Computation of the Streamfunction and Velocity Potential and Reconstruction of the Wind Field

Abstract

A wind field given over a limited domain can be partitioned into nondivergent and irrotational components in an infinity of ways. A particular solution, selected by requiring the velocity potential to vanish on the boundary, has minimum divergent kinetic energy and is numerically easy to obtain. The reconstruction of the wind field from the vorticity and divergence together with the boundary velocity is more difficult, since the potential equations are coupled by the boundary conditions. A numerical procedure is devised, which solves the two potential equations simultaneously, modifying both interior and boundary values in a converging iterative technique. The method is capable of reconstructing the wind field to any accuracy desired.