Microstructure, renormalization, and more efficient vortex methods

Department of Mathematics University of California Berkeley, California 94720-3840, USA

Abstract

The small-scale structure of the flow produced by vortex methods is discussed, and contrasted with the small-scale structure produced by grid methods. Particular attention is paid to the proliferation of vortex hairpins in three dimensions; its origin is analyzed, a statistical description is given, and methods for harmlessly deleting unneeded hairpins are suggested. These methods involve renormalization-group ideas and an expansion in powers of a vortex fugacity. In both theory and applications, magnet variables play a major role.