Algebraic and topological measures based on crossing number relations provide bounds on energy and helicity of ideal fluid flows and can be used to quantify morphological complexity of tangles of magnetic and vortex tubes. In the case of volume-preserving flows we discuss new results useful to determine lower bounds on magnetic energy in terms of topological crossing number and average spacing of the physical system. New relationships between average crossing number, energy and helicity are derived also for homogeneous vortex tangles. These results find interesting applications in the study of possible connections between energy and complexity of structured flows.
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