Numerical And Experimental Investigation Of Higher Harmonics Induced By Multiple Submerged Objects

Submerged object has been commonly used to protect coastal community and infrastructure. It allows seawater to exchange freely between the sheltered region and the open sea, prevents stagnation and the transportation of sediment of the natural seabed. However, multiple submerged objects are also common in costal engineering, such as submerged reefs, submarine oil pipelines or natural-gas pipelines. In the process of wave propagation and transformation over multiple submerged objects, there would be energy transfer from low frequency to high frequency and the generation of higher bound and free harmonic waves due to nonlinear shoaling effect above the objects, which may induce damage to the coastal structures and sailing condition. When waves propagating over next submerged objects, higher harmonics would be different from the case of single object, which is our major concern in this paper. Therefore, it is of practical importance to consider the effects of multiple submerged objects on the induced higher harmonics.Based on potential theory and time-domain higher-order boundary element method, a two-dimensional fully nonlinear numerical wave flume is developed to investigate nonlinear interactions between regular waves and multiple submerged objects. Fully nonlinear kinematics and dynamics boundary conditions are satisfied on the transient free surface. Two damping layers are deployed at both ends of wave flume to dissipate the transmitted and reflected waves, respectively. A mixed Eulerian-Lagrangian technique combined with the fourth-order Runge-Kutta scheme is used as the time marching process to refresh the surface elevation and potential on the free surface. A two-point method is used to separate free and bound harmonics at the same frequency. Besides, the experiments were taken to verify and investigate the high harmonics generated at the lee side of multiple submerged objects in a wave flume.The developed numerical model was verified by comparing the present numerical results with the experimental results and the other published experimental and numerical data for regular wave interaction with different kind of submerged objects, respectively. Then, the numerical tests are performed to study the influences of submerged depths, size of object and the static water depth on the generation of higher harmonics in the case of single object. As for interaction between waves and multiple submerged objects, the extensive numerical tests and experiments are performed to study the influences of submergence, gap distance and geometric shape of submerged structures on the generation of higher harmonics under strong nonlinear wave conditions.