Energy and helicity spectra in the shell model with distributed helicity injection

We present the results of modeling the development of homogeneous and isotropic turbulence with a source of helicity distributed in scale. We use the shell model for numerical simulation of the turbulence at high Reynolds number. Energy in our model is injected at certain large scale only whereas the source of helicity is distributed in scale and its characteristic scale may differ from the characteristic scale of energy source. The idea of our study related to the fact that quite often the helicity associated with the presence of coherent structures of different scales in the turbulent flow (e.g. atmospheric vortexes). The calculations are showed that the distribution helicity injection in scale (with constant injection of energy at the main scale) leads to a significant change in the behavior of the energy and helicity spectra. In particular, we found that, depending on the parameters of the injection helicity in the energy spectrum will be sufficiently extended interval with a slope of "-7 / 3" on a par with the Kolmogorov slope "-5/3". Thus, the proposed approach allows us to extend the shell model to study a broader class of turbulent flows.