Unsteady asymptotic solutions of the two-dimensional Euler equations

A technique is described for deducing a class of unsteady asymptotic solutions of the two-dimensional Euler equations. In contrast to previously known analytical results, the vorticity function [omega(x, y, t)] for these solutions has a complicated dependence on the spatial coordinates (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 into an unsteady, two-dimensional and irrotational basic flow and a disturbance 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 applications.