Eulerian and Lagrangian properties of turbulent flows under multi-scale helical injection

We present numerical and theoretical results concerning the properties of turbulent flows under strong multi-scale helical injection. We perform direct numerical simulations of the Navier-Stokes equations under a random helical stirring with power-law spectrum and with different intensities of energy and helicity injections. We show that there exists three different regimes where the forward energy and helicity inertial transfers are: (i) both leading with respect to the external injections, (ii) energy transfer is leading and helicity transfer is sub-leading, and (iii) both are sub-leading and helicity is maximal at all scales. As a result, the cases (ii-iii) give flows with Kolmogorov-like inertial energy cascade and tunable helicity transfers/contents. We further explore regime (iii) in a Lagrangian domain, by studying the kinetics of point-like isotropic helicoids, particles whose dynamics is isotropic but breaks parity invariance. We investigate small-scale fractal clustering and preferential sampling of intense helical flow structures. Depending on its structural parameters, the isotropic helicoids either preferentially sample co-chiral or anti-chiral flow structures. We explain these findings in limiting cases in terms of what is known for spherical particles of different densities and inertia. Furthermore, we present theoretical and numerical results for a stochastic model where Lagrangian properties can be calculated using analytical perturbation theory. Our study shows that a suitable tuning of the stirring mechanism can strongly modify the small-scale turbulent helical properties and demonstrates that isotropic helicoids are the simplest particles able to preferentially sense helical properties in turbulence.