The universal equilibrium spectra of turbulent velocity and scalar fields

Abstract

Kolmogoroff's (1941) theory of local isotropy and universal similarity predicts that all turbulent velocity spectra are reducible to a single universal curve for the highest wave-numbers and that under certain conditions dimensional analysis may be used to predict spectral shapes. Identical arguments predict that the fine structure of conserved dynamically passive scalar fields mixed by turbulence will also be universally similar.A single-electrode conductivity probe in a bridge circuit was used to measure the spectra and decay of a random homogeneous field of concentration and temperature behind a grid, and a Lintronic constant-temperature hot-film anemometer was used to measure the decay of velocity field. These experimental measurements of absolute turbulent velocity, temperature, and concentration spectra in salt water are here compared with the general predictions of universal similarity and local isotropy theories, as well as a prediction by Batchelor (1959) of the exact large wave-number spectral form for scalar mixing at high Schmidt number (v[Gt ]D. The spectral shapes are found to have the predicted similarity forms, and the data are consistent with Batchelor's predicted spectrum of the scalar field.