Numerical investigation of surface level instability due to tube in vibrating bed of powder

Surface level instability when tube is injected into vibrating bed of powder, which was originally found in experiments, is investigated numerically. We find that thicker (thiner) tube makes surface level inside tube higher (lower) than surface level outside tube. With fixed acceleration amplitude of vibration, surface level inside tube becomes higher as amplitude of vibration increases, which can be explained by considering the dependence upon strength of convective flow.