Mixing by squirmers in stratified fluids

Abstract

We find the mixing induced by a small swimming organism in a density stratified fluid. We model the swimmer as a spherical squirmer and quantify mixing through a mixing efficiency that is the ratio of rate of change of potential energy of fluid to the total work done by the swimmer. Assessing mixing in the near field and far field of the swimmer separately, we find that the near-field mixing aligns with past work, but the overall mixing is much larger than that caused by a point-sized swimmer (like force-dipole), although still small in weak stratification. Equivalent results are also obtained for a homogeneous dilute suspension of non-interacting swimmers. Our study highlights the impact of swimmer size on mixing, revealing that small-sized swimmers cannot induce substantial mixing. However, we propose few (unexplored) pathways through which small swimmers could induce significant mixing, ultimately contributing towards oceanic mixing.

13 pages

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