7 papers
Spontaneous stochasticity and anomalous dissipation in collapsing wave turbulence
Wandrille Ruffenach
We study a focusing Majda--McLaughlin--Tabak type equation undergoing finite-time wave collapse. This singularity terminates the classical smooth solution and opens a post-blowup r…
A Measure-Theoretic Approach to Spontaneous Stochasticity
Wandrille Ruffenach, Eric Simonnet, Nicolas Valade
Spontaneous stochasticity (SpSt), originating in Richardson's picture of turbulent dispersion and Lorenz's Eulerian view of finite-time loss of predictability, was later formulated…
The spatio-temporal statistical structure of the turbulent dissipation field and its stochastic representation as a Gaussian Multiplicative Chaos
Wandrille Ruffenach, Laurent Chevillard
The present article concerns the stochastic modeling of the turbulent dissipation field and in particular its temporal evolution. To do so, we will be calling for a random distribu…
Numerical study of probabilistic well-posedness of one dimensional fractional nonlinear wave equations
Wandrille Ruffenach, Nikolay Tzvetkov
The three dimensional cubic defocusing nonlinear wave equation is known to be ill-posed for general low regularity initial data. However, well-posedness can be recovered globally i…
A spatio-temporal random synthetic turbulent velocity field: The underlying Gaussian structure
Matthieu Chatelain, Júlia Domingues Lemos, Wandrille Ruffenach +5
We develop, simulate and extend an initial proposition by Chaves et al. concerning a random incompressible vector field able to reproduce key ingredients of three-dimensional turbu…
Spontaneous stochasticity in the Armstrong-Vicol passive scalar
Wandrille Ruffenach, Eric Simonnet, Nicolas Valade
Spontaneous stochasticity refers to the emergence of intrinsic randomness in deterministic systems under singular limits, a phenomenon conjectured to be fundamental in turbulence.…