Statistical Theory of Homogeneous Isotropic Turbulence for Incompressible Fluids

Abstract

In the present paper,based upon the statistical vorticity structure theory of homogeneous isotropic turbulence,it is proposed that homogeneous isotropic turbulence has the property of similarity in the period of decay,and the similarity-length is determined by the magnitude of velocity fluctuation and the generalized Taylor's microscale of turbulence which is closely related to the characteristic length of the vortex Introducing the condition of pseudo-similarity,this paper starts from the Navier-Stokes equations of motion to study homogeneous isotropic turbulence.In the calculations,the velocity fluctuation is assumed to be periodic in space with the period being proportional to the generalized Taylor's microscale of turbulence The calculations in the physical space are transformed to that in the spectral space by expanding the velocity fluctuation and other physical quantities into Fourier series.Utilizing the fast Fourier transform,the forward difference formulae and the leap-frog difference foumulae,we study the homogeneous isotropic turbulence in the whole period of decay for the different grid Reynolds numbers.Agreements between the calculations and the experimental data are satisfactory.