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Integrability technique for fluid flow induced deformation of a boundary hair

Jonas Smucker1,*, Zerrin M. Vural1,†, José R. Alvarado1,‡, and Philip J. Morrison2,§

  • 1Department of Physics and Center for Nonlinear Dynamics, The University of Texas at Austin, Austin, Texas 78712, USA
  • 2Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712, USA

  • *jsmucker@chaos.utexas.edu
  • †Present address: Department of Mathematics, UCLA, Los Angeles, CA 90095, USA.
  • ‡alv@chaos.utexas.edu
  • §morrison@physics.utexas.edu
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Phys. Rev. Fluids 7, 084001 – Published 12 August, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.084001

Abstract

The deformation of a dense carpet of hair due to Stokes flow in a channel can be described by a nonlinear integrodifferential equation for the shape of a single hair, which possesses several solutions for a given choice of parameters. Although it was posed in a previous study and it bears a resemblance to the pendulum problem from mechanics, this equation has not been analytically solved until now. Despite the presence on an integral with a nonlinear functional dependence on the dependent variable, the system is integrable. We compare the analytically obtained solution to a finite-difference numerical approach, identify the physically realizable solution branch, and briefly study the solution structure through a conserved energylike quantity. Time-dependent fluid-structure interactions are a rich and complex subject to investigate, and we argue that the solution discussed herein can be used as a basis for understanding these systems.

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Outline

Information

Phys. Rev. Fluids 7, 084001– Published 12 August, 2022
  • Received 30 March 2022
  • Accepted 14 July 2022
Article part of CHORUS
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