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  • Cambridge University Press  (18)
  • American Institute of Physics (AIP)
  • 2005-2009  (18)
  • 1
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    Approximations to the scattering of water waves by steep topography (2006)
    Cambridge University Press
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    Publication Date: 2006-08-14
    Description: A new method is developed for approximating the scattering of linear surface gravity waves on water of varying quiescent depth in two dimensions. A conformal mapping of the fluid domain onto a uniform rectangular strip transforms steep and discontinuous bed profiles into relatively slowly varying, smooth functions in the transformed free-surface condition. By analogy with the mild-slope approach used extensively in unmapped domains, an approximate solution of the transformed problem is sought in the form of a modulated propagating wave which is determined by solving a second-order ordinary differential equation. This can be achieved numerically, but an analytic solution in the form of a rapidly convergent infinite series is also derived and provides simple explicit formulae for the scattered wave amplitudes. Small-amplitude and slow variations in the bedform that are excluded from the mapping procedure are incorporated in the approximation by a straightforward extension of the theory. The error incurred in using the method is established by means of a rigorous numerical investigation and it is found that remarkably accurate estimates of the scattered wave amplitudes are given for a wide range of bedforms and frequencies. © 2006 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 2
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    Private Authority, Technical Authority, and the Globalization of Accounting Standards (2005)
    Cambridge University Press
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    Publication Date: 2005-12-01
    Description: This article starts by highlighting the significance of two forms of authority'private and technical authority'that are becoming increasingly important relative to public authority, which traditionally has been considered the only relevant form of authority in international affairs. It then suggests that public, private and technical authority are related to one another not by the erasure of one by another, but rather through a process of politicized functional differentiation. Functional differentiation involves the transformation of multi-functional units into a set of more autonomous units that are related to one another in specific limited ways. The article explores differentiation between and within each of the three types of authority in the globalization of accounting, and the role of power as well. It challenges the view that globalization necessarily involves a centralized exercise of power or an elimination of differences.
    Print ISSN: 1369-5258
    Electronic ISSN: 1469-3569
    Topics: Political Science , Economics
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  • 3
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    Multi-mode approximations to wave scattering by an uneven bed (2006)
    Cambridge University Press
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    Publication Date: 2006-05-24
    Description: Approximations to the scattering of linear surface gravity waves on water of varying quiescent depth are investigated by means of a variational approach. Previous authors have used wave modes associated with the constant depth case to approximate the velocity potential, leading to a system of coupled differential equations. Here it is shown that a transformation of the dependent variables results in a much simplified differential equation system which in turn leads to a new multi-mode 'mild-slope' approximation. Further, the effect of adding a bed mode is examined and clarified. A systematic analytic method is presented for evaluating inner products that arise and numerical experiments for two-dimensional scattering are used to examine the performance of the new approximations. © 2006 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 4
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    Wave-free motions of isolated bodies and the existence of motion-trapped modes (2007)
    Cambridge University Press
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    Publication Date: 2007-07-25
    Description: A motion trapping structure can be defined as a freely floating structure under natural or externally applied restoring forces, on or below the free surface of a heavy fluid extending to infinity in at least one direction, which generates a persistent local time-harmonic oscillation of the fluid of finite energy at a particular frequency, due to its own motion at that frequency. Such an oscillation is termed a motion-trapped mode. In this paper it is shown, using accurate numerical computations, that a submerged circular cylinder making forced time-harmonic two-dimensional heave or sway motions of small amplitude in a fluid of either finite or infinite depth, can create a local flow field in which no waves radiate to infinity at particular frequencies and depths of submergence of the cylinder. By tethering such a buoyant cylinder to the bottom of a fluid of finite depth, using a vertical inelastic mooring line, it is shown, by suitable choice of buoyancy and length of tether, how the cylinder, moving freely under its mooring forces, can operate as a motion trapping structure. Such a cylinder would, if displaced from its equilibrium position and released, ultimately oscillate indefinitely at the trapped mode frequency. This simple geometry is the first example of a submerged isolated motion trapping structure free to move under its natural mooring forces. © 2007 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 5
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    Examples of trapped modes in the presence of freely floating structures (2008)
    Cambridge University Press
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    Publication Date: 2008-07-10
    Description: A freely floating motion-trapping structure can be defined as one or more rigid bodies floating on the surface of a fluid which extends to infinity in at least one direction, whose free motion under its natural hydrostatic restoring force is coupled to that of the surrounding fluid in such a way that no waves are radiated to infinity. The resulting local time-harmonic oscillation of the structure and the surrounding fluid is called a motion-trapped mode. Such a structure would, if displaced slightly from its equilibrium position and released, ultimately oscillate indefinitely at the trapped-mode frequency. Previous examples of motion-trapping structures have been devised using an inverse approach in which the shape of pairs of such structures is determined implicitly by sketching certain streamlines. In this paper an alternative direct approach to the construction of motion-trapping structures in the form of a pair of identical floating cylinders of rectangular cross-section in two dimensions is presented. It is also shown that a thick-walled axisymmetric heaving circular cylinder can act as a motion-trapping structure. © 2008 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 6
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    Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles. By P. A. Martin. Cambridge University Press, 2006. 450 pp., ISBN 0521 865549. £75 (2007)
    Cambridge University Press
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    Publication Date: 2007-05-21
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 7
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    Water-wave trapping by floating circular cylinders (2009)
    Cambridge University Press
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    Publication Date: 2009-08-25
    Description: Under the assumptions of the linearized theory of small-amplitude water waves, it is proved that plane waves, normally incident upon a semi-immersed cylinder of uniform circular cross-section floating freely on the surface of a fluid of infinite depth, are capable of being totally reflected. Numerically, this is shown to occur at a single non-dimensional frequency. This remarkable result is used to construct examples of motion-trapped modes, involving pairs of freely floating cylinders moving either in phase or out of phase. The former case is equivalent to having a motion-trapped mode for a single such cylinder next to a rigid vertical wall. In the latter out-of-phase case, the pair of cylinders move as if they form the wetted sections of a single rigidly connected catamaran structure. © 2009 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 8
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    Second-order sloshing over an arbitrary bed (2005)
    Cambridge University Press
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    Publication Date: 2005-02-10
    Description: The two-dimensional problem of the free sloshing of an inviscid fluid in a vertically walled tank with an arbitrary bed shape is solved at both first and second order in the Stokes expansion of the velocity potential. The approach employed at both orders uses Green's functions for a flat bed in conjunction with the Cauchy-Riemann equations to derive integral equations for the tangential flux along the varying bed. The first- and second-order potentials everywhere in the fluid may then be related to these fluxes. Significant analytic progress is made with the calculation of various contributions to the integral equations at second order. The equations at first and second order are ultimately solved using a variational principle equivalent to the Galerkin method, giving efficient and accurate results. In particular, the work involved in determining the second-order solution is no more intensive than in solving the first-order problem. The first-order solution is shown to reproduce known results for specific bed shapes. The method is applied to a range of bed shapes and the second-order correction to the free-surface elevation is illustrated. © 2005 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 9
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    Wave scattering in a two-layer fluid of varying depth (2005)
    Cambridge University Press
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    Publication Date: 2005-02-10
    Description: The scattering of waves in a two-layer fluid of varying mean depth is examined in a three-dimensional context using linear theory. A variational technique is used to construct a particular type of approximation which has the effect of removing the vertical coordinate and reducing the problem to two coupled partial differential equations in two independent variables. A transformation of this differential equation system leads to a particularly simple approximate representation of the scattering process. The theory is applied to two-dimensional scattering, for which a set of symmetry relations is derived. A selection of numerical results is presented to illustrate the principle interest in the problem, namely the energy transfer between surface and interfacial waves induced by bed undulations. © 2005 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 10
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    A multi-mode approximation to wave scattering by ice sheets of varying thickness (2007)
    Cambridge University Press
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    Publication Date: 2007-05-02
    Description: The problem of linear wave scattering by an ice sheet of variable thickness floating on water of variable quiescent depth is considered by applying the Rayleigh-Ritz method in conjunction with a variational principle. By using a multi-mode expansion to approximate the velocity potential that represents the fluid motion, Porter & Porter (J. Fluid Mech. vol. 509, 2004, p. 145) is extended and the solution of the problem may be obtained to any desired accuracy. Explicit solution methods are formulated for waves that are obliquely incident on two-dimensional geometry, comparisons are made with existing work and a range of new examples that includes both total and partial ice-cover is considered. © Cambridge University Press 2007.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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