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Richard Porter

Publications and source records attributed to Richard Porter.

9 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↗
arXiv2023

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↗
arXiv2023

A thin plate approximation for ocean wave interactions with an ice shelf

A variational principle is proposed to derive the governing equations for the problem of ocean wave interactions with a floating ice shelf, where the ice shelf is modelled by the full linear equations of elasticity and has an Archimedean draught. The variational principle is used to form a thin-plate approximation for the ice shelf, which includes water--ice coupling at the shelf front and extensional waves in the shelf, in contrast to the benchmark thin-plate approximation for ocean wave interactions with an ice shelf. The thin-plate approximation is combined with a single-mode approximation in the water, where the vertical motion is constrained to the eigenfunction that supports propagating waves. The new terms in the approximation are shown to have a major impact on predictions of ice shelf strains for wave periods in the swell regime.

physics.geo-ph↗
arXiv2022

Modelling Autler-Townes splitting and acoustically induced transparency in a waveguide loaded with resonant channels

We study acoustic wave propagation in a waveguide loaded with two resonant side-branch channels. In the low frequency regime, one-dimensional models are derived in which the effect of the channels are reduced to jump conditions across the junction. When the separation distance is on the scale of the wavelength, which is the case that is usually considered, the jump conditions involve a single channel and acoustically induced transparency (AIT) occurs due to out-of-phase interferences between the two junctions. In contrast, when the separation distance is subwavelength, a single junction has to be considered and the jump conditions account for the evanescent field coupling the two channels. Such channel pairs can scatter as a dipole resulting in perfect transmission due to Autler - Townes splitting (ATS). We show that combining the two mechanisms offers additional degrees of freedom to control the transmission spectra.

physics.class-ph↗
arXiv2022

Acoustics of a partially partitioned narrow slit connected to a half-plane: case study for exponential quasi-bound states in the continuum and their resonant excitation

Localised wave oscillations in an open system that do not decay or grow in time, despite their frequency lying within a continuous spectrum of radiation modes carrying energy to or from infinity, are known as bound states in the continuum (BIC). Small perturbations from the typically delicate conditions for BIC almost always result in the waves weakly coupling with the radiation modes, leading to leaky states called quasi-BIC that have a large quality factor. We study the asymptotic nature of this weak coupling in the case of acoustic waves interacting with a rigid substrate featuring a partially partitioned slit -- a setup that supports quasi-BIC that exponentially approach BIC as the slit is made increasingly narrow. In that limit, we use the method of matched asymptotic expansions in conjunction with reciprocal relations to study those quasi-BIC and their resonant excitation. In particular, we derive a leading approximation for the exponentially small imaginary part of each wavenumber eigenvalue (inversely proportional to quality factor), which is beyond all orders of the expansion for the wavenumber eigenvalue itself. Furthermore, we derive a leading approximation for the exponentially large amplitudes of the states in the case where they are resonantly excited by a plane wave at oblique incidence. These resonances occur in exponentially narrow wavenumber intervals and are physically manifested in cylindrical-dipolar waves emanating from the slit aperture and exponentially large field enhancements inside the slit. The asymptotic approximations are validated against numerical calculations.

physics.flu-dyn↗
arXiv2018

Recovery of compressively sensed ultrasound images with structured Sparse Bayesian Learning

In this paper, we consider the problem of recovering compressively sensed ultrasound images. We build on prior work, and consider a number of existing approaches that we consider to be the state-of-the-art. The methods we consider take advantage of a number of assumptions on the signals including those of temporal and spatial correlation, block structure, prior knowledge of the support, and non-Gaussianity. We conduct a series of intensive tests to quantify the performance of these methods. We find that by altering the parameters of the structured Sparse Bayesian Learning approaches considered, we can significantly improve the objective quality of the reconstructed images. The results we achieve are a significant improvement upon previously proposed reconstruction techniques. In addition, we further show that by careful choice of parameters, we can obtain near-optimal results whilst requiring only a small fraction of the computational time needed for the best reconstruction quality.

eess.SP↗
arXiv2007

Use of detailed kinetic mechanisms for the prediction of autoignitions

This paper describes how automatically generated detailed kinetic mechanisms are obtained for the oxidation of alkanes and how these models could lead to a better understanding of autoignition and cool flame risks at elevated conditions. Examples of prediction of the occurrence of different autoignition phenomena, such as cool flames or two-stage ignitions are presented depending on the condition of pressure, temperature and mixture composition. Three compounds are treated, a light alkane, propane, and two heavier ones, n-heptane and n-decane.

physics.chem-ph↗