Stirring by swimming bodies

Jean Luc Thiffeault; Stephen Childress

doi:10.1016/j.physleta.2010.06.043

Stirring by swimming bodies

Jean Luc Thiffeault
, Stephen Childress

Research output: Contribution to journal › Article › peer-review

73 Scopus citations

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.

Original language	English
Pages (from-to)	3487-3490
Number of pages	4
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	374
Issue number	34
DOIs	https://doi.org/10.1016/j.physleta.2010.06.043
State	Published - 26 Jul 2010
Externally published	Yes

Keywords

Biomixing
Chaotic mixing
Enhanced diffusion

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10.1016/j.physleta.2010.06.043

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@article{218671bca8b64f9b8316175b764b88a5,

title = "Stirring by swimming bodies",

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.",

keywords = "Biomixing, Chaotic mixing, Enhanced diffusion",

author = "Thiffeault, \{Jean Luc\} and Stephen Childress",

note = "Funding Information: The authors are grateful to W. Dewar, R. Ferrari, M. Graham, Z.G. Lin, C. Ortiz–Duenas, Y.-K. Tsang, and W. Young for helpful discussions, as well as to the hospitality of the 2008 Summer Program in Geophysical Fluid Dynamics (supported by NSF and ONR ) at WHOI, where this work began, and the Institute for Mathematics and its Applications (supported by NSF ). S.C. was supported by NSF under grant DMS-0507615 , J.-L.T. under grant DMS-0806821 .",

year = "2010",

month = jul,

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doi = "10.1016/j.physleta.2010.06.043",

language = "English",

volume = "374",

pages = "3487--3490",

journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",

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TY - JOUR

T1 - Stirring by swimming bodies

AU - Thiffeault, Jean Luc

AU - Childress, Stephen

N1 - Funding Information: The authors are grateful to W. Dewar, R. Ferrari, M. Graham, Z.G. Lin, C. Ortiz–Duenas, Y.-K. Tsang, and W. Young for helpful discussions, as well as to the hospitality of the 2008 Summer Program in Geophysical Fluid Dynamics (supported by NSF and ONR ) at WHOI, where this work began, and the Institute for Mathematics and its Applications (supported by NSF ). S.C. was supported by NSF under grant DMS-0507615 , J.-L.T. under grant DMS-0806821 .

PY - 2010/7/26

Y1 - 2010/7/26

N2 - 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.

AB - 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.

KW - Biomixing

KW - Chaotic mixing

KW - Enhanced diffusion

UR - https://www.scopus.com/pages/publications/77955567235

U2 - 10.1016/j.physleta.2010.06.043

DO - 10.1016/j.physleta.2010.06.043

M3 - Article

AN - SCOPUS:77955567235

SN - 0375-9601

VL - 374

SP - 3487

EP - 3490

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 34

ER -

Stirring by swimming bodies

Abstract

Keywords

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