Stirring by swimming bodies

TL;DR

This paper models how swimming bodies like krill stir an inviscid fluid, calculating particle displacement and effective diffusivity, and compares theoretical results with simulations, highlighting the impact of viscosity.

Contribution

It introduces a model for fluid stirring by swimming bodies using non-interacting cylinders or spheres and computes effective diffusivity considering impact parameters.

Findings

Effective diffusivity is five times thermal diffusivity for krill-like parameters.

Viscosity can increase diffusivity estimates by two orders of magnitude.

Model results align with simulation data.

Abstract

We consider the stirring of an inviscid fluid caused by the locomotion of bodies through it. The swimmers are approximated by non-interacting cylinders or spheres moving steadily along straight lines. We find the displacement of fluid particles caused by the nearby passage of a swimmer as a function of an impact parameter. We use this to compute the effective diffusion coefficient from the random walk of a fluid particle under the influence of a distribution of swimming bodies. We compare with the results of simulations. For typical sizes, densities and swimming velocities of schools of krill, the effective diffusivity in this model is five times the thermal diffusivity. However, we estimate that viscosity increases this value by two orders of magnitude.