**6. Conclusions**

Unlike the shallow sea risers, there will be some new dynamic phenomena of deep-sea risers under the complex ocean environment. In order to study the effect of top tension on VIV of TTR, the governing equation of VIV of TTR is established, and the dynamic response of TTR is calculated numerically by FDM based on Van der Pol wake-oscillator model. In addition, a validation experiment in the towing tank of Tianjin University is presented. The following conclusions can be drawn:

The natural frequency of TTR increases as the top tension increases, and it is equivalent to increasing the stiffness of TTR.

With the increase of top tension, the lower order modes are excited in the same current, and the vibration displacement of TTR increases and the bending stress decreases.

The dominant frequency of VIV of TTR is controlled by the current velocity and is barely influenced by the top tension.

**Author Contributions:** All four authors contributed equally to forming the objectives of this paper and discussing the numerical simulations, tests, and results. J.Z. performed the simulations and tests; J.Z. and H.G. analyzed the data, and wrote the paper under the supervision of Y.T. and Y.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research is supported by the National Natural Science Foundation of China (11601323, 41906143) and the State Key Laboratory of Hydraulic Engineering Simulation and Safety (Tianjin University-HESS1904).

**Conflicts of Interest:** The authors declare no conflict of interest.
