OVERVIEW

In this chapter we focus our attention on a particular class of flows that are dominated by the presence or motion of compact regions of concentrated vorticity, concisely called vortices, including vortex filaments and vortex layers. The analysis of these flows and the development of pertinent methods of numerical computation will be conducted under the assumption that the Reynolds number is sufficiently large that viscous forces are confined within thin boundary layers, and the fluid within the main part of the flow may be considered to be truly or nearly inviscid.

In nature and technology, vortices may be generated by a variety of mechanisms, including the deposition of vorticity within compact wakes behind bluff bodies, the rollup of separated boundary layers and vortex layers that are ejected from sharp corners, and the instability of shear layers forming at the interface between two fluids that merge at different speeds. In everyday life, vortices may be seen to develop from the rollup of vortex sheets developing on either side of a blade that is made to move parallel to itself broadside on along a free surface.

To compute the evolution of a flow that is dominated by vortex motions, it is expedient to proceed in an indirect manner that involves computing the evolution of the vorticity field using the vorticity transport equation, and then obtaining the simultaneous evolution of the velocity field by inverting the definition of the vorticity ? = ? u. This method of...