Skip to main content

Hovering of a rigid pyramid in an oscillatory airflow


We investigate the dynamics of rigid bodies (hollow ‘pyramids’) placed within a background airflow, oscillating with zero mean. The asymmetry of the body introduces a net upward force. We find that when the amplitude of the airflow is above a threshold, the net lift exceeds the weight and the object starts to hover. Our results show that the objects hover at far smaller air amplitudes than would be required by a quasi-steady theory, although this theory accounts qualitatively for the behaviour of the system as the body mass becomes small.

Corresponding author
Email address for correspondence:
Hide All
Alexander D. E. 2002 Nature's Flyers: Birds, Insects, and the Biomechanics of Flight. The Johns Hopkins University Press.
Altshuler D. L., Dickson W. B., Vance J. T., Roberts S. P. & Dickinson M. H. 2005 Short-amplitude high-frequency wing strokes determine the aerodynamics of honeybee flight. Proc. Natl Acad. Sci. USA 102, 1821318218.
Batchelor G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Childress S., Vandenberghe N. & Zhang J. 2006 Hovering of a passive body in an oscillating airflow. Phys. Fluids 18, 117103.
Dabiri J. O. 2005 On the estimation of swimming and flying forces from wake measurements. J. Exp. Biol. 208, 35193532.
Dudley R. 1999 The Biomechanics of Insect Flight. Princeton University Press.
Ellington C. P. 1984 The aerodynamics of hovering insect flight. Part I–VI. Phil. Trans. R. Soc. Lond. B305, 1181.
Kanso E., Marsden J. E., Rowley C. W. & Melli-Huber J. B. 2005 Locomotion of articulated bodies in a perfect fluid. J. Nonlinear Sci. 15, 255289.
Mei R. 1994 Flow due to an oscillating sphere and an expression for unsteady drag on the sphere at finite Reynolds number. J. Fluid Mech. 270, 133174.
Odar F. & Hamilton W. S. 1964 Forces on a sphere accelerating in a viscous fluid. J. Fluid Mech. 18, 302314.
Purcell E. M. 1977 Life at low Reynolds number. Am. J. Phys. 45, 311.
Spagnolie S. E. 2008 Flapping, ratcheting, bursting, and tumbling: a selection of problems in fluid-body interaction dynamics. PhD thesis, New York University, New York.
Spagnolie S. E. & Shelley M. J. 2009 Shape-changing bodies in fluid: Hovering, ratcheting, and bursting. Phys. Fluids 21, 013103.
Vogel S. 1996 Life in Moving Fluids, 2nd edn. Princeton University Press.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 21 *
Loading metrics...

Abstract views

Total abstract views: 110 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 18th November 2017. This data will be updated every 24 hours.