# User:Eugene M. Izhikevich/Proposed/Turbulence: Two-Dimensional

Dr. Gregory Falkovich accepted the invitation on 13 October 2010

## Introduction

Fluids naturally tend to form layers. Flows in layers can be often considered two-dimensional. When the fluid velocity $$v$$ is in the plane, then the vorticity $$\omega=\nabla\times v$$ has only one component (perpendicular to the plane) i.e. can be considered a scalar. In an fluid (without friction), Kelvin theorem states that the vorticity of any fluid element is conserved. As a result, two-dimensional flows possess an infinity of local conservation laws, given by arbitrary functions of vorticity, in addition to the kinetic energy.

## Turbulence beyond fluids

Turbulence is a state of a system with many degrees of freedom deviated far from equilibrium. Such states exist not only in fluids.