Dynamic Image Analysis for Electro-Hydrodynamic Convection in Nematic Liquid Crystal

We have investigated the fluctuation in the electro-hydrodynamic convection(EHC) by developing a method for dynamic image analyses. The fluctuation of images is characterized by the two-time correlation function of the spatial Fourier coefficients of images. We measured the time correlation function of patterns in the two turbulent states of EHC:(i) the dynamic scattering mode(DSM) 1 and (ii)DSM2 states. It was found that in the DSM2 state, the correlation time, defined by the time at which the correlation function becomes a half of the initial value, decreases monotonically as the increase of the wave number. In the DSM1 state, on the other hand, the correlation time along the direction perpendicular to the rubbing direction has a peak at the wave number corresponding to the thickness of the cell. The peak value decreases as the applied electric field is raised, and vanishes entirely when the system undergoes the transition from DSM1 to DSM2.