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 [amp;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 tamp;omega; -amp;gt 0+ or tamp;omega; -amp;gt + 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 possibility useful in applications.13; KW - Equations of motion13