User:Eugene M. Izhikevich/Proposed/Turbulence: Two-Dimensional
Dr. Gregory Falkovich accepted the invitation on 13 October 2010
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.