Generalized Langevin Equation for Two-Dimensional Inviscid Barotropic Vorticity

The spectrum form of the two-dimensional inviscid barotropic vorticity equation is reduced to the generalized Langevin equation. The eddy viscosity acting on the vorticity is also discussed. Under the terrestrial synoptic scale condition, the theory derives that the eddy viscosity coefficient is about ten orders of magnitude larger than the molecular viscosity coefficient of the air.