Solution for the Inertial Energy Spectrum of Isotropic Turbulence

Abstract

A dynamic equation for quasi‐stationary, inertially dominated, isotropic turbulence is formulated on the basis of a modified Obukhoff transfer term. By means of an elementary transformation, a self‐similar solution for the energy spectrum is obtained. The closed‐form expression for an inertial range in the quasi‐equilibrium regime obeys previously derived functional laws for large and small wavenumbers. Matching the analytical result with an experimentally determined coefficient in the large wavenumber limit gives consistent scaling of terms over the energy‐containing eddy range of the spectrum.