The Role of Helicity in Turbulent Flow

Helicity is, like energy, a quadratic invariant of the Euler equations, and may therefore be expected to constrain the turbulent cascade of energy from large to small scales. Indeed, in local structures where helicity is maximal, nonlinearity is totally depleted so that such structures tend to persist in coherent manner. Some basic properties of helicity will be reviewed in this lecture, with particular reference to its bearing on dynamo generation of magnetic fields in conducting fluids, and on the existence of Euler flows of arbitrarily complex topology. Recent work on reconnection of vortices will also be described, and it will be demonstrated that helicity (again like energy) s not in general conserved during such reconnection processes.