Using a shell model of turbulence, we have investigated a long-time evolution of magnetic and velocity fields in the MHD turbulence with various types of initial states. For each kind of these states, 24 realizations of the process with random noise in the initial states were modeled simultaneously with the help of a parallel computer cluster at the Research Computing Center of Moscow State University. For most realizations, a coherent state with high alignment between the magnetic and velocity fields has been developed. In the case of establishment of the coherent state, the dissipation rate of energy is found to be substantially reduced. At the same time, there exist few realizations that behave in another manner: they are characterized by a lower level of cross-helicity or an essentially faster energy decay.

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