Steadystate solutions of the Euler equations in two dimensions. II  Local analysis of limiting Vstates
Abstract
Steadystate solutions of the twodimensional incompressible Euler equations (Vstates) are studied analytically. That is, a local expansion is done in the neighborhood of any point on the boundary of a Vstate (which consists of piecewise constant regions of vorticity). It is shown that the limiting Vstates for the numerically calculated translating and rotating Vstates have 90deg corners and not cusps. It is also proven that, at a point which lies on the boundary of only one region, and at which the tangent angle has a jump discontinuity, the difference in t angent angles can only be 90 deg (a corner) or 180 deg (a cusp). The analytical behavior of doubly and triply connected rotating Vstates is also investigated.
 Publication:

SIAM Journal of Applied Mathematics
 Pub Date:
 October 1986
 Bibcode:
 1986SJAM...46..765O
 Keywords:

 Computerized Simulation;
 Euler Equations Of Motion;
 Incompressible Flow;
 Steady State;
 Two Dimensional Flow;
 Angular Velocity;
 Stream Functions (Fluids);
 Taylor Series;
 Vorticity;
 Fluid Mechanics and Heat Transfer