The aspect ratio of slender underwater structures of deep sea platforms such as riser, oil pipelines, tension legs and anchor chains increases with the mining depth increasing, the values of which often approach to 103 order. Investigation results in recent years show that the vortex-induced vibration of the flexible marine risers with large aspect ratio reveals some new phenomena, for example, the vortex-induced wave, multi-mode competition, wide band random vibration, which have brought new challenges to the study of vortex-induced vibration of long flexible risers. In this paper, the dimensionless parameter controlling the wave types of dynamic response of slender risers undergoing vortex-induced vibration is investigated by means of dimensional analysis and finite element numerical simulations (MSC Nastran). Our results indicate that there are three types of response for a slender riser, i.e. standing wave vibration, traveling wave vibration and intermediate state. Based on dimensional analysis the controlling parameter is found to be related to the system damping including fluid damping and structural damping, order number of the locked-in modes and the aspect ratio of riser. Furthermore through numerical simulations and function fitting, the expression and the critical value of the controlling parameter is presented. At last the physical meaning of the parameter is analyzed and discussed.

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