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Swimming sheet in a density-stratified fluid

Published online by Cambridge University Press:  04 July 2019

Rajat Dandekar ,
Vaseem A. Shaik  and
Arezoo M. Ardekani Open the ORCID record for Arezoo M. Ardekani [Opens in a new window]
Rajat Dandekar
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
Vaseem A. Shaik
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
Arezoo M. Ardekani*
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
*
†Email address for correspondence: [email protected]
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Abstract

In this work, we theoretically investigate the swimming velocity of a Taylor swimming sheet immersed in a linearly density-stratified fluid. We use a regular perturbation expansion approach to estimate the swimming velocity up to second order in wave amplitude. We divide our analysis into two regimes of low ($\ll O(1)$) and finite Reynolds numbers. We use our solution to understand the effect of stratification on the swimming behaviour of organisms. We find that stratification significantly influences motility characteristics of the swimmer such as the swimming speed, hydrodynamic power expenditure, swimming efficiency and the induced mixing, quantified by mixing efficiency and diapycnal eddy diffusivity. We explore this dependence in detail for both low and finite Reynolds number and elucidate the fundamental insights obtained. We expect our work to shed some light on the importance of stratification in the locomotion of organisms living in density-stratified aquatic environments.

JFM classification

Biological Fluid Dynamics: Propulsion Geophysical and Geological Flows: Stratified flows Biological Fluid Dynamics: Swimming/flying
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 874 , 10 September 2019 , pp. 210 - 234
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Copyright
© 2019 Cambridge University Press 

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