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181.
The goal in this work is to investigate the effectiveness of time-frequency representations for analysing dispersive waves by comparing the performance of three different methods. In particular, the smoothed pseudo-Wigner distribution, the continuous wavelet transform and the Hilbert-Huang transform are compared and evaluated in terms of their ability to analyse dispersive elastic waves. The waves under consideration are transient flexural ones generated by an impact in a beam. In view of the results of the comparative study, the advantages and shortcomings of each method are presented and discussed. 相似文献
182.
《Comptes Rendus Physique》2013,14(4):352-365
The first generation of ground-based interferometric gravitational wave detectors, LIGO, GEO, and Virgo, have operated and taken data at their design sensitivities over the last few years. The data has been examined for the presence of gravitational wave signals. Presented here is a comprehensive review of the most significant results. The network of detectors is currently being upgraded and extended, providing a large likelihood for observations. These future prospects will also be discussed. 相似文献
183.
In order to understand the nonlinear effect in a two‐layer system, fully nonlinear strongly dispersive internal‐wave equations, based on a variational principle, were proposed in this study. A simple iteration method was used to solve the internal‐wave equations in order to solve the equations stably. The applicability of the proposed numerical computation scheme was confirmed to agree with linear dispersion relation theoretically obtained from variational principle. The proposed computational scheme was also shown to reproduce internal waves including higher‐order nonlinear effect from the analysis of internal solitary waves in a two‐layer system. Furthermore, for the second‐order numerical analysis, the balance of nonlinearity and dispersion was found to be similar to the balance assumed in the KdV theory and the Boussinesq‐type equations. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
184.
The Lagrangian smoothed particle hydrodynamics (SPH) method is used to simulate shock waves in inviscid, supersonic (compressible) flow. It is shown for the first time that the fully Lagrangian SPH particle method, without auxiliary grid, can be used to simulate shock waves in compressible flow. The wall boundary condition is treated with ghost particles combined with a suitable repulsive potential function, whilst corners are treated by a novel ‘angle sweep’ technique. The method gives accurate predictions of the flow field and of the shock angle as compared with the analytical solution. The study shows that SPH is a good potential candidate to solve complex aerodynamic problems, including those involving rarefied flows, such as atmospheric re‐entry. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
185.
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187.
We derive an asymptotic formula for the amplitude distribution in a fully nonlinear shallow-water solitary wave train which is formed as the long-time outcome of the initial-value problem for the Su–Gardner (or one-dimensional Green–Naghdi) system. Our analysis is based on the properties of the characteristics of the associated Whitham modulation system which describes an intermediate “undular bore” stage of the evolution. The resulting formula represents a “non-integrable” analogue of the well-known semi-classical distribution for the Korteweg–de Vries equation, which is usually obtained through the inverse scattering transform. Our analytical results are shown to agree with the results of direct numerical simulations of the Su–Gardner system. Our analysis can be generalised to other weakly dispersive, fully nonlinear systems which are not necessarily completely integrable. 相似文献
188.
Considered herein is the Ostrovsky equation which is widely used to describe the effect of rotation on the surface and internal solitary waves in shallow water or the capillary waves in a plasma. It is shown that the solitary-wave solutions are orbitally stable for certain wave speeds.
189.
We study nonlinear resonance in viscous gravity-driven films flowing over undulated substrates. Numerical solution of the full, steady Navier–Stokes equations is used to follow the emergence of the first few free-surface harmonics with increasing wall amplitude, and to study their parametric dependence on film thickness, inertia and capillarity. Bistable resonance is computed for steep enough bottom undulations. As an analytic approach, we apply the integral boundary-layer method and derive an asymptotic equation valid for rather thin films. The analysis recovers the key numerical findings and provides qualitative understanding. It shows that higher harmonics are generated by a nonlinear coupling of the wall with lower-order harmonics of the free surface. It also accounts for bistable resonance, and produces a minimum model whose solution is similar to that of the Duffing oscillator. 相似文献
190.
Summary. We derive a set of asymptotically exact coupled amplitude-streaming flow ({CASF}) equations governing the evolution of weakly nonlinear nearly inviscid multimode Faraday waves and the associated
streaming flow in finite geometries. The streaming flow is found to play a particularly important role near mode interactions.
Such interactions come about either through a suitable choice of parameters or through breaking of degeneracy among modes
related by symmetry. An example of the first case is provided by the interaction of two nonaxisymmetric modes in a circular
container with different azimuthal wavenumbers. The second case arises when the shape of the container is changed from square
to slightly rectangular, or from circular to slightly noncircular but with a plane of symmetry. The generation of streaming
flow in each of these cases is discussed in detail and the properties of the resulting CASF equations are described. A preliminary
analysis suggests that these equations can resolve discrepancies between existing theory and experimental results in the first
two of the above cases. 相似文献