Helical turbulence with small-scale energy and helicity sources and external intermediate scale noises as the origin of large scale generation

Interactions violating the symmetry of positive and negative total helicity components are considered. In the ideal case where one of the components is zero, the system have two sign-definite integrals of motion, which lead to an inverse energy cascade, as occurs in two-dimensional turbulence. The generation of large-scale modes is considered in the quasi-normal approximation and is manifested as the instability of second moments, a mechanism of which was discussed at the end of previous century. A crucial point in this mechanism is the presence of mean turbulence with large-scale helical disturbances and small-scale sources of energy and helicity. In the case of both helicity components being nonzero, the possibility of the large-scale generation is studied by applying numerical experiments with a shell model and by analyzing special cases of interactions between different shells of the model. In all the approaches used, it is shown that an inverse energy flux (from small to large scales) can exist at a certain level of external helical noises in large-scale modes, which depends on the degree of "mixing" oppositely signed helicity components. (C) 2017 Elsevier B.V. All rights reserved.