The spectrum of turbulence in jets of Active Galactic Nuclei as well
as in solar shock
regions plays an important role for a number of physical processes
including particle
acceleration and radiation signatures of transient phenomena. Unlike
the fully evolved
strong turbulence in the interstellar medium, which exhibits a
Kolmogorov-like spectrum,
here different processes take place. This has a fundamental effect on
acceleration and diffusion in jets.
The evolution of turbulence in jets can be described by means of the
three-wave process
and wave transmission processes. Here we present results of the
analytical treatment of
three-wave interaction of dispersive plasma waves. We will discuss the
implications
on diffusive shock acceleration of our findings.
Additionally the idea of three-wave interaction has been extended to
PiC-simulations.
We will present methods to identify three-wave processes in these simulations.