Mode-bifurcation upon pouring water into a cup that depends on the shape of the cup

Abstract

Mode-bifurcation that included hysteresis was investigated when water was poured into a cup via a water faucet. Three modes, i.e., accumulation flow (mode I), scattering flow (mode II), and open and shut oscillatory flow (mode III), could be produced by laterally changing the distance between the center of the cup and the landing point of water poured at a constant flow rate. Hysteresis in mode-bifurcation was observed when the distance was changed depending on the initial location of the water poured into the cup. Pendulum flow was also observed when water was poured into a shallow cell. The essential features of this mode-switching were reproduced by a numerical calculation as a function of the landing point of the poured water using two-variable (the size of the water hollow and the pressure on the water surface) differential equations that included the nature of reversed flow.