Spectrum of Locally Isotropic Turbulence

Abstract

The concept of locally isotropic turbulence is used in Kolmogoroff's sense. Kolmogoroff's second similarity hypothesis is not used, but other hypotheses are suggested for the similarity of energy transfer in the energy spectrum of turbulence. The spectrum thus obtained is identical with the —5/3 power law in the nonviscous range but falls off rapidly in the viscous high-frequency end. The correlation coefficients agree with Kolmogoroff's predictions for both small r and for large r and give explicit results in the intermediate range. The only free constant in the present theory is R0, a certain Reynolds Number that corresponds to the smallest eddies. Extensive comparison with available energy spectrum and correlation measurements have been made.