Clarifying the relationship between efficiency and resonance for flexible inertial swimmers

Daniel Floryan, Clarence Worth Rowley

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


We study a linear inviscid model of a passively flexible swimmer, calculating its propulsive performance, eigenvalues and eigenfunctions with an eye towards clarifying the relationship between efficiency and resonance. The frequencies of actuation and stiffness ratios we consider span a large range, while the mass ratio is mostly fixed to a low value representative of swimmers. We present results showing how the trailing edge deflection, thrust coefficient, power coefficient and efficiency vary in the stiffness-frequency plane. The trailing edge deflection, thrust coefficient and power coefficient show sharp ridges of resonant behaviour for mid-to-high frequencies and stiffnesses, whereas the efficiency does not show resonant behaviour anywhere. For low frequencies and stiffnesses, the resonant peaks smear together and the efficiency is high. In this region, flutter modes emerge, inducing travelling wave kinematics which make the swimmer more efficient. We also consider the effects of a finite Reynolds number in the form of streamwise drag. The drag adds an offset to the net thrust produced by the swimmer, causing resonant peaks to appear in the efficiency (as observed in experiments in the literature).

Original languageEnglish (US)
Pages (from-to)271-300
Number of pages30
JournalJournal of Fluid Mechanics
StatePublished - Oct 25 2018

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


  • flow-structure interactions
  • propulsion
  • swimming/flying


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