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  • 1
    Electronic Resource
    Electronic Resource
    Strongly Nonlinear Waves (1982)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Fluid Mechanics 14 (1982), S. 39-60 
    Details
    ISSN: 0066-4189
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.fl.14.010182.000351
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    Paper (German National Licenses)
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  • 2
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    Some Results for Surface Gravity Waves on Shear Flows (1973)
    Oxford University Press
    Details
    Publication Date: 1973-01-01
    Print ISSN: 0272-4960
    Electronic ISSN: 1464-3634
    Topics: Mathematics
    Published by Oxford University Press on behalf of Institute of Mathematics and its Applications.
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  • 3
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    Strongly Nonlinear Waves (1982)
    Annual Reviews
    Details
    Publication Date: 1982-01-01
    Print ISSN: 0066-4189
    Electronic ISSN: 1545-4479
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Annual Reviews
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  • 4
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    A Fourier method for solving nonlinear water-wave problems: application to solitary-wave interactions (1982)
    Cambridge University Press
    Details
    Publication Date: 1982-05-01
    Description: A numerical method is developed for solution of the full nonlinear equations governing irrotational flow with a free surface and variable bed topography. It is applied to the unsteady motion of non-breaking water waves of arbitrary magnitude over a horizontal bed. All horizontal variation is approximated by truncated Fourier series. This and finite-difference representation of the time variation are the only necessary approximations. Although the method loses accuracy if the waves become sharp-crested at any stage, when applied to non-breaking waves the method is capable of high accuracy.The interaction of one solitary wave overtaking another was studied using the Fourier method. Results support experimental evidence for the applicability of the Korteweg-de Vries equation to this problem since the waves during interaction are long and low. However, some deviations from the theoretical predictions were observed - the overtaking high wave grew significantly at the expense of the low wave, and the predicted phase shift was found to be only roughly described by theory. A mechanism is suggested for all such solitary-wave interactions during which the high and fast rear wave passes fluid forward to the front wave, exchanging identities while the two waves have only partly coalesced; this explains the observed forward phase shift of the high wave. © 1982, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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  • 5
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    Potential-flow instability theory and alluvial stream bed forms (2000)
    Cambridge University Press
    Details
    Publication Date: 2000-09-10
    Description: The present work constitutes a reassessment of the role of potential-flow analyses in describing alluvial-bed instability. To facilitate the analyses, a new potential-flow description of unsteady alluvial flow is presented, with arbitrary phase lags between local flow conditions and sediment transport permitted implicity in the flow model. Based on the present model, the explicit phase lag between local sediment transport rate and local flow conditions adopted for previous potential-flow models is shown to be an artificial measure that results in model predictions that are not consistent with observed flow system behaviour. Previous potential-flow models thus do not provide correct descriptions of alluvial flows, and the understanding of bed-wave mechanics inferred based upon these models needs to be reassessed. In contrast to previous potential-flow models, the present one, without the use of an explicit phase lag, predicts instability of flow systems of rippled or dune-covered equilirium beds. Instability is shown to occur at finite growth rates for a range of wavelengths via a resonance mechanism occurring for surface waves and bed waves travelling at the same celerity. In addition, bed-wave speeds are predicted to decrease with increasing wavelength, and bed waves are predicted to grow and move at faster rates for flows of larger Froude numbers. All predictions of the present potential-flow model are consistent with observations of physical flow systems. Based on the predicted unstable wavelengths for a given alluvial flow, it is concluded that bed waves are not generated from plane bed conditions by any potential-flow instability mechanism. The predictions of instability are nevertheless consistent with instances of accelerated wave growth occurring for flow systems of larger finite developing waves. Potential-flow description of alluvial flows should, however, no longer form the basis of instability analyses describing bed-form (sand-wavelet) generation from flat bed conditions.
    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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    A Fourier approximation method for steady water waves (1981)
    Cambridge University Press
    Details
    Publication Date: 1981-03-01
    Description: A method for the numerical solution of steadily progressing periodic waves on irrotational flow over a horizontal bed is presented. No analytical approximations are made. A finite Fourier series, similar, to Dean’s stream function series, is used to give a set of nonlinear equations which can be solved using Newton’s method. Application to laboratory and field situations is emphasized throughout. When compared with known results for wave speed, results from the method agree closely. Results for fluid velocities are compared with experiment and agreement found to be good, unlike results from analytical theories for high waves. The problem of shoaling waves can conveniently be studied using the present method because of its validity for all wavelengths except the solitary wave limit, using the conventional first-order approximation that on a sloping bottom the waves at any depth act as if the bed were horizontal. Wave period, energy flux and mass flux are conserved. Comparisons with experimental results show good agreement. © 1981, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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  • 7
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    Cnoidal waves and bores in uniform channels of arbitrary cross-section (1973)
    Cambridge University Press
    Details
    Publication Date: 1973-05-08
    Description: A steady nonlinear dispersive wave theory is developed in terms of three important invariants of channel flow: discharge, energy, and momentum flux. As such, the work is an extension of Benjamin & Lighthill's approach for rectangular channels. Considering the differential equation obtained, we examine the behaviour of flows and wave systems in arbitrary channels for changes of energy and momentum. In particular, the bore problem is studied, and previous approaches to this problem, using linear wave theory, are seen to be invalid. The present theory describes several phenomena of open-channel flow, explains a scatter in previously obtained experimental results, and enables simple design recommendations to be made for channels in which stationary or moving bores are expected. While this work does describe the variation of physical quantities across the channel section, there are some important three-dimensional phenomena, noted experimentally, which remain unexplained. © 1973, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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  • 8
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    Wave forces on vertical bodies of revolution (1978)
    Cambridge University Press
    Details
    Publication Date: 1978-03-01
    Description: The axisymmetry of a body which is diffracting water waves may be exploited to give a line integral equation to be solved for the scattered wave field and forces on the body. Each term in a previously established surface integral equation is shown to be expressible as a Fourier series, which is then integrated once analytically. The resulting one-dimensional equation is shown to possess singularities, previously ignored by Black (1975). This equation, with series transformations and subtraction of singularities such that all series are quickly convergent and that it has to be solved only along a curve, reduces computational effort by some three orders of magnitude. Results obtained by this method give good agreement with previous analytical and experimental results, even if a rather coarse numerical approximation is used. © 1978, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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  • 9
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    A high-order cnoidal wave theory (1979)
    Cambridge University Press
    Details
    Publication Date: 1979-09-11
    Description: A method is outlined by which high-order solutions are obtained for steadily progressing shallow water waves. It is shown that a suitable expansion parameter for these cnoidal wave solutions is the dimensionless wave height divided by the parameter m of the cn functions: this explicitly shows the limitation of the theory to waves in relatively shallow water. The corresponding deep water limitation for Stokes waves is analysed and a modified expansion parameter suggested. Cnoidal wave solutions to fifth order are given so that a steady wave problem with known water depth, wave height and wave period or length may be solved to give expressions for the wave profile and fluid velocities, as well as integral quantities such as wave power and radiation stress. These series solutions seem to exhibit asymptotic behaviour such that there is no gain in including terms beyond fifth order. Results from the present theory are compared with exact numerical results and with experiment. It is concluded that the fifth-order cnoidal theory should be used in preference to fifth-order Stokes wave theory for wavelengths greater than eight times the water depth, when it gives quite accurate results. © 1979, 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
    Published by Cambridge University Press
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