the mathematics of stirring

Question

are there any resources on the mathematics of stirring let's say I stir a coffee cup with a spoon. the result is a diffeomorphism from the disk to itself. By physical intuition... that diffeomorphism should be mixing.

is there any way to formalize this reasoning? I think it's not necessary to solve the Navier-Stokes equations. Instead, we'd need to look at mixing diffeomorphisms of the disk.

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my question is how is a stirring spoon mix? the path is a circle - over and over. And yet our coffee mixes.

Here is a picture of paint being stirred... obviously something is mixing.

Perhaps this question is ill-posed without a choice of physical model.

Answer 1

Wikipedia: Topological Fluid Dynamics

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' (Boyland, Aref & Stremler 2000).

I'd certainly like to know more.