Betz Invariants and Generalization of Vorticity Moment Invariants

摘要

The widely used Betz invariants can be categorized as invariants of vorticity moments or impulsesin plane motion for mostly inviscid vortex flow. These invariants have served as a foundation of vortex roll-up process analysis as well as benchmarks to benchmarks to estimate numerical errors for vortex flow. The analysis starts from a more general integral divergence relation in rational mechanics to extend the analysis for both inviscid and viscous vortex flow cases, with or without finite boundaries. Conditions for the existence of the Betx invariants and their extensions to include viscous effects are discussed.