The helicity cascade in isotropic and homogeneous turbulence

P.D. MININNI; L.N. MARTIN; P. RODRIGUEZ IMAZIO; A. POUQUET; A. ALEXAKIS

Trieste, Italia

Conferencia; International Conference and Advanced School "Turbulent Mixing and Beyond"; 2009

ICTP

Helicity is a quadratic invariant of the Euler equations in three dimensions. As the energy, helicity cascades to smaller scales where it dissipates. However, the role played by helicity in the energy cascade is still unclear. In non-helical flows, the velocity and the vorticity tend to align locally creating patches with opposite signs of helicity. In helical flows helicity also changes sign rapidly in space. Being a non-positive definite quantity, global studies considering its spectral scaling in the inertial range are inconclusive, except for cases where one sign of helicity is dominant. We present studies of the helicity cascade in direct numerical simulations of turbulent flows up to spatial resolutions of 1024^3 grid points and under different mechanical forcings. We consider the shell-to-shell energy transfer and structure functions. We show that after doing the SO(3) decomposition, helical and non-helical flows show the same scaling in the inertial range for all orders computed, independently of the helicity content. Finally, we use the cancellation exponent to characterize the scaling laws followed by helicity fluctuations in helical and non-helical flows. The exponent is a measure of sign-singularity and in some cases can be related to the fractal dimension as well as to the first order scaling exponent of the helicity. The results show that the statistics and scaling laws followed by helicity fluctuations are independent of the global helicity of the flows, and confirms that the geometry of helical structures is filamentary.