Journal of Statistical Physics

, Volume 65, Issue 1, pp 33-52

First online:

Stationary turbulent closure via the Hopf functional equation

  • Hubert H. ShenAffiliated withCenter for Turbulence Research, NASA-Ames/Stanford University
  • , Alan A. WrayAffiliated withNASA-Ames Research Center

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Exact closed-form solutions are exhibited for the Hopf equation for stationary incompressible 3D Navier-Stokes flow, for the cases of homogeneous forced flow (including a solution with depleted nonlinearity) and inhomogeneous flow with arbitrary boundary conditions. This provides an exact method for computing two- and higher-point moments, given the mean flow.

Key words

Navier-Stokes turbulence closure generating functional Hopf equation