COLLAPSING SOLUTIONS TO THE 3-D EULER EQUATIONS

A three-dimensional adaptive mesh code is used to search for singularities in the incompressible Euler equations. For the initial conditions examined, the maximum vorticity eventually grows only exponentially. The small scales are quasi-two-dimensional and the vorticity has a pronounced tendency to develop sharp jumps in magnitude. The vorticity is very nearly parallel to the eigenvector of the rate-of-strain matrix whose eigenvalue is the smallest in magnitude. This eigenvalue is positive and much smaller than the others. © 1990 American Institute of Physics.