Slipping flows and their breaking

The process of breaking inviscid incompressible flows along a rigid body with slipping boundary conditions is studied. Such may be considered compressible on the surface, where normal velocity vanishes. It main reason for formation singularity gradient component parallel to border. Slipping are studied analytically in framework two- and three-dimensional Prandtl equations. Criteria catastrophe found both cases. For 2D equations takes place vorticity gradient. flows, breaking, i.e. fold finite time, occurs symmetric part tensor, as well antisymmetric — vorticity. problem gradients between two plates numerically two-dimensional Euler shown that maximum grows exponentially time simultaneous increase according double exponential law. Careful analysis shows this nothing more than folding, power-law relationship its width: max|ux|∝ℓ−2/3.