Mixing by microorganisms in stratified fluids

We examine the vertical mixing induced by the swimming of microorganisms at low Reynolds and Péclet 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, η, 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 η in terms of the ratio between the typical organism size, a, and an intrinsic length scale for the stratified flow, l = (νκ/N2)1/4, where ν is the kinematic viscosity, κ the diffusivity, and N the buoyancy frequency. In particular, for small organisms in the relevant oceanic limit, a/l