Experiments on the primary wavy instability in a liquid-fluidized bed are designed to test the two-phase flow governing equations. The wave is shown to saturate along the bed. The saturated wave can be well described as a cnoidal wave. The solid-phase viscosity and pressure which are unknown in the two-phase model are deduced from the shape of the saturated wave. The validity of the two-phase Newtonian model is then questioned.