Formulation and Simulation of a Linear Dynamics Leading to a Loss of Regularity

This lecture explores the formulation and simulation of a linear dynamics model that leads to a loss of regularity in fluid systems. Begin with an overview of three-dimensional fluid turbulence phenomenology and the statistical behavior of Navier-Stokes equation solutions under smooth spatial forcing. Discover a proposed linear model capable of generating rough Hölderian-type velocity fields from smooth ingredients over infinite time. Examine the transport phenomenon occurring in Fourier space rather than physical space, which enables energy transfer (cascading) across different scales. Learn about a numerical scheme based on finite spectral volumes that provides a coherent representation of such dynamics. This presentation covers joint research work by Laurent Chevillard with G. Apolinario, G. Beck, C.-E. Bréhier, I. Gallagher, R. Grande, J.-C. Mourrat, and W. Ruffenach.