Numerical Modelling of Vortex Flow Instabilities and Interactions
Abstract
Evolution of vortices and their interactions are investigated in the Lagrangian context using the continuous vortex sheet method. Among the topics investigated are numerical Helmholtz instability on a circular vortex sheet, fractal-pattern instability on an expanding vortex spiral, interactions of vortices with shear layers, and other phenomena related to experimental observations in the laboratory and nature. The starting point is a two-dimensional vortex sheet along which the fluid velocity is discontinuous. A global characteristic of the vortex sheet evolution is stretching, implying that the vortex density (strength) of the sheet is a decreasing function of time. Locally, there may be short-lived contractions of the sheet in which strength increases sharply, preceding sudden qualitative changes such as the onset of roll-up and instabilities. The majority of present-day vortex methods have evolved from the point-vortex approximation by Rosenhead. The vortex particles, which are created at the solid boundary at each time step to satisfy the no-slip boundary condition, are freed in the subsequent time steps to move with the flow and diffuse. However, for the numerical simulation to be accurate, the particles must, to a certain degree, be uniformly distributed. This requires the use of techniques such as redistribution, splitting, and merging of particles. Results obtained in this way are equivalent to gridless solutions of the incompressible-flow Navier-Stokes equations. The continuous vortex sheet method employed in this paper is relatively simple in comparison, but does not have the capabilities of creating or diffusing vorticity. It does, however, model the jump discontinuity across thin vortex sheets, preserving discrete spiral structures of vortices similar to those observed in flow visualizations. (14 figures, 16 refs.)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 2003
- Accession Number
- ADA419102
Entities
People
- M. Mokry
Organizations
- National Research Council Canada