On taylor correlation functions in isotropic turbulent flows

Abstract

A turbulent flow can be characterized by Taylor correlation functions which are obtained empirically, understood by statistical mechanics and regarded as universal. Here, we show that Taylor correlations are analytically derived by hypothesizing turbulence as a phenomenon of superfluids at resonance. Leveraging from a recent study on heat transfer at the speed of sound, we derived and fitted the longitudinal and lateral turbulent velocities in an isotropic, turbulent flow. The concept of the boundary of the second law helps to specify the integration constants in the solution. From the velocity profiles, Taylor’s correlation functions are analytically determined. From the linearity of the eigenfunction, we introduce amplitude and frequency factors. These factors are curve-fitted with two experimental dataset. Additional experimental datasets in the public domain are compared to the correlations, which shows that the theory agrees with experiments very well in isotropic flows. The analytical correlation functions help to elucidate observations that experiments and statistical mechanics have challenges to explain.