Reentrant prewavy instability in competition between rising and twist modes in ac field-driven electroconvection

We report on the prewavy (PW) instability in ac field-driven electrohydrodynamics that is induced in a nematic liquid crystal (NLC) sandwiched between parallel electrodes. The instability is characterized by a twist mode of the NLC director along the vertical orientation to the electrodes (i.e., the z axis), generating a periodic pattern having a large wavelength (λ_{PW}) in the xy plane. The PW periodic to the preferred director n_{0} of the NLC should be distinguished from well-known electroconvection (EC) such as normal rolls (NRs) and abnormal rolls (ARs) with similar wave vectors. A reentrant PW (PW2) was discovered by employing well-adjusted optical conditions and a dynamic image-process method. The wavelength λ_{PW2} of the PW2 accompanying turbulent EC was measured as functions of the applied ac voltage and frequency, which was distinguished from λ_{PW1} of the primary PW (PW1) separated from the NR. Moreover, the appearance, disappearance, and reappearance of the PW were investigated for five frequency regions classified in the ac field-driven EC; it was found that the high frequency and high voltage causes competition between the rising mode (θ, tilting angle to the xy plane) and twist mode (ϕ, in-plane angle to the x axis) of the director through electrohydrodynamic coupling between the director field and flows. We discuss how the PW2 can arise by considering another twist mode known as AR instability.