Bounds for Euler from vorticity moments and line divergence

The inviscid growth of a range of vorticity moments is compared using Euler calculations of anti-parallel vortices with a new initial condition. The primary goal is to understand the role of nonlinearity in the generation of a new hierarchy of rescaled vorticity moments in Navier-Stokes calculations where the rescaled moments obey D-m >= Dm+1, the reverse of the usual Omega(m+1) >= Omega(m) Holder ordering of the original moments. Two temporal phases have been identified for the Euler calculations. In the first phase the 1 < m < infinity vorticity moments are ordered in a manner consistent with the new Navier-Stokes hierarchy and grow in a manner that skirts the lower edge of possible singular growth with D-m(2) -> sup vertical bar omega vertical bar similar to A(m)(T-c - t)(-1) where the A(m) are nearly independent of m. In the second phase, the new D-m ordering breaks down as the Omega(m) converge towards the same super-exponential growth for all m. The transition is identified using new inequalities for the upper bounds for the -dD(m)(2)/dt that are based solely upon the ratios Dm+1/D-m, and the convergent super-exponential growth is shown by plotting log(d log Omega(m)/dt). Three-dimensional graphics show significant divergence of the vortex lines during the second phase, which could be what inhibits the initial power-law growth.