Extraction of coherent structures using direct numerical simulation in 3D turbulent flows and its effects on chemotaxis

A numerical study of chemotaxis in 3D turbulence is presented here. Direct Numerical

Simulation were used to calculate the nutrient uptake for both motile and non-motile bacterial

species and by applying the dynamical systems theory the effect of flow topology on the

variability of chemotaxis is analyzed. It is done by injecting a highly localized patch of nutrient

in the turbulent flow, and analyzing the evolution of reaction associated with the observed

high and low stretching regions. The Gaussian nutrient patch is released at different locations

and the corresponding nutrient uptake is obtained. The variable stretching characteristics of

the flow is depicted by Lagrangian Coherent Structures and the roles they play in affecting the

uptake are analyzed. The Lagrangian Coherent Structures are quantified by the Finite Time

Lyapunov Exponents which is a measure of the average stretching experienced by the flow in

finite time. It is found that in high stretching regions, the motile bacteria are attracted to the

nutrient patch very quickly, but also dispersed quickly; whereas in low stretching regions the

bacteria respond slower towards the nutrient patch. However the total uptake is intricately

determined by stretching history. These reaction characteristics are reflected in the several

realizations of simulations. This helps in understanding turbulence intensity and how it affects

the uptake of the nutrient.