An exact representation of the space-time characteristic functional of turbulent Navier-Stokes flows with prescribed random initial states and driving forces

Abstract

By adopting a formal operator viewpoint, the space-time characteristic functional associated with Navier-Stokes turbulence is expressed in terms of a linear operator acting on the space of functionals. Obtained by a simple similarity transformation of the local translation operator generated by the nonlinear terms in the Navier-Stokes equation, this operator is unitary with respect to the formal scalar product of functionals. The equivalence of this operator representation to the functional integral representation of Rosen is shown and, for Gaussian initial velocity and external force fields, some consequences of this representation are presented.