Cumulative compressibility effects on slow reactive dynamics in turbulent flows

Abstract

Reactions in turbulent flows, chemical reactions or combustion, are common. Typically reaction time scales are much shorter than turbulence timescales. In biological applications, as it is the case for bacterial and plankton populations living under the influence of currents in oceans and lakes, the typical lifetime can be long and thus can fall well within the inertial range of turbulence time scales. Under these conditions, turbulent transport interacts in a very complex way with the dynamics of growth and death of the individuals in the population. In the present paper, we quantitatively investigate the effect of the flow compressibility on the dynamics of populations. Small effective compressibility can be induced by several physical mechanisms, such as, e.g., by the density mismatch, by a small but finite size of microorganisms, and by gyrotaxis (an interaction between swimming and shear). We report, for the first time, how even a tiny effective compressibility can produce a dramatically large effect on global quantities like the carrying capacity of the ecosystem. We interpret our findings by means of a cumulative effect made possible by the long replication times of the organisms with respect to turbulence time scales. A statistical quantification of the fluctuations of population concentration is presented.

Keywords:

• turbulent biological flows
• reacting turbulent flows
• homogeneous turbulence

Acknowledgments

[Acknowledgements] We thank M.H. Jensen and S. Pigolotti for useful discussions. We acknowledge computational support from CASPUR (Roma, Italy under HPC Grant 2009 N. 310), from CINECA (Bologna, Italy), and SARA (Amsterdam, The Netherlands). Support for D R N was provided in part by the National Science Foundation through Grant No. DMR-1005289 and by the Harvard Materials Research Science and Engineering Center through NSF Grant No. DMR-0820484. We acknowledge the COST Action MP0806 for support. PP and FT acknowledge the Kavli Institute of Theoretical Physics for hospitality. This research was supported in part by the National Science Foundation under Grant No. NSF PHY05-51164. Data from this study are publicly available in unprocessed raw format from the iCFDdatabase (http://cfd.cineca.it).