The description of the Moffatt and Parker problem recently revisited by O. Pezzi et al. [Astrophys. J. 834, 166 (2017)1538-435710.3847/1538-4357/834/2/166] is here extended by analyzing the features of the turbulence produced by the interaction of two colliding Alfvénic wave packets in a kinetic plasma. Although the approach based on the presence of linear modes features is still helpful in characterizing some low-energy fluctuations, other signatures, which go beyond the pure linear modes analysis, are recovered, such as the significant weakening of clear dispersion relations and the production of zero frequency fluctuations.