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We investigate the particle trajectories in an irrotational shallow waterflow over a flat bed as periodic waves propagate on the water's free surface.Within the linear water wave theory, we show that there are no closed orbitsfor the water particles beneath the irrotational shallow water waves. Dependingon the strength of underlying uniform current, we obtain that some particletrajectories are undulating path to the right or to the left, some are loopingcurves with a drift to the right and others are parabolic curves or curveswhich have only one loop.

Particle trajectories in linearized irrotational shallow water flows