Two-dimensional turbulence

Abstract

In the past several studies on 2D turbulence were performed to understand this ideal condition that is interesting from the fundamental point of view. Since any basic study should also be linked to real motivations; 2D turbulence is a fundamental topic to understand geophysical flows. The realization in the laboratory of a perfect 2D flow is very difficult. Attempts were done by moving an array of cylinders in a stratified fluid. The 3D wakes behind the cylinders in a short time generated a bunch of 2D vortices that behaved as 2D turbulence (Narimousa et al. 1991). In fact, in presence of a strong stratification the fluctuations in the vertical direction are dumped and the flow can approximately be considered two-dimensional. Rotation plays a similar effect; as a consequence in several laboratories rotating tables are used to study the vortex dynamics in 2D (Hopfmger et al. (1982)). The difference between the two set-ups is that, in rotating tanks the vortices are spanning the full depth, but, at high rotation rates, the Eckman layers on the bottom wall produce a dissipation that can be greater than the viscous dissipation. However the dissipation it is much less than that acting on the pancake vortices forming in a stratified fluid. Soap films are a further method to achieve experimental conditions close to that of 2D turbulence; in this case the imperfect realization of a 2D flow is related to a slight compressibility (Couder & Basdevant (1986)).