Topological fluid dynamics

Topological ideas are relevant to fluid dynamics at the kinematic level, since any fluid flow involves continuous deformation of any transported scalar or vector field. Problems of stirring and mixing are particularly susceptible to topological techniques. Thus, for example, the Thurston–Nielsen classification has been fruitfully applied to the problem of stirring in two-dimensions by any number of stirrers following a time-periodic 'stirring protocol'. Other studies are concerned with flows having chaotic particle paths, and associated exponential rates of mixing.

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