Study on the Propagation and Focusing Mechanism of Long Waves over A Submerged Atoll

An analytical solution for long waves propagating over a submerged atoll is established. The atolls involved in this study are annular coral reefs with large lagoons in the middle, and the expression of the cross section is a trinomial function of the radial distance, i.e., h=ar(2s)-br~s+h_0, where s is the positive rational number. This analytical solution extends the theory by Wang et al.(2018) as s is no longer limited to s=2/m, where m is the positive integer. In addition, by adjusting the terrain parameters properly, the analytic solution can be degenerated to describe the wave propagation over topography with a hump or pit. According to the relationship between wave rays and wave energy, the distribution characteristics and formation mechanism of energy over the topography are expounded. When the lagoon is non-existent, all wave rays converge at the x-axis, which results in an abrupt amplification of the wave amplitude around the convergence point. When a lagoon is mounted on the top of the atoll, the rays are scattered due to the refraction of the lagoon, and only some rays converge at the symmetrical axis and the ridges on both sides,which results in the amplification of wave amplitudes in these areas.

Calculating the Wave Force on Partially Immersed Large-Scale Horizontal Cylinders

Large-scale interceptors constitute the main structure of offshore self-driven floating marine litter collection devices,and the structural stability of such interceptors under the action of waves directly influences the overall safety of the device.When the ratio of the diameter of a horizontal cylinder in such interceptors to the incident wavelength is larger than 0.25,the wave force can be calculated by using the diffraction theory,by considering the problem as that of the interaction between the waves and a partially immersed large-scale horizontal cylinder.In this study,an analytical approach to calculate the wave force on a partially immersed large-scale horizontal cylinder was formulated by using the stepwise approximation method.Physical model tests were conducted to investigate the effects of different factors(wave height,period,and immersion depth)on the wave force on a large-scale horizontal cylinder under conditions involving short-period waves.The results show that both horizontal and vertical wave forces on the cylinder increase as the wave height(immersion depth)increases in most cases.The vertical wave force decreases with the decrease of the period.For the horizontal wave force,it increases with the decrease of the period when the wavelength is larger than the diameter of the cylinder and decreases with the decrease of the period when the wavelength is smaller than the diameter of the cylinder.