The fundamental solution of a turbulent kinetic theory

The fundamental solution of a Fokker-Planck type kinetic equation governing the probability density function of fluid elements in velocity space was obtained. The kinetic equation was treated as linear by assuming that the ensemble means appeared in the kinetic equation as known quantities with respect to the pdf (probability density function). By utilizing subsidiary transformations, the kinetic equation was transformed into a simpler diffusion type equation. Further integral transformations were performed on this diffusion type equation and the fundamental solution satisfying the instantaneous point source conditions in phase space was then established.