In this study, cascade systems describing noniso-tropic disturbance propagation are generalized with respect to the scale spectrum in turbulence, In addition to the energy integral, the systems under consideration may conserve the helicity integral and naturally include external rotations. On the basis of the results of calculations, a transition from the -5/3 power spectrum to steeper dependences, in particular, the -2 power spectrum, is discussed. The problem of modeling the helicity cascade in systems with the corresponding spectrum exponents (-5/3 and -4/3) is also considered.
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