Quasilinear theory of the 2D euler equation
We develop a quasilinear theory of the 2D Euler equation and derive an integrodifferential equation for the evolution of the coarse-grained vorticity omega;(r,t). This equation respects all of the invariance properties of the Euler equation and conserves angular momentum in a circular domain and linear impulse in a channel. We show under which hypothesis we can derive an H theorem for the Fermi-Dirac entropy and make the connection with statistical theories of 2D turbulence.
Chavanis
PH
Laboratoire de Physique Quantique, Universite Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France.