Extended self-similarity and abnormal intermittency factor of hierarchical velocity structures in micro electrokinetic turbulence

Experimental investigations on electrokinetic turbulence (EKT) that generated by high-intensity AC electric field have been done in a 240μm high, 130μm wide and 5mm long microchannel, by laser induced fluorescence photobleaching anemometer. Under low bulk flow Re (~0.4), the velocity structure functions (VSF) of the highly random flow exhibit apparent extended self-similarity (ESS). An inertial subrange with scaling exponent of 2/3 has been observed. Further investigations indicate, the scaling exponents of high-order VSF in ESS model are relatively smaller than that predicted by Kolmogorov 1941 law and the experimental results in homogeneous and isotropic (HI) turbulence (Benzi et al., Physica D, 1996, 96, 162). This indicates the inertial subrange of EKT has stronger intermittency, which is further related to an abnormal curled-up of the exponential tail in the probability density function of velocity gradient. The intermittency of the inertial subrange of EKT is further investigated by the intermittency factor (β) of SL94 law (She and Leveque, Phys. Rev. Lett., 1994, 72, 336), where 0<β<1. However, in the EKT, β is around 1.1 to 1.2, which is beyond the limits of β in SL94 law. The abnormal β may imply an inverse energy cascade in the inertial subrange of EK turbulent flow.