Betz Invariants and Generalization of Vorticity Moment Invariants
نویسنده
چکیده
The widely used Betz invariants can be categorized as invariants of vorticity moments or impulses in plane motion for mostly inviscid vortex ow. These invariants have served as a foundation of vortex roll-up process analysis as well as benchmarks to estimate numerical simulation errors for vortex ow. The analysis starts from a more general integral divergence relation in rationalmechanics to extend the analysis for both inviscid and viscous vortex ow cases, with or without nite boundaries. Conditions for the existence of the Betz invariants and their extensions to include viscous effects are discussed. These extensions can be used as analyticalmeans for theoretical modeling of complicated vortex systems, especially in ows with viscous effects and nite boundaries. The goal of this study is to clearly establish when the Betz invariants and the generalized vorticity moment invariants are applicable. The approach uses rigorous mathematical analysis, and the physical interpretations of the results are discussed. A trailing vortex pair is used as an example to illustrate the applications of the theoretical study.
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