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Three-dimensional transition after wake deflection behind a flapping foil.

Jian Deng1, C P Caulfield2

  • 1Department of Mechanics, Zhejiang University, Hangzhou 310027, People's Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 15, 2015
PubMed
Summary
This summary is machine-generated.

We identified unstable, three-dimensional flow patterns in the wake of flapping foils. A short-wavelength instability dominates at high Reynolds numbers, influencing fluid dynamics in fish and bird locomotion.

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Area of Science:

  • Fluid dynamics
  • Biomimetic locomotion
  • Instability theory

Background:

  • Propulsive wakes generated by flapping foils mimic biological systems like fish fins and bird wings.
  • The wake dynamics exhibit distinct patterns (Bénard-von Kármán vortex streets, reverse BvK, deflected wakes) with increasing flapping amplitude.

Purpose of the Study:

  • To investigate the three-dimensional linear instabilities present in the propulsive wake of a flapping foil.
  • To characterize the critical conditions and nature of these instabilities at varying flow parameters.

Main Methods:

  • Analysis of wake patterns under increasing flapping amplitude.
  • Introduction of three-dimensional spanwise periodic perturbations.
  • Floquet multiplier analysis to identify unstable modes and their wavelengths.

Main Results:

  • A dominant, unstable
  • short wavelength
  • mode (β=30, λ=0.21) was identified at a Reynolds number (Re) of approximately 600.
  • A
  • long wavelength
  • mode (β=6, λ=1.05) was found to be critical at higher Reynolds numbers but less dominant.
  • The short wavelength mode exhibits a periodicity approximately twice that of the base flow, suggesting potential subharmonic or quasiperiodic behavior.

Conclusions:

  • The study reveals critical three-dimensional instabilities in flapping foil wakes.
  • A short-wavelength instability is the primary mode at high Reynolds numbers, with implications for biomimetic propulsion.
  • Further research is needed to definitively classify the nature of the short-wavelength instability.