1,958 research outputs found
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
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 waveâbreaking point is considered for the integrable KaupâBoussinesq (KB) shallow water system. In the framework of the Whitham modulation theory, an analytic solution of the GurevichâPitaevskii type of problem for a generic âcubicâ breaking regime is obtained using a generalized hodograph transform, and a further reduction to a linear EulerâPoisson 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
Attachment Theory and Self-Disclosure of HIV Status
This study examined the influence of attachment style on self-disclosure of HIV seropositive status. Subjects were classified according to Bartholomew\u27s model of adult attachment (i.e., secure, preoccupied, fearful, or dismissing). Steps were then taken to assess differences in the subjects\u27 willingness to disclose their HIV seropositive status, the communication style chosen for disclosure, the subjects\u27 perceptions of the importance of disclosing their HIV seropositive status, and the feared negative consequences of disclosure. To increase generalizability subjects were asked to assess their self-disclosure to three types of target persons: lover, same-sex friend, and opposite-sex friend. Attachment style significantly affected perceived importance of disclosure, specific communication directness/indirectness measures, and feared consequences measures. Overall the results reflected the differing stereotypical characteristics of each attachment style. Results also suggested that self-disclosure of one\u27s HIV seropositive status is affected by the intimacy of the relationship. It was concluded that subjects appeared most confident in the relationship with their lover and viewed this particular disclosure with the most importance
New periodic orbits in the solar sail three-body problem
We identify displaced periodic orbits in the circular restricted three-body problem, wher the third (small) body is a solar sail. In particular, we consider solar sail orbits in the earth-sun system which are high above the exliptic plane. It is shown that periodic orbits about surfaces of artificial equilibria are naturally present at linear order. Using the method of Lindstedt-Poincare, we construct nth order approximations to periodic solutions of the nonlinear equations of motion. In the second part of the paper we generalize to the solar sail elliptical restricted three-body problem. A numerical continuation, with the eccentricity, e, as the varying parameter, is used to find periodic orbits above the ecliptic, starting from a known orbit at e=0 and continuing to the requied eccentricity of e=0.0167. The stability of these periodic orbits is investigated
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âWe have a big crowdâ: The different referents of the first-person plural in U.S. presidential candidatesâ talk on entertainment-political interviews
During U.S. presidential elections, today, interviews at late-night talk shows are commonplace. As political and entertainment discourse co-occur in this type of communication, we refer to this genre as the Entertainment-Political Interview (EPI). Yet, research is lacking in clarifying how candidates, through their talk, appeal to their audience on these shows to realize their political goals. In this study, the different extralinguistic referents for the first-person plural (i.e. we, us, our) are investigated in order to understand which groups are referred to by U.S. presidential candidates, how these groups are presented and how this positions the candidate with respect to their audience in order to construct a discursive presentation of the world. Namely, even as we is a deictic term produced by a speaker, the referent can still be any group of people including the speaker. Investigating these genre-specific foundational group memberships is essential to understand this mode of political discourse as the discursive world projected through the talk serves as the context of interpretation for the audience.
To study possible referents of we in EPIs, we use the taxonomy developed by Dori-Hacohen (2014) as a starting point, as it classifies different types of we based on the exclusivity of the group referred to (i.e. everyone on earth (humanity we), a group including the speaker and hearer (general we), a group including the speaker but not the hearer (social delimited we), and a group just consisting of the speaker and hearer (conversation we)). The genre-specific referents of we are U.S. society (general we), desirable social groups and political teams (social delimited we)
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