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"Porter, R"
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An extended linear shallow-water equation
An extension to the classical shallow-water equation (SWE) is derived that exactly satisfies the bed condition and can be regarded as an approximation to wave scattering at the next order in the small parameter
$(h/\\unicode[STIX]{x1D706})^{2}$
(depth to wavelength ratio squared). In the frequency domain, the extended SWE shares the same simple structure as the standard SWE with coefficients modified by terms relating to the bed variation. In three dimensions the governing equation demonstrates that variable topography gives rise to anisotropic effects on wave scattering not present in the standard SWE, with consequences for the design of water wave metamaterials. Numerical examples illustrate that approximations to wave scattering using the extended SWE are significantly improved in comparison with the standard SWE.
Journal Article
Water wave propagation through arrays of closely spaced surface-piercing vertical barriers
This paper presents and compares two different approaches to solving the problem of wave propagation across a large finite periodic array of surface-piercing vertical barriers. Both approaches are formulated in terms of a pair of integral equations, one exact and based on a spacing $\\delta > 0$ between adjacent barriers and the other approximate and based on a continuum model formally developed by using homogenisation methods for small $\\delta$. It is shown that the approximate method is simpler to evaluate than the exact method which requires eigenvalues and eigenmodes related to propagation in an equivalent infinite periodic array of barriers. In both methods, the numerical effort required to solve problems is independent of the size of the array. The comparison between the two methods allows us to draw important conclusions about the validity of homogenisation models of plate array metamaterial devices. The practical interest in this problem stems from the result that for an array of barriers there exists a critical value of radian frequency, $\\omega _c$, dependent on $\\delta$, below which waves propagate through the array and above which it results in wave decay. When $\\delta \\to 0$, the critical frequency is given by $\\omega _c = \\sqrt {g/d}$, where $d$ is the plate submergence and $g$ is the acceleration due to gravity, which relates to the resonance in narrow channels and is an example of local resonance, studied extensively in metamaterials. The results have implications for proposed schemes to harness energy from ocean waves and other problems related to rainbow trapping and rainbow reflection.
Journal Article
Wave scattering by an array of metamaterial cylinders
In this paper, a semi-analytical model based on linear potential flow theory and an eigenfunction expansion method is developed to study wave scattering by an array of structured cylinders in water of finite depth. Each cylinder is formed by a closely spaced array of thin vertical plates, between which fluid can flow, extending through the depth. In order to consider the wave attenuation and energy dissipation in narrow gaps between the thin vertical plates, a damping mechanism is introduced at the surface of the fluid occupied by the structured cylinders. In addition to a direct calculation of the energy dissipation, an indirect method based on Kochin functions is derived with the employment of energy identities. The present model is shown to be in excellent agreement with both the published data and those obtained by using different methods. The validated model is then applied to study the effect of a pair of structured cylinders on wave focusing/blocking, scattered far-field amplitude and wave power dissipation. Results show that wave focusing/blocking can be achieved by the appropriate choice of plate alignment. The structured cylinders hold profound potential for wave power extraction.
Journal Article
The man behind the bow tie : Arthur Porter on business, politics and intrigue
Arthur Porter tells his own story, beginning with his boyhood in Sierra Leone, his rise through the medical, corporate and political arenas in Canada, through to the confines of La Joya Prison where he is detained on charges of fraud.
Book
Inequitable patterns of US flood risk in the Anthropocene
Current flood risk mapping, relying on historical observations, fails to account for increasing threat under climate change. Incorporating recent developments in inundation modelling, here we show a 26.4% (24.1–29.1%) increase in US flood risk by 2050 due to climate change alone under RCP4.5. Our national depiction of comprehensive and high-resolution flood risk estimates in the United States indicates current average annual losses of US$32.1 billion (US$30.5–33.8 billion) in 2020’s climate, which are borne disproportionately by poorer communities with a proportionally larger White population. The future increase in risk will disproportionately impact Black communities, while remaining concentrated on the Atlantic and Gulf coasts. Furthermore, projected population change (SSP2) could cause flood risk increases that outweigh the impact of climate change fourfold. These results make clear the need for adaptation to flood and emergent climate risks in the United States, with mitigation required to prevent the acceleration of these risks.Climate change is increasing flood risk, yet models based on historical data alone cannot capture the impact. Granular mapping of national flood risk shows that losses caused by flooding in the United States will increase substantially by 2050 and disproportionately burden less advantaged communities.
Journal Article
Crop responses to climatic variation
The yield and quality of food crops is central to the well being of humans and is directly affected by climate and weather.
Initial studies of climate change on crops focussed on effects of increased carbon dioxide (CO
Journal Article