Author

# John D. Fenton

Other affiliations: University of Cambridge, Cooperative Research Centre, University of Melbourne ...read more

Bio: John D. Fenton is an academic researcher from Vienna University of Technology. The author has contributed to research in topics: Numerical analysis & Nonlinear system. The author has an hindex of 22, co-authored 77 publications receiving 3211 citations. Previous affiliations of John D. Fenton include University of Cambridge & Cooperative Research Centre.

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TL;DR: In this article, an alternative Stokes theory for steady waves in water of constant depth is presented where the expansion parameter is the wave steepness itself, and the first step in application requires the solution of one nonlinear equation, rather than two or three simultaneously as has been previously necessary.

Abstract: An alternative Stokes theory for steady waves in water of constant depth is presented where the expansion parameter is the wave steepness itself. The first step in application requires the solution of one nonlinear equation, rather than two or three simultaneously as has been previously necessary. In addition to the usually specified design parameters of wave height, period and water depth, it is also necessary to specify the current or mass flux to apply any steady wave theory. The reason being that the waves almost always travel on some finite current and the apparent wave period is actually a Dopplershifted period. Most previous theories have ignored this, and their application has been indefinite, if not wrong, at first order. A numerical method for testing theoretical results is proposed, which shows that two existing theories are wrong at fifth order, while the present theory and that of Chappelear are correct. Comparisons with experiments and accurate numerical results show that the present theory ...

488 citations

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469 citations

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TL;DR: In this article, a finite Fourier series is used to give a set of nonlinear equations which can be solved using Newton's method for the numerical solution of steadily progressing periodic waves on irrotational flow over a horizontal bed.

Abstract: 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.

424 citations

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TL;DR: In this article, the authors measured the dimensionless threshold stress and its dependence on grain protrusion and found that the threshold stress for grains resting on the top of an otherwise flat bed in a turbulent stream was measured and found to be 0.01 -considerably less than previously reported values of 0.03-0.06 for beds where all grains were at the same level.

Abstract: Shields (1936) found that the dimensionless shear stress necessary to move a cohesionless grain on a stream bed depended only on the grain Reynolds number. He ignored the degree of exposure of individual grains as a separate parameter. This report describes experiments to measure the dimensionless threshold stress and its dependence on grain protrusion, which was found to be very marked. The threshold stress for grains resting on the top of an otherwise flat bed in a turbulent stream was measured and found to be 0.01 –considerably less than previously-reported values of 0.03–0.06 for beds where all grains were at the same level. It is suggested that the new lower value be used in all turbulent flow situations where the bed is of natural sediments or unlevelled material. An hypothesis is proposed that the conventional Shields diagram implicitly contains variation with protrusion between the two extremes of (i) large grains and large Reynolds numbers, with small relative protrusion, and (ii) small grains, low Reynolds numbers, and protrusion of almost a complete grain diameter. In view of this, the extent of the dip in the Shields plot is explicable in that it represents a transition between two different standards of levelling as well as the transition between laminar and turbulent flow past the grains, the range of which it overlaps considerably.

286 citations

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TL;DR: In this article, it was shown that for a given wave speed, there can exist, when the wave is near its maximum, two quite distinct solitary waves, and the maximum wave height, as determined in this way, is 0.790.

Abstract: By accurate calculation it is found that the speed $F$ of a solitary wave, as well as its mass, momentum and energy, attains a maximum value corresponding to a wave of less than the maximum amplitude. Hence for a given wave speed $F$ there can exist, when $F$ is near its maximum, two quite distinct solitary waves. The calculation is made possible, first, by the proof in an earlier paper ($I$) of some exact relations between the momentum and potential energy, which enable the coefficients in certain series to be checked and extended to a high order; secondly, by the introduction of a new parameter $\omega $ (related to the particle velocity at the wave crest) whose range is exactly known; and thirdly by the discovery that the series for the mass $M$ and potential energy $V$ in powers of $\omega $ can be accurately summed by Pade approximants. From these, the values of $F$ and of the wave height $\epsilon $ are determined accurately through the exact relations $3V=(F^{2}-1)M$ and $2\epsilon =(\omega +F^{2}-1$. The maximum wave height, as determined in this way, is $\epsilon \_{\max}$ = 0.827, in good agreement with the values found by Yamada (1957) and Lenau (1966), using completely different methods. The speed of the limiting wave is $F$ = 1.286. The maximum wave speed, however, is $F\_{\max}$ = 1.294, which corresponds to $\epsilon =0.790$. The relation between $\epsilon $ and $F$ is compared to the laboratory observations made by Daily & Stephan (1952), with reasonable agreement. An important application of our results is to the understanding of how waves break in shallow water. The discovery that the highest solitary wave is not the most energetic helps to explain the qualitative difference between plunging and spilling breakers, and to account for the marked intermittency which is characteristic of spilling breakers.

219 citations

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12 Feb 2001TL;DR: In this article, the basic principles of specific energy, momentum, uniform flow, and uniform flow in alluvial channels are discussed, as well as simplified methods of flow routing.

Abstract: Chapter 1 Basic Principles Chapter 2 Specific Energy Chapter 3 Momentum Chapter 4 Uniform Flow Chapter 5 Gradually Varied Flow Chapter 6 Hydraulic Structures Chapter 7 Governing Equations of Unsteady Flow Chapter 8 Numerical Solution of the Unsteady Flow Equations Chapter 9 Simplified Methods of Flow Routing Chapter 10 Flow in Alluvial Channels

2,397 citations

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TL;DR: In this article, a classification of channel-reach morphology in mountain drainage basins synthesizes stream morphologies into seven distinct reach types: colluvial, bedrock, and five alluvial channel types (cascade, step pool, plane bed, pool rime and dune ripple).

Abstract: A classification of channel-reach morphology in mountain drainage basins synthesizes stream morphologies into seven distinct reach types: colluvial, bedrock, and five alluvial channel types (cascade, step pool , plane bed, pool rime, and dune ripple). Coupling reach-level channel processes with the spatial arrangement of reach morphologies, their links to hillslope processes, and external forcing by confinement, ripar ian vegetation, and woody debris defines a process-based framework within which to assess channel condition and response potential in mountain drainage basins. Field investigations demonstrate character istic slope, grain size, shear stress, and roughness ranges for different reach types, observations consistent with our hypothesis that alluvial channel morphologies reflect specific roughness configurations ad justed to the relative magnitudes of sediment supply and transport ca pacity. Steep alluvial channels (cascade and step pool) have high ratios of transport capacity to sediment supply and are resilient to changes in discharge and sediment supply, whereas low-gradient alluvial channels (pool rime and dune ripple) have lower transport capacity to supply ra tios and thus exhibit significant and prolonged response to changes in sediment supply and discharge. General differences in the ratio of transport capacity to supply between channel types allow aggregation of reaches into source, transport, and response segments, the spatial distribution of which provides a watershed-level conceptual model linking reach morphology and channel processes. These two scales of channel network classification define a framework within which to in vestigate spatial and temporal patterns of channel response in moun tain drainage basins.

1,889 citations

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TL;DR: In this article, the use of acoustic fields, principally ultrasonics, for application in microfluidics is reviewed, and the abundance of interesting phenomena arising from nonlinear interactions in ultrasound that easily appear at these small scales is considered, especially in surface acoustic wave devices that are simple to fabricate with planar lithography techniques.

Abstract: This article reviews acoustic microfiuidics: the use of acoustic fields, principally ultrasonics, for application in microfiuidics. Although acoustics is a classical field, its promising, and indeed perplexing, capabilities in powerfully manipulating both fluids and particles within those fluids on the microscale to nanoscale has revived interest in it. The bewildering state of the literature and ample jargon from decades of research is reorganized and presented in the context of models derived from first principles. This hopefully will make the area accessible for researchers with experience in materials science, fluid mechanics, or dynamics. The abundance of interesting phenomena arising from nonlinear interactions in ultrasound that easily appear at these small scales is considered, especially in surface acoustic wave devices that are simple to fabricate with planar lithography techniques common in microfluidics, along with the many applications in microfluidics and nanofluidics that appear through the literature.

975 citations

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TL;DR: In this article, the authors used data compiled from eight decades of incipient motion studies to calculate dimensionless critical shear stress values of the median grain size, t* c 50.

Abstract: Data compiled from eight decades of incipient motion studies were used to calculate dimensionless critical shear stress values of the median grain size, t* c 50 . Calculated t* c 50 values were stratified by initial motion definition, median grain size type (surface, subsurface, or laboratory mixture), relative roughness, and flow regime. A traditional Shields plot constructed from data that represent initial motion of the bed surface material reveals systematic methodological biases of incipient motion definition; t* c 50 values determined from reference bed load transport rates and from visual observation of grain motion define subparallel Shields curves, with the latter generally underlying the former; values derived from competence functions define a separate but poorly developed field, while theoretical values predict a wide range of generally higher stresses that likely represent instantaneous, rather than time-averaged, critical shear stresses. The available data indicate that for high critical boundary Reynolds numbers and low relative roughnesses typical of gravel-bedded rivers, reference-based and visually based studies have t* c50 ranges of 0.052-0.086 and 0.030-0.073, respectively. The apparent lack of a universal t*50 for gravel-bedded rivers warrants great care in choosing defendable t* c50 values for particular applications.

919 citations