Micromotions and controllability of a swimming model in an incompressible fluid governed by 2D or 3D Navier--Stokes equations

TL;DR

This paper investigates how bio-mimetic swimmers can control their movement in 2D and 3D incompressible fluids governed by Navier-Stokes equations, focusing on shape changes and internal forces.

Contribution

It analyzes the local controllability of swimmers with finitely many parts linked by internal forces in Navier-Stokes fluids, extending previous models.

Findings

Demonstrates controllability under certain geometric and force conditions

Provides explicit descriptions of internal forces affecting shape changes

Extends previous work to more complex fluid-structure interactions

Abstract

We study the local controllability properties of 2D and 3D bio-mimetic swimmers employing the change of their geometric shape to propel themselves in an incompressible fluid described by Navier-Stokes equations. It is assumed that swimmers' bodies consist of finitely many parts, identified with the fluid they occupy, that are subsequently linked by the rotational and elastic internal forces. These forces are explicitly described and serve as the means to affect the geometric configuration of swimmers' bodies. Similar models were previously investigated in [6]-[13].