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  • 1
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    Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation (2013)
    Cambridge University Press
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    Publication Date: 2013-11-08
    Description: Transcritical flow of a stratified fluid past a broad localised topographic obstacle is studied analytically in the framework of the forced extended Korteweg-de Vries, or Gardner, equation. We consider both possible signs for the cubic nonlinear term in the Gardner equation corresponding to different fluid density stratification profiles. We identify the range of the input parameters: the oncoming flow speed (the Froude number) and the topographic amplitude, for which the obstacle supports a stationary localised hydraulic transition from the subcritical flow upstream to the supercritical flow downstream. Such a localised transcritical flow is resolved back into the equilibrium flow state away from the obstacle with the aid of unsteady coherent nonlinear wave structures propagating upstream and downstream. Along with the regular, cnoidal undular bores occurring in the analogous problem for the single-layer flow modelled by the forced Korteweg-de Vries equation, the transcritical internal wave flows support a diverse family of upstream and downstream wave structures, including kinks, rarefaction waves, classical undular bores, reversed and trigonometric undular bores, which we describe using the recent development of the nonlinear modulation theory for the (unforced) Gardner equation. The predictions of the developed analytic construction are confirmed by direct numerical simulations of the forced Gardner equation for a broad range of input parameters. ©2013 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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    Two-dimensional pulse dynamics and the formation of bound states on electrified falling films (2018)
    Cambridge University Press
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    Publication Date: 2018-09-14
    Description: The flow of an electrified liquid film down an inclined plane wall is investigated with the focus on coherent structures in the form of travelling waves on the film surface, in particular, single-hump solitary pulses and their interactions. The flow structures are analysed first using a long-wave model, which is valid in the presence of weak inertia, and second using the Stokes equations. For obtuse angles, gravity is destabilising and solitary pulses exist even in the absence of an electric field. For acute angles, spatially non-uniform solutions exist only beyond a critical value of the electric field strength; moreover, solitary-pulse solutions are present only at sufficiently high supercritical electric-field strengths. The electric field increases the amplitude of the pulses, can generate recirculation zones in the humps and alters the far-field decay of the pulse tails from exponential to algebraic with a significant impact on pulse interactions. A weak-interaction theory predicts an infinite sequence of bound-state solutions for non-electrified flow, and a finite set for electrified flow. The existence of single-hump pulse solutions and two-pulse bound states is confirmed for the Stokes equations via boundary-element computations. In addition, the electric field is shown to trigger a switch from absolute to convective instability, thereby regularising the dynamics, and this is confirmed by time-dependent simulations of the long-wave model. © 2018 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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  • 3
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    Modelling spreading dynamics of nematic liquid crystals in three spatial dimensions (2013)
    Cambridge University Press
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    Publication Date: 2013-07-16
    Description: We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth-order nonlinear parabolic partial differential equation governing the free surface evolution is derived. The influence of elastic distortion energy and of imposed anchoring variations at the substrate are explored through linear stability analysis and scaling arguments, which yield useful insight and predictions for the behaviour of spreading droplets. This behaviour is captured by fully nonlinear time-dependent simulations of three-dimensional droplets spreading in the presence of anchoring variations that model simple defects in the nematic orientation at the substrate. © 2013 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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    Laminar dispersion in curved tubes and channels (1972)
    Cambridge University Press
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    Publication Date: 1972-01-25
    Description: Dispersion in curved tubes and channels is treated analytically, using the velocity distribution of Topakoglu (1967) for tubes and that of Goldstein (1965) for curved channels. The result for curved tubes is compared with that obtained previously by Erdogan & Chatwin (1967) and it is found that the presentdispersion coefficient contains the Erdogan & Chatwin result as a limiting case. The most striking difference between the results is that Erdogan & Chatwin predict that the dispersion coefficient is always decreased by curvature if the Schmidt number exceeds 0.124, which is the ease for essentially all systems of practical interest. In contrast, the present result, equation (76), predicts that the dispersion coefficient may be increased substantially by curvature in low Reynolds number flows, particularly in liquid systems which would be of interest in biological systems. Two competing mechanisms of dispersion are present in curved systems. Curvature increases the variation in residence time across the flow in comparison with straight systems and this in turn increases the dispersion coefficient. The secondary flow which occurs in curved tubes creates a transverse mixing which decreases the dispersion coefficient. The results demonstrate that the relative importance of these two effects changes with the Reynolds number, since the dispersion coefficient first increases and then decreases as the Reynolds number increases. Since secondary flows are not present in curved channels the dispersion coefficient is increased over that in straight channels for all cases. © 1972, 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
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  • 5
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    Viscous flow over a cone at moderate incidence. Part 2. Supersonic boundary layer (1973)
    Cambridge University Press
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    Publication Date: 1973-07-17
    Description: A finite-difference method recently developed to study three-dimensional viscous flow is applied here to the supersonic boundary layer on a sharp cone at moderate angles of incidence (α/θ ≤ 2, angle of attack α, cone half-angle θ). The present analysis differs from previous investigations of this region in that (i) boundary-layer similarity is not assumed, (ii) the system of governing equations incorporates lateral diffusion and centrifugal force effects, and (iii) an improved numerical scheme for three-dimensional viscous flows of the type considered here is used. Solutions are shown to be non-similar at the separation streamline with local shear-layer formation. Detailed flow structure, including surface heat transfer, boundary-layer profiles and thickness, and the formation of swirling pairwise symmetric vortices, associated with cross-flow separation, are obtained. Good agreement is obtained between the present theoretical results and the existing experimental data. © 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
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  • 6
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    Pathogenic fungal protein-induced resistance and its effects on vegetable diseases (2017)
    Cambridge University Press
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    Publication Date: 2017-03-31
    Description: SUMMARYPlant defence systems can be induced by biotic and abiotic stress. Experiments were undertaken to explore the feasibility of different fungal proteins for the reduction of vegetable diseases. Total proteins purified from three soil-borne and five foliar fungal pathogens had no fungistatic effects nor did they trigger hypersensitive reactions on test plants. The abilities to promote plant growth and to reduce disease severity varied among test proteins and plants. Depending on test proteins, experiments have demonstrated that exogenous application of fungal proteins could reduce Alternaria brassicicola-induced black spot severity on cabbage, Colletotrichum spp.-induced anthracnose on Chinese cabbage and cucumber, Rhizoctonia solani-induced damping-off on sweet pepper and Chinese cabbage, and powdery mildew on cucumber seedlings. An Alternariaprotein effector 1 (Ape1)-coding gene was cloned from two Alternaria spp. and expressed in Escherichia coli. The expressed Ape1 reduced anthracnose incidence on cucumber leaves, indicating that Ape1 was the primary activator in the crude protein extracts responsible for disease reduction. Application of Alternaria proteins onto Chinese cabbage seedlings caused an increase of phenylalanine ammonia lyase and peroxidase activities in treated seedlings, which may have played a role in host defence.
    Print ISSN: 0021-8596
    Electronic ISSN: 1469-5146
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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  • 7
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    Nonidet p-40, a novel inducer, activates cucumber disease resistance against cucumber anthracnose disease (2013)
    Cambridge University Press
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    Publication Date: 2013-10-07
    Description: SUMMARYThe present study found that a protein lysis buffer, used for the extraction of proteins from cells, showed efficacy in reducing the disease severity of cucumber anthracnose, which is caused by the anthracnose fungus. The lysis buffer and its individual components were examined for their function in reducing disease development of cucumber anthracnose on cucumber plants. Nonidet P-40, a nonionic detergent commonly used to isolate cell membrane complexes, was the most effective component of the lysis buffer for disease control. The treatment of cucumber plants with Nonidet P-40 at a concentration of 50 μl/l suppressed development of cucumber anthracnose, but it did not inhibit spore germination of the fungus. Cucumber plants were inoculated with the pathogen 30 min after treatment with Nonidet P-40, and a reduction in disease severity was observed. Expression of genes related to disease resistance (acidic class III chitinase, phenylalanine ammonialyase 1, peroxidase and pathogenesis-related protein 1-1a) were also examined after plants were treated with Nonidet P-40 and inoculated with the pathogen. The results indicate that Nonidet P-40 functions as a trigger for a stereotypic defence response in cucumber plants, including an increase in the expression levels of genes related to disease resistance.
    Print ISSN: 0021-8596
    Electronic ISSN: 1469-5146
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Published by Cambridge University Press
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