On modal time correlations of turbulent velocity and scalar fields

Abstract

We consider Eulerian two-point, two-time correlations of a turbulent velocity field and those of a passive scalar mixed by a turbulent velocity field. Integral expressions are derived for the modal time-correlation functions of the velocity and scalar fields using the stretched-spiral vortex model. These expressions are evaluated using asymptotic methods for high wavenumber and, alternatively, using numerical integration. If the motion of the centres of the vortex structures is neglected, then an inertial time scaling (εk ²)^−1/3, where ε is the energy dissipation rate and k the wavenumber, is found to collapse the velocity and scalar modal time-correlation functions to universal forms. Allowing the centres of the vortex structures to move introduces a sweeping time scale, (uk)⁻¹, where u is the rms velocity of the centres of the vortex structures. The sweeping time scale dominates the inertial time scale for sufficiently large wavenumbers. Results are also reported for a direct numerical simulation of passive scalar mixing by a turbulent velocity field at a Taylor Reynolds number of 265. The velocity and scalar modal time-correlation functions were calculated in the simulation. They coincide for large enough wavenumbers and are found to collapse to universal forms when a sweeping time scale is used.