Analytical Studies To Reflection And Bragg Resonant Relfection For Linear Waves Propagating Over Submerged Breakwaters

The construction of submerged breakwaters in the coastal region is one of importantengineering methods in coastal protection. Based on the consideration of ecological environ-ment, natural view and hydrophilic nature, submerged breakwaters are widely used in ofshoreengineering such as coastal protection, land reclamation and water diversion.In this thesis, an analytical solution to the modified mild-slope equation (MMSE) forwave reflection by a submerged rectangular breakwater with two scour trenches is explored.The solution is not only valid in the whole wave range from shallow water waves to deepwater waves, but also valid for topographies not restricted to be varying moderately. Based onthe solution, the influence of the width, depth and shape of the scour trench to the reflectioncoefcient is investigated.It is found at first time that, a well-known conclusion obtained by previous scholars thatthe reflection coefcient for wave reflected by a single rectangular breakwater is periodic withkh is incorrect. This incorrectness comes from the approximation error when the long-waveapproximation is used in the linear dispersion relation, phase velocity and group velocity.Our intensive analysis shows that the reflection coefcient is an oscillation function with itsoscillation amplitude varying with kh and finally decaying to zero as kh increases.It is shown by theoretical research and engineering experiments that, for a series of sub-merged breakwater in the coastal region parallel to the coastline, if the wavelength of theincident waves is twice of the distance between two breakwater, most of the incident waveswill be reflection by the water column of Bragg resonance. The research of reflection to seriesof breakwaters is significant to protect coastal and save engineering materials. In the secondpart of this thesis, an analytical modeling to Bragg resonant reflection by a multi-array ofsubmerged triangular breakwaters with curved edges is conducted. An analytical solution tothe MMSE for linear waves reflected by a multi-array of submerged triangular breakwaterswith curved edges is given. Based on the solution, the efect of the height, width, space andnumber of submerged breakwaters to the Bragg resonant reflection is discussed.