Computation of Vortex Sheet Roll-Up

Abstract

 

Vortex sheets are commonly used in fluid dynamics to model thin shear layers in slightly viscous flow. A flat vortex sheet typically rolls up into a spiral with concentrated circulation. Examples of a rolled-up vortex sheet include the trailing wake behind an airplane, and the vortex rings created due to the instability of a circular jet. Vortex sheet computations encounter several difficulties due to Kelvin-Helmholtz instability and singularity formation. A Lagragian particle method has been developed that overcomes these difficulties by using regularized point-vortices. Two recent projects will be described: the onset of chaos in planar and axisymmetric vortex sheet flow, and an adaptive treecode algorithm that reduces the cost of evaluating the particle velocities in 3-D flow from O(N^2) to O(N\log N). This is joint work with Monika Nitsche (University of New Mexico) and Keith Lindsay (NCAR).