An Exact Gaussian Solution for Two-Dimensional Incompressible Inviscid Turbulent Flow

An exact Gaussian solution for two-dimensional incompressible inviscid turbulence is obtained by using the Wiener-Hermite expansion with the time-dependent ideal random function. The one-time characteristic functional corresponding to this solution is found to agree with the one obtained by Cook and Taylor, but the present method gives more information about the time dependence of the ideal random function, which is useful for dealing with the many-time correlation and extending to the viscous turbulence.