The Dissipation Properties of Transport Noise

Abstract

The aim of this work is to present, in a compact way, the latest results about the dissipation properties of transport noise in fluid mechanics. Starting from the reasons why transport noise is natural in a passive scalar equation for the heat diffusion and transport, several results about enhanced dissipation due to the noise are presented. Rigorous statements are matched with numerical experiments in order to understand that the sufficient conditions stated are not yet optimal but give a first useful indication.