Hierarchical structure parameters in three dimensional turbulence: She-Leveque model

Hierarchical structure parameters, proposed in She-Leveque model, are investigated for velocity components obtained from different flow types over a large range of Reynolds numbers 255 < Re_λ < 720. The values of intermittency parameter β, with respect to a fixed velocity component, are observed nearly same for all four types of turbulence. The parameter γ, for streamwise velocity components is nearly the same but significantly different for vertical components in different flows. It is also observed that for both parameters, an obvious relation between the longitudinal and transverse components β_T < β_L (and γ_T < γ_L) always holds. However, the difference between β_L and β_T is found very small in all types of turbulent flows, we studied here. It is evidenced that at low Reynolds numbers, the deviations from K41 scaling are mainly due to the most intense structures and slightly because of more heterogeneous hierarchy of fluctuation structures. However, at higher Reynolds numbers the deviations seem as a consequence of the most intense structures only. Over all, the study suggests that the hierarchy parameter β may be consider as a universal constant.