A minimal flow unit for the study of turbulence with passive scalars

Abstract

The concept of a minimal flow unit (MFU) for the study of the basic physics of turbulent flows is introduced. The MFU is an initial vorticity configuration that consists of a few simple well-defined large-scale vortex structures. The form and position of these structures are chosen so that their interaction produces turbulence capturing many of the essential characteristics of isotropic homogeneous turbulence produced from random-phase initial conditions or that produced by continual random-phase forcing. The advantage of using the MFU is that the evolution of the vortex structures can be followed more clearly and the relationship between the evolving vortex structures and the various ranges in the energy spectrum can be more clearly defined. The addition of passive scalar fields to the MFU permits an investigation of passive scalar mixing that is relevant to the study of combustion. With a particular choice of the MFU, one that produces a trend to a finite-time singularity in the vorticity field, it is demonstrated that passive scalar distributed in the original large-scale vortices will develop intense gradients in the region where the vorticity is tending toward a singularity. In viscous flow, the evolution of the MFU clearly shows how the volume of the regions where originally well-separated passive scalars come into contact increases with increasing Reynolds number.