Expansion Functions for Two-Dimensional Incompressible Fluid Flow in Arbitrary Domains

Expansion functions are presented for two-dimensional incompressible fluid flow in arbitrary domains that optimally conserve the 2D structure of vortex dynamics. This is obtained by conformal mapping of the domain onto a circle and by constructing orthogonal radial polynomials and angular harmonics on the new domain such that the kinetic energy is diagonal and the separate components satisfy all of the required physical boundary conditions.