Poincare recurrence and intermittent destruction of the Kelvin wave cascade in turbulence

Spacecraft data for solar wind turbulence shows a more sophisticated magnetic energy spectra than the simple k$^{-5/3}$ Kolmogorov spectrum of fluid turbulence. In particular data shows that while the low wave number magnetic energy spectrum follows the Kolmogorov k$^{-5/3}$ cascade, there is a clear break in the spectral exponent with the spectrum having a somewhat steeper power law decay at the kinetic ion scales. A unitary lattice algorithm, based on interleaved unitary collision-stream operators, is implemented to study turbulence of the nonlinear Schrodinger equation. Because of the near perfect parallelization of this unitary algorithm simulations were performed on 5760$^{3}$ grids, yielding multi-scale physics seen in the multi-cascade behavior of the incompressible kinetic energy. Very short Poincare recurrence times have been seen with the intermittent destruction of the Kelvin wave cascade.