Helicity and Super-Helicity in Homogeneous Turbulent Shear Flow

Initial mean helicity is imposed on direct numerical simulations of homogeneous turbulent shear flow. As time is advanced in the simulations, an approximately exponential growth of the turbulent kinetic energy is found, but the mean helicity is observed to decay. Distributions of helicity are skewed according to its initial value. A wavelet-based scale-dependent analysis shows that this skewness is largest for large scales of the turbulent motion and decreases for smaller scales. In addition, a trend to two-dimensionalization for large scales of motion and a preference for helical motion at small scales is found. Joint probability distribution functions show a strong correlation of the signs of helicity and super-helicity for all cases, including Gaussian fields. This correlation supports the conjecture that super-helicity dissipates helicity.