Quasilinear theory of the 2D Euler equation

We develop a quasilinear theory of the 2D Euler equation and derive an inte grodifferential equation for the evolution of the coarse-grained vorticity <(omega)over bar>(r, t). This equation respects all of the invariance prope rties of the Euler equation and conserves angular momentum in a circular do main and linens impulse in a channel. We show under which hypothesis we can derive an H theorem for the Fermi-Dirac entropy and make the connection wi th statistical theories of 2D turbulence.