Wave interaction with metamaterials and cracked ice sheets

Abstract

This thesis is dichotomised into two main types of problems which are briefly introduced in Chapter 1. In the first, linear water wave theory is used to understand the interaction of small amplitude gravity waves with a particular type of submerged metamaterials in finite water depth. Within this study, metamaterials are viewed as arrays of closely-spaced thin vertical barriers protruding from the sea bed.
A summary of linear water wave theory in the framework of this study, is provided in Chapter 2, followed by the problem of scattering of obliquely-incident plane waves by a submerged metamaterial, in Chapter 3. Three different barrier orientations are analysed, whose solutions require different mathematical techniques. Whereas these all ultimately require numerical computation, simplified expressions for the reflected and transmitted wave amplitudes are derived explicitly under a shallow water assumption. The focus of this chapter relates to the unusual wave propagation properties of the plate array, particularly that of negative refraction. In Chapter 4 we consider a final example of wave interaction with an immersed plate array. The plate array is made to extend fully through the water depth and occupies periodic arrangement of triangular inclusions embedded into a wall. The inclusion of damping in a water wave setting or an analogous acoustic setting allows us to consider the broadbanded absorption characteristics of this device.
In the second part of this thesis, the scattering of incident waves by an open water lead in an otherwise infinite and thin ice sheet on water, is considered. A variety of problems, with different degree of complexity are solved with the ultimate goal being to derive a model capable of describing energy loss due to viscous effects in narrow gaps between ice floes. The scattering problem of an obliquely-incident flexural wave across a crack of finite width, is considered in Chapter 5. A much simpler closed-form solution is derived in the case when the two semi-infinite ice sheets are separated by a narrow crack. Finally, the fluid in the narrow gap between the two vertical faces of opposing ice sheets is replaced by a viscous fluid which complicates the interaction between the ice sheet and the fluid and introduces dissipation. A basic outline calculation is made to determine if this proposed model for energy dissipation fits reported field data for wave attenuation in regions of broken ice.

Date of Award	12 May 2022
Original language	English
Awarding Institution	University of Bristol
Supervisor	Richard Porter (Supervisor)