Local estimates of Hölder exponents in turbulent vector fields

Nguyen, Florian; Laval, Jean-Philippe; Kestener, Pierre; Cheskidov, Alexey; Shvydkoy, Roman; Dubrulle, Bérengère

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1103/PhysRevE.99.053114

Title :

Local estimates of Hölder exponents in turbulent vector fields

Author(s) :

Nguyen, Florian [Auteur]
Laboratoire de Mécanique des Fluides de Lille - Kampé de Fériet [LMFL]
Laval, Jean-Philippe [Auteur]

Laboratoire de Mécanique des Fluides de Lille - Kampé de Fériet [LMFL]
Kestener, Pierre [Auteur]
Maison de la Simulation [MDLS]
Cheskidov, Alexey [Auteur]
University of Illinois [Chicago] [UIC]
Shvydkoy, Roman [Auteur]
University of Illinois [Chicago] [UIC]
Dubrulle, Bérengère [Auteur]
Service de physique de l'état condensé [SPEC - UMR3680]

Journal title :

Physical Review E

Publisher :

American Physical Society (APS)

Publication date :

2019-05-21

ISSN :

2470-0045

HAL domain(s) :

Physique [physics]/Physique [physics]/Dynamique des Fluides [physics.flu-dyn]

English abstract : [en]

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 ...
Show more >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. not necessarily differentiable) at small scales. Different methods have already been proposed to explore the regularity properties of the velocity field, and the estimate of its Hölder exponent h. A first method is to detect of potential singularities via extrema of an ”inertial” dissipation D ∗ = lim ` → 0 D I ` that is independent on viscosity [1]. Another possibility is to use the concept of multifractal analysis that provides fractal dimensions of the subspace of exponents h. However, the multifractal analysis is a global statistical method that only provides a globalinformation about local Hölder exponents, via their probability of occurrence. In order to explore the local regularity properties of a velocity field, we have developed a local statistical analysis, that estimates locally the Hölder continuity. We have compared outcomes of our analysis, with results using the inertial energy dissipation DI`. We observe that the dissipation term indeed gets bigger for velocity fields that are less regular according to our estimates. The exact spatial distribution of the local HÖlder exponents however shows non trivial behavior and does not exactly match the distribution of the inertial dissipation.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Etude expérimentale des structures dissipatives en turbulence

Collections :