UNSTEADY ASYMPTOTIC SOLUTIONS OF THE 2-DIMENSIONAL EULER EQUATIONS

A technique is described for deducing a class of unsteady asymptotic s olutions of the two-dimensional Euler equations. In contrast to previo usly known analytical results, the vorticity function [omega(x, y, t)] for these solutions has a complicated dependence on the spatial coord inates (x, y) and time (t). The results obtained are in implicit form and are valid in those regions of space and time where t omega --> 0() or t omega --> +infinity. These asymptotic solutions may be split in to an unsteady, two-dimensional and irrotational basic flow and a dist urbance that is strongly nonlinear at appropriate locations within the domain of validity. The generality and complexity of these solutions make them theoretically interesting and possibly useful in application s.