May 12, 2014 16:20 Journal of Turbulence rb14 Journal of Turbulence Vol. 00, No. 00, 2010, 1–20 RESEARCH ARTICLE A minimal flow unit for the study of turbulence with passive scalars Paolo Orlandi † , Sergio Pirozzoli †, Matteo Bernardini †, and George F. Carnevale ‡ † Dipartimento di Ingegneria Meccanica e Aerospaziale, Universit` a La Sapienza Via Eudossiana 16, I-00184, Roma ‡ Scripps Institution of Oceanography, University of California, San Diego La Jolla, USA (May 12, 2014) 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 is 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. 1. Introduction The complex physics of passive scalars advected by turbulent flows has been tra- ditionally studied by direct numerical simulations (DNS) of isotropic turbulence randomly forced at low wavenumbers. This setup allows one to a achieve a statis- tically stationary state in a few eddy turnover times, and consequently to collect large data sets to analyze the behavior of high-order statistics. It would be difficult to cite here all the papers describing forced isotropic turbulence with and without passive scalars. The review by Ishihara et al. [1] lists the relevant papers with- out passive scalars, while those with passive scalars are given by Donzis et al. [2] and Gotoh and Yeung [3]. Those studies have been important for understanding differences and similarities between velocity and passive scalar statistics, and in particular their spectra. However, it is not known to what extent the results are affected by the specific type of forcing. Furthermore, the evolution of the spectra, in particular, and their evolution towards power laws, is usually disregarded. A different approach consists in performing DNS of decaying turbulence starting by a flow with an assigned spectrum and random phases. These initial conditions are typically far from realistic and, in addition, do not permit the achievement of high values of Taylor based Reynolds numbers. In a paper devoted to understanding Email: orlandi@kolmogorov.ing.uniroma1.it ISSN: 1468-5248 (online only) c  2010 Taylor & Francis DOI: 10.1080/14685240YYxxxxxxx http://www.informaworld.com