Journal of Fluid Mechanics

The force on a sphere in a uniform flow with small-amplitude oscillations at finite Reynolds number

Phillip M.  Lovalenti a1 and John F.  Brady a1
a1 Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA

Article author query
lovalenti pm   [Google Scholar] 
brady jf   [Google Scholar] 


The unsteady force acting on a sphere that is held fixed in a steady uniform flow with small-amplitude oscillations is evaluated to O(Re) for small Reynolds number Re. Good agreement is shown with the numerical results of Mei, Lawrence & Adrian (1991) up to Re [approximate] 0.5. The analytical result is transformed by Fourier inversion to allow for an arbitrary time-dependent motion which is small relative to the steady uniform flow. This yields a history-dependent force which has an integration kernel that decays exponentially for large time.

(Published Online April 26 2006)
(Received December 1 1992)
(Revised May 27 1993)