In this paper we introduce and discuss new concepts useful to analyse and characterize patterns of vortex lines in fluid flows. We define measures of tropicity to identify ‘tubeness’, ‘sheetness’ and ‘bulkiness’ of vortex lines and to measure the spreading of field lines about preferred directions. Algebraic, geometric and topological measures based on crossing number information are discussed and are put in relation to the kinetic helicity and the energy of the fluid system.
Ricca, R. (2001). Tropicity and complexity measures for vortex tangles. In C.F. Barenghi, R.J. Donnelly, W.F. Vinen (a cura di), Quantized Vortex Dynamics and Superfluid Turbulence (pp. 366-372). Berlin Heidelberg : Springer [10.1007/3-540-45542-6_36].
Tropicity and complexity measures for vortex tangles
RICCA, RENZO
2001
Abstract
In this paper we introduce and discuss new concepts useful to analyse and characterize patterns of vortex lines in fluid flows. We define measures of tropicity to identify ‘tubeness’, ‘sheetness’ and ‘bulkiness’ of vortex lines and to measure the spreading of field lines about preferred directions. Algebraic, geometric and topological measures based on crossing number information are discussed and are put in relation to the kinetic helicity and the energy of the fluid system.
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