Wave Interactions with Arrays of Bottom-Mounted Circular Cylinders: Investigation of Optical and Acoustical Analogies

Abstract

Wave scattering by arrays of cylinders has received special attention by many authors and analytical solutions have been derived. The investigation of optical and acoustical analogies to the problem of interaction of water waves with rigid and flexible cylinder arrays is the main focus of this thesis. In acoustics, a sound may be attenuated while it propagates through a layer of bubbly liquid. In fact, if the natural frequency of the bubbles is in the range of the wave periods, the attenuation becomes more evident. The ultimate objective of the research described herein is to determine if this phenomenon may also be found in the interaction between water waves and arrays of flexible cylinders. In a first approach, arrays of rigid cylinders are studied in shallow water. The array is treated as an effective medium, which allows for the definition of reflection and transmission coefficients for the array, and theories from Hu and Chan (2005) associated with the Fabry-Perot interferometer are compared against direct computations of wave scattering using the commercial code WAMIT. Reflection and transmission coefficients from WAMIT are evaluated by applying a Maximum Likelihood Method. The results from WAMIT were found to be in good agreement with those obtained from the effective medium theory. Due to observed inconsistencies for short wave periods and small incident angles, the effective width of the medium is defined and corrected. For the case of a flexible cylinder, generalized modes corresponding to deformations of the cylinder's surface are formulated and added to WAMIT's subroutine. Equations of motion are derived from the theory of vibration for thin shells and mass and stiffness matrices are defined. The objective is to maximize wave attenuation from the array of flexible cylinders. Therefore, the natural periods of the "breathing" mode for these cylinders is set in the range of the studied wave periods. Then, material properties, as well as mass and stiffness matrices, are chosen to achieve this effect.