DOES CONTOUR DYNAMICS GO SINGULAR

It has recently been claimed that the "contour-dynamics" model of two-dimensional inviscid vortex dynamics spontaneously develops tangent-slope discontinuities, implying infinite contour curvature, within a finite time. The claim was made on the basis of numerical experimentation on three examples of vortex-patch merging, for one of which details were presented. This note presents contrary numerical evidence for the same example, strongly suggesting that no such singularity develops in the time claimed. The results are generated using overwhelmingly high spatial and temporal resolution. Comparisons with coarser-resolution calculations verify that the effects of resolution have been reduced to an insignificant level at the locations in question. It appears likely that contour smoothness persists for all finite time. © 1990 American Institute of Physics.