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Linear drag law for high-Reynolds-number flow past an oscillating body

Natalie Agre1, Stephen Childress1, Jun Zhang1,2, and Leif Ristroph1

  • 1Applied Math Laboratory, Courant Institute, New York University, New York, New York 10012, USA
  • 2Department of Physics, New York University, New York, New York 10003, USA and Department of Physics, New York University Shanghai, Pudong, Shanghai 200122, China

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Phys. Rev. Fluids 1, 033202 – Published 11 July, 2016

DOI: https://doi.org/10.1103/PhysRevFluids.1.033202

Abstract

An object immersed in a fast flow typically experiences fluid forces that increase with the square of speed. Here we explore how this high-Reynolds-number force-speed relationship is affected by unsteady motions of a body. Experiments on disks that are driven to oscillate while progressing through air reveal two distinct regimes: a conventional quadratic relationship for slow oscillations and an anomalous scaling for fast flapping in which the time-averaged drag increases linearly with flow speed. In the linear regime, flow visualization shows that a pair of counterrotating vortices is shed with each oscillation and a model that views a train of such dipoles as a momentum jet reproduces the linearity. We also show that appropriate scaling variables collapse the experimental data from both regimes and for different oscillatory motions into a single drag-speed relationship. These results could provide insight into the aerodynamic resistance incurred by oscillating wings in flight and they suggest that vibrations can be an effective means to actively control the drag on an object.

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Phys. Rev. Fluids 1, 033202– Published 11 July, 2016
  • Received 12 January 2016

©2016 American Physical Society

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