Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

Oscillating-water-column wave energy converters and air turbines: A review

Global food demand is rising, and serious questions remain about whether supply can increase sustainably1 Land-based expansion is possible but may exacerbate climate change and biodiversity loss, and compromise the delivery of other ecosystem services2–6 As food from the sea represents only 17% of the current production of edible meat, we ask how much food we can expect the ocean to sustainably produce by 2050 Here we examine the main food-producing sectors in the ocean—wild fisheries, finfish mariculture and bivalve mariculture—to estimate ‘sustainable supply curves’ that account for ecological, economic, regulatory and technological constraints We overlay these supply curves with demand scenarios to estimate future seafood production We find that under our estimated demand shifts and supply scenarios (which account for policy reform and technology improvements), edible food from the sea could increase by 21–44 million tonnes by 2050, a 36–74% increase compared to current yields This represents 12–25% of the estimated increase in all meat needed to feed 98 billion people by 2050 Increases in all three sectors are likely, but are most pronounced for mariculture Whether these production potentials are realized sustainably will depend on factors such as policy reforms, technological innovation and the extent of future shifts in demand Modelled supply curves show that, with policy reform and technological innovation, the production of food from the sea may increase sustainably, perhaps supplying 25% of the increase in demand for meat products by 2050

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The future of food from the sea.

The scattering of water waves by an array of N bottom-mounted vertical circular cylinders is solved exactly (under the assumption of linear water wave theory) using the method proposed by Spring & Monkmeyer in 1974. A major simplification to this theory has been found which makes the evaluation of quantities such as the forces on the cylinders much simpler. New formulae are given for the first and mean second-order forces together with one for the free-surface elevation in the vicinity of a particular cylinder. Comparisons are made between the exact results shown here and those generated using the approximate method of McIver & Evans (1984). The behaviour of the forces on the bodies in the long-wave limit is also examined for the special case of two cylinders with equal radii.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112090002750

The interaction of waves with arrays of vertical circular cylinders

An accurate three-dimensional numerical model, applicable to strongly non-linear waves, is proposed. The model solves fully non-linear potential flow equations with a free surface using a higher-order three-dimensional boundary element method (BEM) and a mixed Eulerian–Lagrangian time updating, based on second-order explicit Taylor series expansions with adaptive time steps. The model is applicable to non-linear wave transformations from deep to shallow water over complex bottom topography up to overturning and breaking. Arbitrary waves can be generated in the model, and reflective or absorbing boundary conditions specified on lateral boundaries. In the BEM, boundary geometry and field variables are represented by 16-node cubic ‘sliding’ quadrilateral elements, providing local inter-element continuity of the first and second derivatives. Accurate and efficient numerical integrations are developed for these elements. Discretized boundary conditions at intersections (corner/edges) between the free surface or the bottom and lateral boundaries are well-posed in all cases of mixed boundary conditions. Higher-order tangential derivatives, required for the time updating, are calculated in a local curvilinear co-ordinate system, using 25-node ‘sliding’ fourth-order quadrilateral elements. Very high accuracy is achieved in the model for mass and energy conservation. No smoothing of the solution is required, but regridding to a higher resolution can be specified at any time over selected areas of the free surface. Applications are presented for the propagation of numerically exact solitary waves. Model properties of accuracy and convergence with a refined spatio-temporal discretization are assessed by propagating such a wave over constant depth. The shoaling of solitary waves up to overturning is then calculated over a 1:15 plane slope, and results show good agreement with a two-dimensional solution proposed earlier. Finally, three-dimensional overturning waves are generated over a 1:15 sloping bottom having a ridge in the middle, thus focusing wave energy. The node regridding method is used to refine the discretization around the overturning wave. Convergence of the solution with grid size is also verified for this case. Copyright © 2001 John Wiley & Sons, Ltd.

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A fully non‐linear model for three‐dimensional overturning waves over an arbitrary bottom

Step-by-step improvement of MPS method in simulating violent free-surface motions and impact-loads

The authors studied the diffraction, to second order, of plane monochromatic incident gravity waves by a vertically axisymmetric body. The second-order double-frequency diffraction potential is obtained explicitly. A sequence of one-dimensional integral equations along the generator of the body involving free-surface ring sources of general order are formulated and solved for the circumferential components of the second-order potential. The solution is expedited by analytic integrations in the entire local-wave-free outer field of a requisite free-surface integral. The method is validated by extensive convergence tests and comparisons to semi-analytic results for the second-order forces and moments on a uniform vertical circular cylinder. Complete second-order forces, moments, surface pressures and run-up on the vertical cylinder as well as a truncated vertical cone are presented. A summary is given of the most important findings.

The complete second-order diffraction solution for an axisymmetric body Part 1. Monochromatic incident waves

Freely floating-body simulation by a 2D fully nonlinear numerical wave tank

In Part 1 (Kim & Yue 1989), we considered the second-order diffraction of a plane monochromatic incident wave by an axisymmetric body. A ring-source integral equation method in conjunction with a novel analytic free-surface integration in the entire local-wave-free domain was developed. To generalize the second-order theory to irregular waves, say described by a continuous spectrum, we consider in this paper the general second-order wave–body interactions in the presence of bichromatic incident waves and the resulting sum- and difference-frequency problems. For completeness, we also include the radiation problem and second-order motions of freely floating or elastically moored bodies. As in Part 1, the second-order sum- and difference-frequency potentials are obtained explicitly, revealing a number of interesting local behaviours of the second-order pressure. For illustration, the quadratic transfer functions (QTF's) for the sum- and difference-frequency wave excitation and body response obtained from the present complete theory are compared to those of existing approximation methods for a number of simple geometries. It is found that contributions from the second-order potentials, typically neglected, can dominate the total load in many cases.

The complete second-order diffraction solution for an axisymmetric body Part 2. Bichromatic incident waves and body motions

The interaction of oblique monochromatic incident waves with horizontal/inclined/dual porous plates is investigated in the context of two-dimensional linear potential theory and Darcy's law (the normal velocity of fluid passing through a thin porous plate is linearly proportional to the pressure difference across it). The developed theory is verified by both small-scale and full-scale experiments. First, matched eigenfunction expansion (MEE) solutions for a horizontal porous plate are obtained. The relationship between the plate porosity and the porous parameter is obtained from systematic model tests by using six porous plates with different sizes and spacing of circular holes. Secondly, a multi-domain boundary-element method (BEM) using simple-sources (second-kind modified Bessel function) is developed to confirm the MEE solutions and to apply to more general cases including inclined or multiple porous plates. The BEM-based inner solutions are matched to the eigenfunction-based outer solutions to satisfy the outgoing radiation condition in the far field. Both analytical and BEM solutions with the developed empirical porous parameter agree with each other and correlate well with both small-scale data from a two-dimensional wave-tank test and full-scale measurement in a large wave basin. Using the developed predictive tools, wave-absorption efficiency is assessed for various combinations of porosity, water depth, submergence depth, wave heading, and plate/wave characteristics. In particular, it is found that the performance can be improved by imposing the proper inclination angle near the free surface. The optimal porosity is near porosity P=0.1 and the optimal inclination angle is around 10° as long as the plate length is greater than 20% of the wavelength. Based on the selected optimal parameters (porosity=0.1 and inclination angle=11.3°), the effective wave-absorption system for MOERI's square basin is designed.

Moo-Hyun Kim

Papers

Step-by-step improvement of MPS method in simulating violent free-surface motions and impact-loads

The complete second-order diffraction solution for an axisymmetric body Part 1. Monochromatic incident waves

Freely floating-body simulation by a 2D fully nonlinear numerical wave tank

The complete second-order diffraction solution for an axisymmetric body Part 2. Bichromatic incident waves and body motions

Wave absorbing system using inclined perforated plates