Mixing by microorganisms in stratified fluids

TL;DR

This study investigates the vertical mixing caused by microorganisms in stratified ocean waters, finding that their contribution is negligible and providing models to estimate their mixing efficiency.

Contribution

The paper introduces two approaches—scaling arguments and numerical simulations—to estimate the mixing efficiency of microorganisms in stratified fluids, revealing it is very low.

Findings

Microorganisms' mixing efficiency is at most 8%.

Efficiency scales as (a/ell)^3 for small organisms.

Numerical results confirm the scaling predictions.

Abstract

We examine the vertical mixing induced by the swimming of microorganisms at low Reynolds and P\'eclet numbers in a stably stratified ocean, and show that the global contribution of oceanic microswimmers to vertical mixing is negligible. We propose two approaches to estimating the mixing efficiency, $\eta$, or the ratio of the rate of potential energy creation to the total rate-of-working on the ocean by microswimmers. The first is based on scaling arguments and estimates $\eta$ in terms of the ratio between the typical organism size, $a$, and an intrinsic length scale for the stratified flow, $\ell = \left ( \nu \kappa / N^2 \right )^{1/4}$, where $\nu$ is the kinematic viscosity, $\kappa$ the diffusivity, and $N$ the buoyancy frequency. In particular, for small organisms in the relevant oceanic limit, $a / \ell \ll 1$, we predict the scaling $\eta \sim (a / \ell)^3$. The second estimate of $\eta$ is formed by solving the full coupled flow-stratification problem by modeling the swimmer as a regularized force dipole, and computing the efficiency numerically. Our computational results, which are examined for all ratios $a/\ell$, validate the scaling arguments in the limit $a / \ell \ll 1$ and further predict $\eta \approx 1.2 \left ( a / \ell \right )^3$ for vertical swimming and $\eta \approx 0.15 \left ( a / \ell \right )^3$ for horizontal swimming. These results, relevant for any stratified fluid rich in biological activity, imply that the mixing efficiency of swimming microorganisms in the ocean is at very most 8\% and is likely smaller by at least two orders of magnitude.