Cascade of turbulent energy and scalar variance in DC electrokinetic turbulence

Abstract

Abstract Turbulent flow can be generated by DC electrokinetic (EK) mechanism resulted from the electric conductivity and permittivity variation in fluids, as has been demonstrated by Varshney et al (2016), where a −1.4 slope of velocity power spectrum is observed. Here, we theoretically investigate the scaling exponents of both velocity and scalar structure functions in DC EK turbulence. The scaling exponents of the second order structure functions of velocity and scalar in the so-called electric body force (EBF) dominant subrange are 2/5 (equivalent to the −7/5 slope of velocity power spectrum) and 4/5 respectively. The theory directly explains the experimental results of Varshney et al. (2016). Based on Karman–Howarth equation with forcing terms, the third order structure function of velocity which is the representative of energy transport process is investigated in the DC EK turbulence. Compared with the conventional hydrodynamic turbulence, the energy transport in DC EK turbulence has an additional scaling subrange and is governed by additional small length scales.