arXiv subjects

Lloyd Dafydd

Publications and source records attributed to Lloyd Dafydd.

3 recordsLinked to original sources

arXiv2026

Wave propagation through periodic arrays of freely floating rectangular floes

The two-dimensional propagation of small-amplitude waves through an infinite periodic array of freely-floating rectangular floes is considered under the assumptions of inviscid linearised wave theory. Fluid gaps between adjacent floes allow a complex interaction of the fluid with heave, surge and pitch motions. In particular, the presence of fluid resonance in the vertical channels between floes has a significant influence on wave propagation around certain critical frequencies. Bloch-Floquet theory is used and encodes the wavenumber for propagating waves into periodic boundary conditions. Solutions of the resulting boundary-value problem posed in a fundamental cell are formulated in terms of integral equations in which the three rigid body modes of the problem are treated individually. The dispersion relationship between frequency and wavenumber is expressed in terms of the vanishing of a 3 x 3 determinant which encodes the hydrodynamic coupling between the modes. Accurate numerical solutions are determined using Galerkin's method to approximate solutions to the integral equations. A particular focus of the paper is determining simple explicit approximations for the dispersion relation by assuming the gap between adjacent floes is small compared to the submerged draft of the floe. Approximations are shown to compare well to numerical results for a large range of gap sizes and some surprising results emerge for low-frequency wave propagation. This is particularly relevant to the application area that motivates this study: the modelling of wave propagation through broken ice. Supplementary Material: https://github.com/LloydDafydd/pre-prints/blob/caa889f1ee1eb51980785271bd8d27ce5213bda7/wave-propogation-fff-supp-mat.pdf

physics.flu-dyn↗

arXiv2025

On the attenuation of waves through broken ice of randomly-varying thickness on water of finite depth

The recent work of Dafydd and Porter [2024] on the attenuation of waves propagating through floating broken ice of random thickness is extended to consider water of non-shallow depth. A theoretical model of broken floating ice is analysed using a multiple scales analysis to provide an explicit expression for the attenuation of waves as they propagate from a region of constant thickness ice into a semi-infinite region of ice whose thickness is a slowly-varying random function of distance. Theoretical predictions are shown to compare well to numerical simulations of scattering over long finite regions of ice of randomly-varying thickness computed from an approximate depth-averaged model derived under a mild-slope assumption. The theory predicts a low-frequency attenuation proportional to the eighth power of frequency and a roll-over effect at higher frequencies. The relationship between the results and field measurements are discussed.

physics.ao-ph↗

arXiv2024

Attenuation of long waves through regions of irregular floating ice and bathymetry

Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is presented which corrects this and is shown to conserve energy. New theoretical predictions are supported by numerical results which use averaging of simulations of wave scattering over finite sections of random bathymetry for which transfer matrix eigenvalues are used to accurately measure decay. The model of wave propagation used in this paper is derived from a linearised long wavelength assumption whereby depth averaging leads to time harmonic waves being represented as solutions to a simple ordinary differential equation. In this paper it is shown how this can be adapted to incorporate a model of a continuous covering of the surface by fragmented floating ice. Attenuation of waves through broken ice of random thickness is then analysed in a similar manner as bed variations previously and some comparisons are made with published field data for attenuation of waves in the marginal ice zones. Key features of the data are reproduced by theory including the attenuation being proportional to a power of frequency between 2 and 4 as well as capturing the "roll-over effect" at high frequencies.

physics.flu-dyn↗