Geometric aspects of transformations of forces acting upon a swimmer in a3-D incompressible fluid

Alexander Khapalov; Giang Trinh

doi:10.3934/dcds.2013.33.1513

Article Contents

2013, Volume 33, Issue 4: 1513-1544. Doi: 10.3934/dcds.2013.33.1513

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Geometric aspects of transformations of forces acting upon a swimmer in a 3-D incompressible fluid

Alexander Khapalov^1, and
Giang Trinh^1,

1.
Department of Mathematics, Washington State University, Pullman, WA 99164-3113

Received: September 30, 2011

Revised: March 31, 2012

Published: March 2013

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Abstract

Our goal in this paper is to investigate how the geometric shape of a swimmer affects the forces acting upon it in a 3-$D$ incompressible fluid, such as governed by the non-stationary Stokes or Navier-Stokes equations. Namely, we are interested in the following question: How will the swimmer's internal forces (i.e., not moving the center of swimmer's mass when it is not inside a fluid) ``transform'' their actions when the swimmer is placed into a fluid (thus, possibly, creating its self-propelling motion)?We focus on the case when the swimmer's body consists of either small parallelepipeds or balls. Such problems are of interest in biology and engineering application dealing with propulsion systems in fluids.

Keywords:

Swimming models,
fluid mechanics,
Navier-Stokes equations,
stokes equations,
hybrid pde/integro-differential ode systems.

Mathematics Subject Classification: Primary: 35Q30, 76D99; Secondary: 70Q05.

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