Impulse formulation of the Euler equations: General properties and numerical methods

The gauge freedom of the incompressible Euler equations is explored. We present various forms of the Euler equations written in terms of the impulse density. It is shown that these various forms are related by a gauge transformation. We devise a numerical method to solve the impulse form of the Euler equations in a variety of gauges. The numerical scheme is implemented both in two and three space dimensions. Numerical results are presented showing that the impulse density tends to concentrate on sheets.