Abundant singularities

Abstract

We show that a generic Euler flow or a generic ideal magnetostatic equilibrium contains an intricate structure of tangential discontinuities which are vortex sheets or current sheets, respectively. The discontinuities are present at all spatial scales and are dense at least in some parts of the volume occupied by the fluid. Possible implications for the energy dissipation in turbulent flows and for the structure of equilibria in tokamaks are discussed.