Hamiltonian structure and dynamics of a neutrally buoyant rigid sphere interacting with thin vortex rings

Banavara N. Shashikanth, Artan Sheshmani, Scott David Kelly, Mingjun Wei

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

In a previous paper, we presented a (noncanonical) Hamiltonian model for the dynamic interaction of a neutrally buoyant rigid body of arbitrary smooth shape with N closed vortex filaments of arbitrary smooth shape, modeled as curves, in an infinite ideal fluid in R3 . The setting of that paper was quite general, and the model abstract enough to make explicit conclusions regarding the dynamic behavior of such systems difficult to draw. In the present paper, we examine a restricted class of such systems for which the governing equations can be realized concretely and the dynamics examined computationally. We focus, in particular, on the case in which the body is a smooth sphere. The equations of motion and Hamiltonian structure of this dynamic system, which follow from the general model, are presented. Following this, we impose the constraint of axisymmetry on the entire system and look at the case in which the rings are all circles perpendicular to a common axis of symmetry passing through the center of the sphere. This axisymmetric model, in our idealized framework, is governed by ordinary differential equations and is, relatively speaking, easily integrated numerically. Finally, we present some plots of dynamic orbits of the axisymmetric system.

Original languageEnglish (US)
Pages (from-to)335-353
Number of pages19
JournalJournal of Mathematical Fluid Mechanics
Volume12
Issue number3
DOIs
StatePublished - Aug 2010
Externally publishedYes

Keywords

  • fluid-solid interactions
  • noncanonical Hamiltonian structure
  • Sphere+vortex rings

ASJC Scopus subject areas

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics

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