LYAPUNOV EXPONENTS AND THE MERGER OF POINT-VORTEX CLUSTERS

Vortex clusters in two-dimensional inviscid flow are studied by long-time integration of the point-vortex equations. We compute Lyapunov exponents and the Kolmogorov-Sinai entropy (KSE) as functions of the dimensionless centroid separation μ between two clusters, each of them containing two or four point vortices of equal strengths. It is demonstrated that the KSE of two four-vortex clusters increases rapidly if μ becomes smaller than μc3.2, and the merger time increases faster than exponentially for μ>μc. This result supports the conjecture that the merger of distant continuous vorticity fields is so exceedingly slow as to be numerically unidentifiable. © 1995 The American Physical Society.