Kinetic equation for Lagrange particles and turbulence of an incompressible fluid

A self-consistent equation for the two-point distribution function of the velocity and the pressure gradient is derived. A scaling analysis of the equation obtained is employed to determine the spectral properties of a turbulent flow; the role of the vorticity distribution in a turbulent flow (turbulence intermediacy) is considered. It is shown that the intermediacy is associated with the boundary conditions. The geometry of the intermediacy is determined. The vorticity distribution and, accordingly, the role of intermediacy are found to be quite different in flows with and without helicity. The flows with helicity are analyzed for different values of the dimensionless parameter χ=ν1/3G4/3/W, which characterizes the relation between the helicity of the fluid and the power supplied from an external source