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Interaction of a columnar vortex with a long circular cylinder translated normal to the vortex axis is examined for the case where the cylinder diameter is much larger than the vortex core radius. The study focuses on understanding and quantifying the limitations of traditional vortex lament models arising from vortex-induced separation of the cylinder boundary layer and vortex core shape deformation. These limitations are examined over a wide range of values of the impact parameter, de ned as the ratio of the ambient normal velocity past the cylinder to the maximum vortex azimuthal velocity. Filament model predictions of vortex displacement are compared to experimental data both before and after vortex-induced boundary-layer separation. Experimental data are presented showing the importance of the ambient normal velocity to the cylinder in delaying vortex-induced boundary-layer separation, so that for cases with high impact parameter the ow is governed by inviscid effects even as the vortex moves quite close to the cylinder surface. The inviscid shape deformation of the vortex core is modest in the cases examined, even for close vortex-cylinder interaction, and is shown to have small effect on the surface pressure. The topology of secondary vorticity structures ejected from the cylinder boundary layer is examined using a two-color laserinduced uorescence technique and is found to be qualitatively different for cases with high and low values of the impact parameter.

Numerical methods may require derivatives of functions whose values are known only on irregularly spaced calculation points. This document presents and quantifies the performance of Moving Least-Squares (MLS), a method of derivative evaluation on irregularly spaced points that has a number of inherent advantages. The user selects both the spatial dimension of the problem and order of the highest conserved moment. The accuracy of calculations is maintained on highly irregularly spaced points. Not required are creation of additional calculation points or interpolation of the calculation points onto a regular grid. Implementation of the method requires the use of only a relatively small number of calculation points. The method is fast, robust and provides smooth results even as the order of the derivative increases.

A computational study of three-dimensional vortex–cylinder interaction is reported for the case where the nominal orientation of the cylinder axis is normal to the vortex axis. The computations are performed using a new tetrahedral vorticity element method for incompressible viscous fluids, in which vorticity is interpolated using a tetrahedral mesh that is refit to the Lagrangian computational points at each timestep. Fast computation of the Biot-Savart integral for velocity is performed using a box-point multipole acceleration method for distant tetrahedra and Gaussian quadratures for nearby tetrahedra. A moving least-square method is used for differentiation, and a flux-based vorticity boundary condition algorithm is employed for satisfaction of the no-slip condition. The velocity induced by the primary vortex is obtained using a filament model and the Navier–Stokes computations focus on development of boundary-layer separation from the cylinder and the form and dynamics of the ejected secondary vorticity structure. As the secondary vorticity is drawn outward by the vortex-induced flow and wraps around the vortex, it has a substantial effect both on the essentially inviscid flow field external to the boundary layer and on the cylinder surface pressure field. Cases are examined with background free-stream velocity oriented in the positive and negative directions along the cylinder axis, with free-stream velocity normal to the cylinder axis, and with no free-stream velocity. Computations with no free-stream velocity and those with free-stream velocity tangent to the cylinder axis exhibit similar secondary vorticity structures, consisting of a vortex loop (or hairpin) that wraps around the primary vortex and is attached to the cylinder boundary layer at two points. Computations with free-stream velocity oriented normal to the cylinder axis exhibit secondary vorticity structure of a markedly different character, in which the secondary eddy remains close to the cylinder boundary and has a quasi-two-dimensional form for an extended time period.