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

Time scales and species coexistence in chaotic flows

“…Several studies suggest that patchiness in plankton populations is related to the Damköhler number characterising the ratio between the time scales associated with the flow and the biological processes respectively [5,6,11]. Theoretical models have been used to study the dynamics of species coexistence in flowing environments [6][7][8][12][13][14][15][16]. Some of this work focuses on the emerging spatial structures, including the formation of filaments in chaotic flows [4,5,17].…”

Oceanic frontal divergence alters phytoplankton competition and distribution

“…This argument can be extended to organisms that experience a force confining them to a sub-surface depth [37]. The strength of the effective compressibility experienced by a population depends on both the magnitude of the divergence and the growth characteristics of the population, since rapidly reproducing phytoplankton can maintain a constant density even in the presence of a positively divergent flow [38].…”

Clustering of vertically constrained passive particles in homogeneous, isotropic turbulence

“…It is known that while non-inertial particles follow exactly the flow streamlines, and are homogeneously distributed in the fluid volume, inertial particles lighter than the fluid tend to be trapped inside vortices, as opposed to heavier inertial particles, that tend to accumulate in straindominated regions of the flow [1,3,10,11]. This preferential concentration has important consequences in the dynamics of particles under the influence of gravity [9], and in all the situations where the clustering of particles may have non-trivial consequences, as in, for example, cloud formation [12][13][14] or the biology of aquatic microorganisms [15][16][17][18].…”