Spatial evolution of the helical behavior and the 2/3 power-law in single-square-grid-generated turbulence

Direct numerical simulations are performed to investigate the helical properties of single-square-grid-generated turbulence. The streamwise evolution of the probability density functions of the relative helicity density h reveals the existence of a transition from a quasi-two-dimensional state to a three-dimensional state. The correlations between the helicity and the enstrophy level as well as the dissipation level are examined. When conditioned on a high level of dissipation or enstrophy, in the energy decay region the velocity and vorticity vectors in both instantaneous and fluctuating fields become more aligned. However, this correlation does not hold in the production region. We also study the second-order structure function and reveal that a well-defined power-law can be found at a location quite close to the grid, where the turbulent flow is still in the transition state.