Experiments are performed for the characteristics of internal waves generated by four horizontally towed models, including a sphere and three slender models with different aspect ratios in a density stratified fluid with a strong halocline. The Reynolds number ranges within 3500 < Re = UD/ν < 126 000, and the Froude number ranges within 0.4 < Fr = U/N_maxD < 18. Based on the time histories of the density perturbation and analysis of the correlation velocity of internal waves generated by the towed models, it is shown that the body-generated waves are stationary multiple-mode Lee waves, while the wake-generated waves are non-stationary wake waves mainly produced by the large-scale coherent structure in turbulent wakes acting as a moving excitation source. The transition between body-generated and wake-generated internal waves occurs at a critical Froude number Fr_c which is linearly dependent on the model aspect ratio. Before the transition, when the wave height H changes with the variation of Fr, a peak value of H can be observed and its corresponding Froude number Fr_p increases linearly with growing aspect ratio. After the transition, the Froude number Fr_iw associated with the internal wave correlation velocity fluctuates within a certain range. The wave height linearly increases with increasing Fr regardless of the aspect ratios, and the wave pattern is dominated by a non-stationary wake-generated wave. According to the experimental configuration, a theoretical model is proposed to simulate the body-generated and wake-generated internal waves. The numerical results obtained by this theoretical model show general agreement with the experiments.

The present work aims to investigate the free surface wave system of a volume source translating in a stratified fluid. In this paper, a modified model is established with linearized governing equations and the free surface condition. This modified model can describe both the internal and surface waves excited by a volume source with arbitrary density profiles. The wave characteristics that are analyzed include the half-wedge angle, crestlines, the maximum amplitude, and the apparent angle. The results show that the entire wave system is complex and composed by an infinite number of single wave modes. The different modes can be divided into surface modes (mode number n = 0) and internal modes (n ≥ 1). It is found that internal modes have many similarities to each other but are quite different from surface modes. In the subcritical area [$Fr<F{r}_n$ , where the Froude number is $Fr=U/\sqrt{gL}$ and the critical Froude number of mode n is $F{r}_n=c_{pn}\left(0\right)/\sqrt{gL}$ ], the wave structure of the nth mode contains divergent and transverse waves, and the half-wedge angle of surface mode waves increases from the Kelvin-wave angle of 19°28′ to 90°, while the half-wedge angle of internal mode waves increases from 0° to 90°. In the supercritical domain (Fr ≥ Fr_n), there are only divergent waves, and the half-wedge angle of all mode waves decays as sin⁻¹(Fr_n/Fr). The amplitude of waves is related to the velocity of the source, the location of the source, the depth of the fluid, the Brunt–Väisälä frequency, the thickness of the pycnocline, and the center location of the pycnocline. The effects of these factors have been discussed in this paper. The apparent angle, which indicates the highest peak of waves, is also discussed. The results show that the apparent angle of all mode waves scales like Fr⁻¹ at large Froude numbers.

Scale effect of ISWs loads on Floating Production Storage and Offloading (FPSO) is studied in this paper. The application conditions of KdV, eKdV and MCC ISWs theories are used in the numerical method. The depthaveraged velocities induced by ISWs are used for the velocity-inlet boundary. Three scale ratio numerical models λ=1, 20 and 300 were selected, which the scale ratio is the size ratio of numerical models to the experimental model. The comparisons between the numerical and former experimental results are performed to verify the feasibility of numerical method. The comparisons between the numerical and simplified theoretical results are performed to discuss the applicability of the simplified theoretical model summarized from the load experiments. Firstly, the numerical results of λ=1 numerical model showed a good agreement with former experimental and simplified theoretical results. It is feasible to simulate the ISWs loads on FPSO by the numerical method. Secondly, the comparisons between the results of three scale ratio numerical models and experimental results indicated that the scale ratios have more significant influence on the experimental horizontal forces than the vertical forces. The scale effect of horizontal forces mainly results from the different viscosity effects associated with the model’s dimension. Finally, through the comparisons between the numerical and simplified theoretical results for three scale ratio models, the simplified theoretical model of the pressure difference and friction forces exerted by ISWs on FPSO is applied for large-scale or full-scale FPSO.