Material symmetries and inhomogeneous waves in piezoelectric media

Summary This study is an experimental investigation on a novel oscillation phenomenon of a water rivulet on a smooth hydrophobic surface. It is found that the water rivulet running down on a smooth Plexiglass plate exhibits all together four distinctive patterns with increasing either the Froude number, the Weber number or the Reynolds number. Once either the Froude number, the Weber number or the Reynolds number exceeds the third critical value, the rivulet on a smooth Plexiglass plate is restabilized, and becomes almost straight. However, in the restable rivulet, several beads of a rosary are formed following immediately downstream of the pipe mouth. This is no more than the novel oscillation phenomenen of the water rivulet on a smooth Plexiglass plate. The oscillatory motion is steady in the hydrodynamical sense, because the phase of the oscillation is always the same at each point in space.It is found that with increasing either the Froude number, the Weber number or the Reynolds number, not only the wave-length and width of the beads in the restable rivulet increase, but also the rivulet itself becomes more straight and stable. On one hand, with increasing distance from the pipe mouth along the central axis of the rivulet, the local maximum width of each of the beads decreases, but its wave-length increases.It is suggested that the oblique surface waves generated at the left and right contact lines of the rivulet play a primary role in the contraction process of the novel oscillation phenomenon of the restable rivulet.