A model for fully developed turbulence

Abstract

A model for stationary, fully developed turbulence is presented in which the turbulent spectral energy function is completely determined once the time scale for the energy fed into the eddy interaction is known. The form of the eddy correlation time scale determining the turbulent viscosity is suggested by the basic equation of the model itself, up to a dimensionless constant that is fixed by demanding that the coefficient of the spectrum in the Heisenberg-Kolmogoroff inertial range of wavenunmbers be the experimental value. The model makes quantitative predictions that are compared with data on turbulent convection; the k-epsilon and Smagorinsky relations; the spectral function, transfer term, and dissipation term; the skewness factor; the Kolmogoroff and Batchelor constants; and the inertial-conductive and inertial-convective ranges.