In this paper we present and discuss ideas and new results in three different research areas of topological fluid mechanics. First, we propose a conjectured experiment to produce and observe, for the first time, vortex knotting in real fluids. Next we provide a new ropelength bound for tight, magnetic knots in ideal magnetohydrodynamics. Finally, we present a novel interpretation of eigenvalue analysis of tensor fields in terms of integral geometry by using the information on form factors provided by structural complexity analysis
Ricca, R. (2009). New developments in topological fluid mechanics. IL NUOVO CIMENTO C, 32(1), 185-192 [10.1393/ncc/i2009-10355-2].
New developments in topological fluid mechanics
RICCA, RENZO
2009
Abstract
In this paper we present and discuss ideas and new results in three different research areas of topological fluid mechanics. First, we propose a conjectured experiment to produce and observe, for the first time, vortex knotting in real fluids. Next we provide a new ropelength bound for tight, magnetic knots in ideal magnetohydrodynamics. Finally, we present a novel interpretation of eigenvalue analysis of tensor fields in terms of integral geometry by using the information on form factors provided by structural complexity analysis
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