Mixing in manipulated turbulence

Abstract

A numerical investigation of turbulent flow, subject to deterministic broadband forcing, is presented. Explicit forcing procedures are included that represent the simultaneous agitation of a wide spectrum of length scales, including both large scales and a band of much smaller scales. Such forcing induces a multiscale modulation of turbulent flow that is motivated by flow through complex objects and along irregular boundaries. Two types of forcing procedures are investigated; with reference to the collection of forced modes these procedures are classified as ‘constant energy’ or ‘constant-energy input rate’. It is found that a considerable modulation of the traditional energy cascading can be introduced with a specific forcing strategy. In spectral space, forcing yields strongly localized deviations from the common Kolmogorov scaling law, directly associated with the explicitly forced scales. In addition, the accumulated effect of forcing induces a significant non-local alteration of the kinetic energy including the spectrum for the large scales. Consequently, a manipulation of turbulent flow can be achieved over an extended range, well beyond the directly forced scales. Compared to flow forced in the large scales only, the energy in broadband forced turbulence is found to be transferred more effectively to smaller scales. The turbulent mixing of a passive scalar field is also investigated, in order to quantify the physical-space modifications of transport processes in multiscale forced turbulence. The surface area and wrinkling of level sets of the scalar field are monitored as measures of the influence of explicit forcing on the local and global mixing efficiency. At small Schmidt numbers, the values of surface area are mainly governed by the large-scale sweeping effect of the flow while the wrinkling is influenced mainly by the agitation of the smaller scales.

Acknowledgments

The work is supported by the Foundation for Fundamental Research on Matter (FOM), Utrecht, the Netherlands. Simulations were performed at SARA; special thanks goes to Willem Vermin for support with the parallelization. The computations were made possible through grant SC-213 of the Dutch National Computing Foundation (NCF). AKK would like to thank David McComb for many stimulating discussions during research visits at the University of Edinburgh. BJG gratefully acknowledges support from the Turbulence Working Group (TWG) at the Center for Non-Linear Studies (CNLS) at Los Alamos National Laboratory, which facilitated an extended research visit in 2005 and allowed many fruitful discussions. Special thanks goes to Darryl Holm.

This paper is associated with the focus issue Multi-scale Interactions in Turbulent Flows.