2005A&A...437....1V

We calculate the evolution of Alfven waves in super-Alfvenic flows, such as the downstream region of a fast-mode shock, via three-wave interactions between two Aflven waves and a sound wave. We show that the process has a significant influence on the evolution of the Alfven wave spectra, driving the system toward a degenerate normalized cross-helicity, H_c-±1. Typical distances in which the system evolves are evaluated, and the effects of the calculated turbulence evolution on test-particle acceleration in super-Alfvenic quasi-parallel shocks are studied. We show that typically the spectrum of accelerated particles is determined by the first-order Fermi acceleration process as described earlier by Vainio & Schlickeiser (1998A&A...331..793V; 1999A&A...343..303V), and identify some regions of parameter space, where the earlier results are significantly modified either by changes in the predicted scattering-center compression ratio or by stochastic acceleration in the downstream plasma.