Transformation of a shoaling undular bore

We consider the propagation of a shallow-water undular bore over a gentle monotonic bottom slope connecting two regions of constant depth, in the framework of the variable-coefficient Korteweg-de Vries equation. We show that, when the undular bore advances in the direction of decreasing depth, its interaction with the slowly varying topography results, apart from an adiabatic deformation of the bore itself, in the generation of a sequence of isolated solitons - an expanding large-amplitude modulated solitary wavetrain propagating ahead of the bore. Using nonlinear modulation theory we construct an asymptotic solution describing the formation and evolution of this solitary wavetrain. Our analytical solution is supported by direct numerical simulations. The presented analysis can be extended to other systems describing the propagation of undular bores (dispersive shock waves) in weakly non-uniform environments

Transcritical flow of a stratified fluid: The forced extended Korteweg-de Vries model

Transcritical, or resonant, flow of a stratified fluid over an obstacle is studied using a forced extended Korteweg-de Vries model. This model is particularly relevant for a two-layer fluid when the layer depths are near critical, but can also be useful in other similar circumstances. Both quadratic and cubic nonlinearities are present and they are balanced by third-order dispersion. We consider both possible signs for the cubic nonlinear term but emphasize the less-studied case when the cubic nonlinear term and the dispersion term have the same-signed coefficients. In this case, our numerical computations show that two kinds of solitary waves are found in certain parameter regimes. One kind is similar to those of the well-known forced Korteweg-de Vries model and occurs when the cubic nonlinear term is rather small, while the other kind is irregularly generated waves of variable amplitude, which may continually interact. To explain this phenomenon, we develop a hydraulic theory in which the dispersion term in the model is omitted. This theory can predict the occurence of upstream and downstream undular bores, and these predictions are found to agree quite well with the numerical computations. © 2002 American Institute of Physics.published_or_final_versio

Steady transcritical flow over an obstacle: Parametric map of solutions of the forced extended Korteweg-de Vries equation

Transcritical flow of a stratified fluid over an obstacle is often modeled by the forced Korteweg-de Vries equation, which describes a balance among weak nonlinearity, weak dispersion, and small forcing effects. However, in some special circumstances, it is necessary to add an additional cubic nonlinear term, so that the relevant model is the forced extended Korteweg-de Vries equation. Here we seek steady solutions with constant, but different amplitudes upstream and downstream of the forcing region. Our main interest is in the case when the forcing has negative polarity, which represents a hole. The effects of the width of the hole and the amplitude of the hole on these steady solutions are then investigated. © 2011 American Institute of Physics.published_or_final_versio

Cuspons, peakons and regular gap solitons between three dispersion curves

A general wave model with the cubic nonlinearity is introduced to describe a situation when the linear dispersion relation has three branches, which would intersect in the absence of linear couplings between the three waves. Actually, the system contains two waves with a strong linear coupling between them, to which a third wave is then coupled. This model has two gaps in its linear spectrum. Realizations of this model can be made in terms of temporal or spatial evolution of optical fields in, respectively, a planar waveguide or a bulk-layered medium resembling a photonic-crystal fiber. Another physical system described by the same model is a set of three internal wave modes in a density-stratified fluid. A nonlinear analysis is performed for solitons which have zero velocity in the reference frame in which the group velocity of the third wave vanishes. Disregarding the self-phase modulation (SPM) term in the equation for the third wave, we find two coexisting families of solitons: regular ones, which may be regarded as a smooth deformation of the usual gap solitons in a two-wave system, and cuspons with a singularity in the first derivative at their center. Even in the limit when the linear coupling of the third wave to the first two vanishes, the soliton family remains drastically different from that in the linearly uncoupled system; in this limit, regular solitons whose amplitude exceeds a certain critical value are replaced by peakons. While the regular solitons, cuspons, and peakons are found in an exact analytical form, their stability is tested numerically, which shows that they all may be stable. If the SPM terms are retained, we find that there again coexist two different families of generic stable soliton solutions, namely, regular ones and peakons.Comment: a latex file with the text and 10 pdf files with figures. Physical Review E, in pres

The cascade structure of linear instability in collapsible channel flows

This paper studies the unsteady behaviour and linear stability of the flow in a collapsible channel using a fluid–beam model. The solid mechanics is analysed in a plane strain configuration, in which the principal stretch is defined with a zero initial strain. Two approaches are employed: unsteady numerical simulations solving the nonlinear fully coupled fluid–structure interaction problem; and the corresponding linearized eigenvalue approach solving the Orr–Sommerfeld equations modified by the beam. The two approaches give good agreement with each other in predicting the frequencies and growth rates of the perturbation modes, close to the neutral curves. For a given Reynolds number in the range of 200–600, a cascade of instabilities is discovered as the wall stiffness (or effective tension) is reduced. Under small perturbation to steady solutions for the same Reynolds number, the system loses stability by passing through a succession of unstable zones, with mode number increasing as the wall stiffness is decreased. It is found that this cascade structure can, in principle, be extended to many modes, depending on the parameters. A puzzling ‘tongue’ shaped stable zone in the wall stiffness–Re space turns out to be the zone sandwiched by the mode-2 and mode-3 instabilities. Self-excited oscillations dominated by modes 2–4 are found near their corresponding neutral curves. These modes can also interact and form period-doubling oscillations. Extensive comparisons of the results with existing analytical models are made, and a physical explanation for the cascade structure is proposed

Systematic review of economic evaluations and cost analyses of guideline implementation strategies

Objectives To appraise the quality of economic studies undertaken as part of evaluations of guideline implementation strategies; determine their resources use; and recommend methods to improve future studies. Methods Systematic review of economic studies undertaken alongside robust study designs of clinical guideline implementation strategies published (1966-1998). Studies assessed against the BMJ economic evaluations guidelines for each stage of the guideline process (guideline development, implementation and treatment). Results 235 studies were identified, 63 reported some information on cost. Only 3 studies provided evidence that their guideline was effective and efficient. 38 reported the treatment costs only, 12 implementation and treatment costs, 11 implementation costs alone, and two guideline development, implementation and treatment costs. No study gave reasonably complete information on costs. Conclusions Very few satisfactory economic evaluations of guideline implementation strategies have been performed. Current evaluations have numerous methodological defects and rarely consider all relevant costs and benefits. Future evaluations should focus on evaluating the implementation of evidence based guidelines. Keywords: Cost-effectiveness analysis, physician (or health care professional) behaviour, practice guidelines, quality improvement, systematic review.Peer reviewedAuthor versio

Brief communication: Modulation instability of internal waves in a smoothly stratified shallow fluid with a constant buoyancy frequency

Unexpectedly large displacements in the interior of the oceans are studied through the dynamics of packets of internal waves, where the evolution of these displacements is governed by the nonlinear Schrödinger equation. In cases with a constant buoyancy frequency, analytical treatment can be performed. While modulation instability in surface wave packets only arises for sufficiently deep water, “rogue” internal waves may occur in shallow water and intermediate depth regimes. A dependence on the stratification parameter and the choice of internal modes can be demonstrated explicitly. The spontaneous generation of rogue waves is tested here via numerical simulation.</p

Nonlinear interfacial waves in a constant-vorticity planar flow over variable depth

Exact Lagrangian in compact form is derived for planar internal waves in a two-fluid system with a relatively small density jump (the Boussinesq limit taking place in real oceanic conditions), in the presence of a background shear current of constant vorticity, and over arbitrary bottom profile. Long-wave asymptotic approximations of higher orders are derived from the exact Hamiltonian functional in a remarkably simple way, for two different parametrizations of the interface shape.Comment: revtex, 4.5 pages, minor corrections, summary added, accepted to JETP Letter

Unsteady undular bores in fully nonlinear shallow-water theory

We consider unsteady undular bores for a pair of coupled equations of Boussinesq-type which contain the familiar fully nonlinear dissipationless shallow-water dynamics and the leading-order fully nonlinear dispersive terms. This system contains one horizontal space dimension and time and can be systematically derived from the full Euler equations for irrotational flows with a free surface using a standard long-wave asymptotic expansion. In this context the system was first derived by Su and Gardner. It coincides with the one-dimensional flat-bottom reduction of the Green-Naghdi system and, additionally, has recently found a number of fluid dynamics applications other than the present context of shallow-water gravity waves. We then use the Whitham modulation theory for a one-phase periodic travelling wave to obtain an asymptotic analytical description of an undular bore in the Su-Gardner system for a full range of "depth" ratios across the bore. The positions of the leading and trailing edges of the undular bore and the amplitude of the leading solitary wave of the bore are found as functions of this "depth ratio". The formation of a partial undular bore with a rapidly-varying finite-amplitude trailing wave front is predicted for ``depth ratios'' across the bore exceeding 1.43. The analytical results from the modulation theory are shown to be in excellent agreement with full numerical solutions for the development of an undular bore in the Su-Gardner system.Comment: Revised version accepted for publication in Phys. Fluids, 51 pages, 9 figure

Designing theoretically-informed implementation interventions

Clinical and health services research is continually producing new findings that may contribute to effective and efficient patient care. However, the transfer of research findings into practice is unpredictable and can be a slow and haphazard process. Ideally, the choice of implementation strategies would be based upon evidence from randomised controlled trials or systematic reviews of a given implementation strategy. Unfortunately, reviews of implementation strategies consistently report effectiveness some, but not all of the time; possible causes of this variation are seldom reported or measured by the investigators in the original studies. Thus, any attempts to extrapolate from study settings to the real world are hampered by a lack of understanding of the effects of key elements of individuals, interventions, and the settings in which they were trialled. The explicit use of theory offers a way of addressing these issues and has a number of advantages, such as providing: a generalisable framework within which to represent the dimensions that implementation studies address, a process by which to inform the development and delivery of interventions, a guide when evaluating, and a way to allow for an exploration of potential causal mechanisms. However, the use of theory in designing implementation interventions is methodologically challenging for a number of reasons, including choosing between theories and faithfully translating theoretical constructs into interventions. The explicit use of theory offers potential advantages in terms of facilitating a better understanding of the generalisability and replicability of implementation interventions. However, this is a relatively unexplored methodological area