## 5 Conclusions  
In this paper, the hydrodynamic loads on semi-submerged cylinder in an oscillatory flow are experimentally studied. To generate the equivalent oscillatory flow, the semi-submerged cylinder is forced to oscillate in various combinations of different amplitudes and periods. The KC number, Stokes number and Froude number respectively ranges from 6.3 to 37.7, from 5434 to 11,364 and from 0.12 to 1.55. The hydrodynamic loads in both IL and CF directions are measured. The main hydrodynamic features are observed and summarized. The empirical prediction formula of the lift force in the CF direction and the relationships among the hydrodynamic coefficient, KC number, Stokes number and Froude number are further investigated. The main conclusions are as follows:  
1. Similar to the results in steady flow, a significant mean downward lift force of semi-submerged cylinder can also be witnessed. The dominant frequencies of fluctuating lift forces are always twice the forced oscillation frequency. 2. Based on the observed load features, a novel empirical prediction formula of the lift force on semi-submerged cylinder under oscillatory flow was first proposed, which expresses the lift forces as proportional to the square of the oscillatory flow velocity in the IL direction. This novel empirical prediction formula is also used to predict the lift force on semi-submerged cylinder. Figure 17: The water surface waveforms and the sketches at the maximum forced motion velocity, the time histories of forced motion and hydrodynamic force in both CF and IL directions changing with KC number under the same Stokes number. (**a,e,i,m**) The pictures of water surface waveforms at the maximum forced motion velocity; (**b,f,j,n**) Corresponding sketches of water surface waveforms; (**c,d,g,h,k,l,o,p**) time histories of forced motion and hydrodynamic forces. formula directly explains the underlying mechanism of twice frequency oscillation observed in lift forces, which also provides a more accurate prediction of dynamic load. This formula can well describe the main lift force features including mean value, oscillation that with frequency twice of the oscillatory flow frequency and the leading phase difference. 3. The maximum lift coefficient can be found to be 1.5, which is larger than the typical values of drag coefficient (\(C_{\text{D}}=1.2\)) for a fully submerged cylinder with infinite depth. Such a large lift force may cause related structure damage and should be considered in real engineering projects. 4. With KC number increasing, the significant evolution trends between drag coefficients, added mass coefficients, lift coefficient and phase difference angle with Froude number under the same KC number were found. It suggests that using the Froude number and KC number to predict the hydrodynamic coefficient is more reasonable when the Stokes number and Froude number are in the conflict for the semi-submerged cylinder. Conceptualization, H.R., S.F. and C.L. ; methodology, H.R. ; validation, M.Z., Y.X., S.D. and S.F. ; formal analysis, H.R. ; investigation, H.R., S.F. ; resources, S.F. ; data curation, H.R. ; writing--original draft preparation, H.R. ; writing--review and editing, H.R. ; visualization, H.R. ; supervision, S.F. ; project administration, S.F. ; funding acquisition, S.F. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (No. 51825903, 51909159), the Shanghai Science and Technology Program (No. 19 XD1402000, 19 JC1412800, 19 JC1412801), the Joint Funds of the National Natural Science Foundation of China (No. U19B2013), the Key Projects for Intergovernmental Cooperation in International Science (No. 2018 YFE0125100). The authors gratefully acknowledge the support from the National Natural Science Foundation of China (No. 51825903, 51909159), the Shanghai Science and Technology Program (No. 19 XD1402000, 19 JC1412800, 19 JC1412801), the Joint Funds of the National Natural Science Foundation of China (No.