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Pumped storage hydropower plants are renewable energy systems that are effective in saving energy and solving electricity peak-on shortage. Seawater pumped storage hydropower plants are a novel type of pumped storage hydropower plant specifically supplying electric power for ocean islands with the support of solar energy and wind energy. Compared with traditional pumped storage hydropower plants that are constructed on the mainland, seawater pumped storage hydropower plants should take the influence of the complex marine environment, such as extreme waves and winds, into consideration. Taking the characteristics of waves near islands in the East China Sea as an example, we explored the transient hydraulic characteristics in the draft tube of a pump turbine under wave disturbance using a sliding grid interface and the detached eddy simulation (DES) turbulence model. By analyzing the characteristics of unsteady flow in the draft tube, the vortex characteristics under the Q criterion, the frequency characteristics of the pressure pulsation, the evolution law of the internal fluid, and the propagation law of the pressure pulsation were explored. For the situation without wave disturbance, an obvious eccentric vortex in the straight cone section of the draft tube was observed in the case where the opening of the guide vane was small. With the increase in the opening of the guide vane, the eccentric vortex gradually dissipated. For the situation with wave disturbance, the main frequency of the draft tube equaled the frequency of the wave disturbance, the maximum pressure pulsation at the selected monitoring points increased 5 to 15 times, and the superposition of the wave pressure pulsation signals and the draft tube pressure pulsation produced more low-frequency, high-amplitude pressure pulsation signals. Even though the pressure pulsation frequency spectrum varied a lot, the frequency domain of the pressure pulsation without wave disturbance still existed. In addition, the wave disturbance merely varied with the pressure of the draft tube. The influence of wave disturbance on the pressure distribution in the draft tube was relatively small. The results can provide a reference for the operation of seawater pumped storage hydropower plants.