Viscous-Flow-Based Analysis of Wave Near-Trapped in a Four-Cylinder Structure

The hydrodynamic analysis of multi-floating bodies is important and widely used in marine engineering. In this study, we systematically simulated the wave diffraction problem of a fixed vertical four-cylinder structure in regular waves in the time domain in a viscous numerical wave tank. The hydrodynamic interaction of waves with a bottom-mounted structure consisting of four vertical cylinders arranged at the corners of a square shows a complicated interference phenomenon. In this paper, we illustrate and analyze the run-up around the structure and the corresponding wave forces. To investigate the viscous effect on the near-trapping phenomenon, we pay particular attention to investigating the waves near-trapped inside the four-cylinder structure,and make a comparative study of the viscous-and inviscid-flow solutions with the experimental measurements. The results show that the maximum wave elevation occurs on the inner side of the leeside cylinder, and that the wave elevations on the outer side of the cylinders are lower than those on the inner side. We can conclude that viscosity has an obvious damping effect on wave elevations inside the structure. The cylinders show a tendency to drift apart from each other when the near-trapping phenomenon occurs.

Focusing phenomenon and near-trapped modes of SH waves

In this study, the null-field boundary integral equation method （BIEM） and the image method are used to solve the SH wave scattering problem containing semi-circular canyons and circular tunnels. To fully utilize the analytical property of Circular geometry, the polar coordinates are used to expand the closed-form fundamental solution to the degenerate kernel, and the Fourier series is also introduced to represent the boundary density. By collocating boundary points to match boundary condition on the boundary, a linear algebraic system is constructed. The unknown coefficients in the algebraic system can be easily determined. In this way, a semi-analytical approach is developed. Following the experience of near-trapped modes in water wave problems of the full plane, the focusing phenomenon and near-trapped modes for the SH wave problem of the half-plane are solved, since the two problems obey the same mathematical model. In this study, it is found that the SH wave problem containing two semi-circular canyons and a circular tunnel has the near-trapped mode and the focusing phenomenon for a special incident angle and wavenumber. In this situation, the amplification factor for the amplitude of displacement is over 300.

Effect of pontoons on free surface elevation around a TLP platform

Tension leg platform(TLP)is a typical compliant offshore structure for oil/gas resources exploitation.In the design process,the prediction of the free surface elevation is of great importance for the determination of the air gap.So far,the existing researches for predicting the air gap of the TLPs focus on the supporting columns while pay little attention to the horizontal pontoons.For the second order diffraction problem or long incident wave condition,the velocity potential decays slowly with water depth and the effect of pontoons should not be neglected.Herein the effect of pontoons on the diffracted wave field in the vicinity of a TLP platform is investigated in this study.The diffraction of regular waves by a square array of truncated cylinders and a whole TLP structure is studied in detail by using both the linear and the second-order diffraction theory.Numerical calculation is performed for the free surface elevation and wave run up.Numerical results show that the near-trapping phenomenon can occur inside the TLP and leads to significantly increased wave height.To study the effect of pontoons on the free surface elevation comparisons are carried out between the results of these two structures with and without pontoons.It is found that pontoons have an appreciable effect on the diffracted wave field for long incident regular waves and increase the largest response notably when the near-trapping phenomenon occurs at the second-order.