Inverse energy cascade in developed turbulence at the breaking of the symmetry of helical modes

The interactions breaking the symmetry of the positive and negative components of the total helicity have been considered with quasinormal approximations and the cascade model of helical turbulence. In the ideal case of the absence of one of them, the equations have two sign-definite integrals of motion; as a result, an inverse energy cascade occurs, as for two-dimensional turbulence. Owing to the instability of the second moments, whose mechanism was proposed in A. Belian, O. Chkhetiani, E. Golbraikh, and S. Moiseev, Physica A 258, 55 (1998), the generation of large-scale modes has been considered within the Fourier equations of hydrodynamics under the assumption of a quasinormal velocity field. The presence of background turbulence with large-scale helical perturbations and small-scale sources of the energy and helicity is a determining circumstance in this mechanism. The possibility of the inverse cascade in the case of incomplete degeneracy of one of the helicity components has been studied in the numerical experiments with the cascade model. It has been shown that the existence of the inverse (toward large scales) energy flux from small-scale perturbations requires a certain external-action-generated level of helical noise in large modes, which depends on the degree of “mixing” of different-sign helical components of the velocity field.