Isotropic Turbulence and Inertial-Range Structure

The abridged Lagrangian-History Direct Interaction closure approximation is interpreted physically and used to analyze energy transfer, effective eddy viscosities, and Lagrangian spacetime statistics in stationary and decaying isotropic turbulence. The results are then specialized to the inertial range. Numerical values are predicted for the Kolmogorov constant, the asymptotic eddy viscosities due to inertial-range wavenumbers, and the dimensionless constant in Inoue's formula for the mean-square change of Lagrangian velocity with time. Computed curves are presented for the localness of energy transfer, for Lagrangian spacetime structure functions, and for Lagrangian spacetime acceleration-acceleration and velocity-acceleration covariances. The Kolmogorov dissipation spectrum is computed, and the predicted spectra for the inertial and dissipation ranges are compared with experiment.