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. Finially, 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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