Mixing in modulated turbulence. Analytical results

TL;DR

This paper provides an analytical study of how periodic modulation in turbulence affects scalar mixing rates, revealing that modulation can either enhance or diminish mixing depending on the forcing frequency.

Contribution

It introduces a simple turbulence model to analytically explain the impact of forcing modulation on scalar mixing rates in turbulent flows.

Findings

Large amplitude modulation enhances energy transfer but reduces scalar transfer.

Modulation negatively influences mixing when applied to random stirring protocols.

Asymptotic behavior of scalar response is derived for low and high forcing frequencies.

Abstract

Recent numerical results show that if a scalar is mixed by periodically forced turbulence, the average mixing rate is directly affected for forcing frequencies small compared to the integral turbulence frequency. We elucidate this by an analytical study using simple turbulence models for spectral transfer. Adding a large amplitude modulation to the forcing of the velocity field enhances the energy transfer and simultaneously diminishes the scalar transfer. Adding a modulation to a random stirring protocol will thus negatively influence the mixing rate. We further derive the asymptotic behaviour of the response of the passive scalar quantities in the same flow for low and high forcing frequencies.