Generation of undular bores in the shelves of slowly-varying solitary waves

We study the long-time evolution of the trailing shelves that form behind solitary waves moving through an inhomogeneous medium, within the framework of the variable-coefficient Korteweg-de Vries equation. We show that the nonlinear evolution of the shelf leads typically to the generation of an undular bore and an expansion fan, which form apart but start to overlap and nonlinearly interact after a certain time interval. The interaction zone expands with time and asymptotically as time goes to infinity occupies the whole perturbed region. Its oscillatory structure strongly depends on the sign of the inhomogeneity gradient of the variable background medium. We describe the nonlinear evolution of the shelves in terms of exact solutions to the KdV-Whitham equations with natural boundary conditions for the Riemann invariants. These analytic solutions, in particular, describe the generation of small "secondary" solitary waves in the trailing shelves, a process observed earlier in various numerical simulations

Coupled Ostrovsky equations for internal waves in a shear flow

In the context of fluid flows, the coupled Ostrovsky equations arise when two distinct linear long wave modes have nearly coincident phase speeds in the presence of background rotation. In this paper, nonlinear waves in a stratified fluid in the presence of shear flow are investigated both analytically, using techniques from asymptotic perturbation theory, and through numerical simulations. The dispersion relation of the system, based on a three-layer model of a stratified shear flow, reveals various dynamical behaviours, including the existence of unsteady and steady envelope wave packets.Comment: 47 pages, 39 figures, accepted to Physics of Fluid

Transcritical shallow-water flow past topography: finite-amplitude theory

We consider shallow-water flow past a broad bottom ridge, localized in the flow direction, using the framework of the forced SuGardner (SG) system of equations, with a primary focus on the transcritical regime when the Froude number of the oncoming flow is close to unity. These equations are an asymptotic long-wave approximation of the full Euler system, obtained without a simultaneous expansion in the wave amplitude, and hence are expected to be superior to the usual weakly nonlinear Boussinesq-type models in reproducing the quantitative features of fully nonlinear shallow-water flows. A combination of the local transcritical hydraulic solution over the localized topography, which produces upstream and downstream hydraulic jumps, and unsteady undular bore solutions describing the resolution of these hydraulic jumps, is used to describe various flow regimes depending on the combination of the topography height and the Froude number. We take advantage of the recently developed modulation theory of SG undular bores to derive the main parameters of transcritical fully nonlinear shallow-water flow, such as the leading solitary wave amplitudes for the upstream and downstream undular bores, the speeds of the undular bores edges and the drag force. Our results confirm that most of the features of the previously developed description in the framework of the unidirectional forced Kortewegde Vries (KdV) model hold up qualitatively for finite amplitude waves, while the quantitative description can be obtained in the framework of the bidirectional forced SG system. Our analytic solutions agree with numerical simulations of the forced SG equations within the range of applicability of these equations

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

The Role of Contextual Clues in the Creation of Information Overload

There has been an explosion of new forms of communications media for interpersonal communication. There is anecdotal evidence of people suffering from 'information overload' as a result of these developments. This paper presents the results from, and analysis of, a case study of a perceived problem of information overload from e-mail in a large international organization: Watson Wyatt Partners. The research took two approaches to exploring the problem. The first was a survey of 1500 members of staff in the UK and Europe. This was aimed at collecting factual information. The second approach was to conduct follow up interviews with 19 people at two sites in the UK to explore some of the issues raised by the survey in greater depth. In the paper, we argue that for CMCs (Computer Mediated Communications) to be effective there is a need to establish a 'context' in which the message can be interpreted. In doing so, we will demonstrate that ignoring the degree of 'context' a media provides can adversely affect the users perceptions of that media.Electronic mail, e-mail, CMC, communication technology, contextual clues, information overload

Wave Breaking and the Generation of Undular Bores in an Integrable Shallow Water System

The generation of an undular bore in the vicinity of a wave‐breaking point is considered for the integrable Kaup–Boussinesq (KB) shallow water system. In the framework of the Whitham modulation theory, an analytic solution of the Gurevich–Pitaevskii type of problem for a generic “cubic” breaking regime is obtained using a generalized hodograph transform, and a further reduction to a linear Euler–Poisson equation. The motion of the undular bore edges is investigated in detail

Evolution of solitary waves and undular bores in shallow-water flows over a gradual slope with bottom friction

This paper considers the propagation of shallow-water solitary and nonlinear periodic waves over a gradual slope with bottom friction in the framework of a variable-coefficient Korteweg-de Vries equation. We use the Whitham averaging method, using a recent development of this theory for perturbed integrable equations. This general approach enables us not only to improve known results on the adiabatic evolution of isolated solitary waves and periodic wave trains in the presence of variable topography and bottom friction, modelled by the Chezy law, but also, importantly, to study the effects of these factors on the propagation of undular bores, which are essentially unsteady in the system under consideration. In particular, it is shown that the combined action of variable topography and bottom friction generally imposes certain global restrictions on the undular bore propagation so that the evolution of the leading solitary wave can be substantially different from that of an isolated solitary wave with the same initial amplitude. This non-local effect is due to nonlinear wave interactions within the undular bore and can lead to an additional solitary wave amplitude growth, which cannot be predicted in the framework of the traditional adiabatic approach to the propagation of solitary waves in slowly varying media

Action, actor, context, target, time (AACTT): a framework for specifying behaviour

BACKGROUND: Designing implementation interventions to change the behaviour of healthcare providers and other professionals in the health system requires detailed specification of the behaviour(s) targeted for change to ensure alignment between intervention components and measured outcomes. Detailed behaviour specification can help to clarify evidence-practice gaps, clarify who needs to do what differently, identify modifiable barriers and enablers, design interventions to address these and ultimately provides an indicator of what to measure to evaluate an intervention's effect on behaviour change. An existing behaviour specification framework proposes four domains (Target, Action, Context, Time; TACT), but insufficiently clarifies who is performing the behaviour (i.e. the Actor). Specifying the Actor is especially important in healthcare settings characterised by multiple behaviours performed by multiple different people. We propose and describe an extension and re-ordering of TACT to enhance its utility to implementation intervention designers, practitioners and trialists: the Action, Actor, Context, Target, Time (AACTT) framework. We aim to demonstrate its application across key steps of implementation research and to provide tools for its use in practice to clarify the behaviours of stakeholders across multiple levels of the healthcare system. METHODS AND RESULTS: We used French et al.'s four-step implementation process model to describe the potential applications of the AACTT framework for (a) clarifying who needs to do what differently, (b) identifying barriers and enablers, (c) selecting fit-for-purpose intervention strategies and components and (d) evaluating implementation interventions. CONCLUSIONS: Describing and detailing behaviour using the AACTT framework may help to enhance measurement of theoretical constructs, inform development of topic guides and questionnaires, enhance the design of implementation interventions and clarify outcome measurement for evaluating implementation interventions