ON THE PRODUCTION OF DISSIPATION THROUGH THE INTERACTION OF FORCED OSCILLATING WAVES IN FLUID DYNAMICS

Abstract

This article is devoted to the study of some bidimensional fluid model with a source term implying oscillations. In this context, we can construct a family of exact solutions uεindexed by ε ∈ ]0, 1], defined on a strip [0, T] × ℝ2with [Formula: see text] fixed, and involving three types of scales: ε-2t for a boundary layer at time t = 0, ε-2x1for oscillations in the direction x1, and ε-1x2for a concentration near the position x2= 0. We show that the propagation and the interaction of these singularities produce a turbulent effect that manifests itself through the addition of some (unusual) diffusion when describing the underlying modulation equations.