Abstract. This is mostly a pedagogical review of some mathematical aspects of incompressible fluid flow. Many Lie theoretic ideas familiar to particle physicists illuminate aspects of fluid mechanics. There is a close analogy with the dynamics of a rigid body. For example, helicity is a quadratic Casimir invariant analogous to the square of angular momentum. Making another analogy with the Bogomolny inequality in the theory of instantons, I derive a new inequality for the dissipation of energy, relating it to helicity.

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