Abstract
A simple two-point closure scheme for homogeneous axisymmetric turbulence is developed. For the isotropic case it is essentially an eddy-viscosity assumption in real space for the Kármán-Howarth equation. The eddy-viscosity function for large internal Reynolds numbers is derived from Kolmogoroff's 1941 theory. For moderate Reynold's numbers of order 102, approximately the same expression for the eddy-viscosity function is determined from experimental data. The resulting closed equation for the double-correlation function is solved numerically for both large and moderate Reynolds numbers, and the results are compared with experimental data. Self-similar solutions of the basic equation predict turbulent energy decay inversely proportional to time. It is shown that the departure from this ‘initial-period decay law’ observed in laboratory data is due to the behaviour of grid-produced correlation functions for large separation distances.
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