Physical space properties of helicity in quasi-homogeneous forced turbulence

Three main results of this Letter are closely related to finite dissipation of helicity defined as the integral of the scalar product of velocity and vorticity, H=∫u⋅ωdx: (i) the self-production property of superhelicity Hs=∫ω⋅curlωdx (which is proportional to helicity dissipation) in the sense that forcing does not play any role in production of superhelicity, i.e., the dissipation of helicity; (ii) finiteness of helicity dissipation is the manifestation of the lack of reflection symmetry of the small scales; (iii) this lack of reflectional symmetry should increase with the Reynolds number, following from our third main result that the normalized helicity dissipation tends to remain finite as the Reynolds number increases, just like the energy dissipation, in the spirit of Kolmogorov 41. The results were obtained from DNS of Navier-Stokes equations in a simplest flow geometry with periodical boundary conditions.