypothesis for Time Varying Climate Problems: Illustration on a Conceptual Model for the Seasonal Cycle.

We investigated the applicability of the maximum entropy production hypothesis to time-varying problems, in particular, the seasonal cycle using a conceptual model. Contrarily to existing models, only the advective part of the energy fluxes is optimized, while conductive energy fluxes that store energy in the ground are represented by a diffusive law. We observed that this distinction between energy fluxes allows for a more realistic response of the system.

Phase transition in time-reversible Navier-Stokes equations.

We present a comprehensive study of the statistical features of a three-dimensional (3D) time-reversible truncated Navier-Stokes (RNS) system, wherein the standard viscosity ν is replaced by a fluctuating thermostat that dynamically compensates for fluctuations in the total energy. We analyze the statistical features of the RNS steady states in terms of a non-negative dimensionless control parameter R_{r}, which quantifies the balance between the fluctuations of kinetic energy at the forcing length scale ℓ_{f} and the total energy E_{0}. For small R_{r}, the RNS equations are found to produce "warm" stationary statistics, e.

Local estimates of Hölder exponents in turbulent vector fields.

It is still not known whether solutions to the Navier-Stokes equation can develop singularities from regular initial conditions. In particular, a classical and unsolved problem is to prove that the velocity field is Hölder continuous with some exponent h<1 (i.e.

About Universality and Thermodynamics of Turbulence.

This paper investigates the universality of the Eulerian velocity structure functions using velocity fields obtained from the stereoscopic particle image velocimetry (SPIV) technique in experiments and direct numerical simulations (DNS) of the Navier-Stokes equations. It shows that the numerical and experimental velocity structure functions up to order 9 follow a log-universality (Castaing et al. 1993); this leads to a collapse on a universal curve, when units including a logarithmic dependence on the Reynolds number are used.

Dissipation, intermittency, and singularities in incompressible turbulent flows.

We examine the connection between the singularities or quasisingularities in the solutions of the incompressible Navier-Stokes equation (INSE) and the local energy transfer and dissipation, in order to explore in detail how the former contributes to the phenomenon of intermittency. We do so by analyzing the velocity fields (a) measured in the experiments on the turbulent von Kármán swirling flow at high Reynolds numbers and (b) obtained from the direct numerical simulations of the INSE at a moderate resolution. To compute the local interscale energy transfer and viscous dissipation in experimental and supporting numerical data, we use the weak solution formulation generalization of the Kármán-Howarth-Monin equation.

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 quasistationary states and transition rates among them, the effective dimensions, and the continuity of the first Lyapunov exponents.

Experimental characterization of extreme events of inertial dissipation in a turbulent swirling flow.

The three-dimensional incompressible Navier-Stokes equations, which describe the motion of many fluids, are the cornerstones of many physical and engineering sciences. However, it is still unclear whether they are mathematically well posed, that is, whether their solutions remain regular over time or develop singularities. Even though it was shown that singularities, if exist, could only be rare events, they may induce additional energy dissipation by inertial means.

Role of boundary conditions in helicoidal flow collimation: Consequences for the von Kármán sodium dynamo experiment.

We present hydrodynamic and magnetohydrodynamic (MHD) simulations of liquid sodium flow with the PLUTO compressible MHD code to investigate influence of magnetic boundary conditions on the collimation of helicoidal motions. We use a simplified cartesian geometry to represent the flow dynamics in the vicinity of one cavity of a multiblades impeller inspired by those used in the Von-Kármán-sodium (VKS) experiment. We show that the impinging of the large-scale flow upon the impeller generates a coherent helicoidal vortex inside the blades, located at a distance from the upstream blade piloted by the incident angle of the flow.

Probing turbulence intermittency via autoregressive moving-average models.

We suggest an approach to probing intermittency corrections to the Kolmogorov law in turbulent flows based on the autoregressive moving-average modeling of turbulent time series. We introduce an index Υ that measures the distance from a Kolmogorov-Obukhov model in the autoregressive moving-average model 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 traditional intermittency corrections computed from structure functions.

Superfluid high REynolds von Kármán experiment.

The Superfluid High REynolds von Kármán experiment facility exploits the capacities of a high cooling power refrigerator (400 W at 1.8 K) for a large dimension von Kármán flow (inner diameter 0.78 m), which can work with gaseous or subcooled liquid (He-I or He-II) from room temperature down to 1.

Dynamo efficiency controlled by hydrodynamic bistability.

Hydrodynamic and magnetic behaviors in a modified experimental setup of the von Kármán sodium flow-where one disk has been replaced by a propeller-are investigated. When the rotation frequencies of the disk and the propeller are different, we show that the fully turbulent hydrodynamic flow undergoes a global bifurcation between two configurations. The bistability of these flow configurations is associated with the dynamics of the central shear layer.

Cross-helicity in rotating homogeneous shear-stratified turbulence.

We consider homogeneous shear-stratified turbulence in a rotating frame, that exhibits complex nonlinear dynamics. Since the analysis of relative orientation between coupled fluctuating fields helps us to understand turbulence dynamics, we focus on the alignment properties of both the velocity and gravity fields with the potential vorticity gradient. With the help of statistical mechanics, we define a vector field which plays a role in the analogous so-called cross-helicity in magnetohydrodynamics.

Evidence for forcing-dependent steady states in a turbulent swirling flow.

We study the influence on steady turbulent states of the forcing in a von Karman flow, at constant impeller speed, or at constant torque. We find that the different forcing conditions change the nature of the stability of the steady states and reveal dynamical regimes that bear similarities to low-dimensional systems. We suggest that this forcing dependence may be applicable to other turbulent systems.

Dynamo threshold detection in the von Kármán sodium experiment.

Predicting dynamo self-generation in liquid metal experiments has been an ongoing question for many years. In contrast to simple dynamical systems for which reliable techniques have been developed, the ability to predict the dynamo capacity of a flow and the estimate of the corresponding critical value of the magnetic Reynolds number (the control parameter of the instability) has been elusive, partly due to the high level of turbulent fluctuations of flows in such experiments (with kinetic Reynolds numbers in excess of 10(6)). We address these issues here, using the von Kármán sodium experiment and studying its response to an externally applied magnetic field.

Kinematic α tensors and dynamo mechanisms in a von Kármán swirling flow.

We provide experimental and numerical evidence of in-blades vortices in the von Kármán swirling flow. We estimate the associated kinematic α-effect tensor and show that it is compatible with recent models of the von Kármán sodium (VKS) dynamo. We further show that depending on the relative frequency of the two impellers, the dominant dynamo mechanism may switch from α2 to α - Ω dynamo.

Phase transitions and marginal ensemble equivalence for freely evolving flows on a rotating sphere.

The large-scale circulation of planetary atmospheres such as that of the Earth is traditionally thought of in a dynamical framework. Here we apply the statistical mechanics theory of turbulent flows to a simplified model of the global atmosphere, the quasigeostrophic model, leading to nontrivial equilibria. Depending on a few global parameters, the structure of the flow may be either a solid-body rotation (zonal flow) or a dipole.