Computer Extension of Perturbation Series in Fluid Mechanics

Abstract

In a regular perturbation expansion, the routine labor of calculating higher approximations can often effectively be delegated to a computer. Then dozens or even hundreds of terms can typically be found. These may suffice to permit the structure of the solution to be analyzed, and the series then recast to improve its utility. Although special languages are being developed for algebraic and other nonnumerical manipulation, effective computations can be carried out using simply FORTRAN or the like. A number of recent applications in fluid mechanics are surveyed. Details are presented of two new computations inspired by work of Sydney Goldstein: impulsive heating of a flat plate in boundary-layer flow and the decay of an array of cubical vortices.