Dynamic Stability of Wave-Convection Transport

A flexible inextensible horizontal belt is assumed to be formed, by closely spaced vertical push rods, into a traveling sine wave. A spherical object resting at the bottom of a trough will tend to be convected with the trough as the wave travels. The dynamic stability of such wave-convection transport is considered. Assuming the wave to be shallow, the governing nonlinear equations are expanded (through second order) in the ‘shallowness parameter’, and thus reduced to a single equation, essentially of forced Duffing type, which is integrated numerically, over the parameter space of practical interest, to yield a stability criterion.