Mathematika

Research Article

ON INTERACTION BETWEEN FALLING BODIES AND THE SURROUNDING FLUID

Frank T. Smitha1 and Andrew S. Ellisa2

a1 Department of Mathematics, UCL, Gower Street, London WC1E 6BT, U.K. (email: frank@math.ucl.ac.uk)

a2 Department of Mathematics, UCL, Gower Street, London WC1E 6BT, U.K.

Abstract

Interactions between a finite number of bodies and the surrounding fluid, in a channel for instance, are investigated theoretically. In the planar model here the bodies or modelled grains are thin solid bodies free to move in a nearly parallel formation within a quasi-inviscid fluid. The investigation involves numerical and analytical studies and comparisons. The three main features that appear are a linear instability about a state of uniform motion, a clashing of the bodies (or of a body with a side wall) within a finite scaled time when nonlinear interaction takes effect, and a continuum-limit description of the body–fluid interaction holding for the case of many bodies.

(Received May 06 2009)

MSC (2000)

  • 76Z05;
  • 74K35 (primary);
  • 74F10;
  • 70E55 (secondary)