Characteristic Functional for Homogeneous and Isotropic Turbulence

Classical theory for two-point correlations in homogeneous and isotropic flows is covered, and the von Karman–Howarth PDE for the two-point correlation is derived. The Hopf FDE w.r.t. a solenoidal Schauder basis for homogeneous and isotropic turbulence is established. A formal solution for the two-point correlation is obtained in terms of the second derivative of the characteristic functional at the origin of its domain of definition. Two-point correlations, homogeneous and isotropic flows, von Karman–Howarth PDE, Hopf FDE for homogeneous and isotropic turbulence, formal solution.