Wave breaking in Boussinesq models for undular bores

A nonlinear dispersive model equation is used to study the onset of breaking in long waves behind the front of an undular bore. According to experiments conducted by Favre (1935) [1], weak bores have a smooth, but oscillatory structure, with undulations appearing behind the bore front. With increasing bore strength, the amplitude of these oscillations grows until one or several of them start breaking. The change in type from the purely undular bore occurs at a sharply defined depth ratio which is under review in this article. A convective breaking criterion is put forward, and numerical computations are used to compare the predictions of this model to Favre?s wavetank experiments. It appears that the numerical results underpredict the appearance of breaking waves, but are in good qualitative agreement with the experiments. The results are interpreted with the aid of exact solitary-wave solutions, and it is found that the transition from purely undular to breaking bore may be recast with the help of a breaking criterion for solitary waves.     

A short comment on the effect of a shear layer on nonlinear water waves

In this paper we study nonlinear periodic deep water waves propagating on a background shear current,which decays exponentially with depth.We extend the study of Cheng,Cang and Liao(2009) by introducing a second parameter which measures the depth of the shear current.A high-order convergent analytical series solution is obtained by the homotopy analysis method(HAM).A detailed analysis of the impact of the depth parameter is given.We find that increasing this parameter so that the shear current is thinner re...     

Spectrotemporal analysis of guided-wave pulse-echo signals: Part 1. Dispersive systems

In this paper, a wavelet-based time frequency analysis is presented to analyze guided-wave signals for rapid inspection of thin-walled structural members. The overall objective is to detect and locate discontinuities using a single broadband signal. Part 1 of this paper shows how the wavelet transform can be used to analyze a dispersive system. A straightforward procedure is developed to extract group delay information from the computed wavelet transform coefficients. The procedure is demonstrated by a simulation study for single-mode and simple dual-mode dispersion signals. Part 2 is an experimental study of multimode dispersion.     

The effects of rigid polystyrene particles on the glass transition characteristics and mechanical wave attenuation of styrene‐butadiene rubber: Particle size and acoustic mismatch

Glass transition characteristics and mechanical wave attenuation of the neat and filled styrene‐butadiene rubber (SBR) containing 10 wt % of rigid monosize polystyrene particles of various diameters from several hundred microns down to several tens of nanometers were investigated by dynamic mechanical thermal analysis, impedance tube, and ultrasonic spectroscopy. The results showed the matrix damping capacity and the breadth of glass transition increase by reducing the size of rigid particles due to the matrix‐particles interfacial area increase as the major governing parameter. Matrix glass transition broadening toward higher temperatures was attributed to the increased dynamic heterogeneity induced by fillers, whereas the damping capacity increase was assigned to contribution of interfacial friction loss mechanism. The proposed postulation was confirmed based on the calculated temperature distribution of the relaxing matrix volume fraction. Sound wave attenuation by the matrix and PS particles filled systems led to a broad absorption peak for the former and appearance of a secondary absorption peak at lower frequencies for the latter. Intensity of this secondary peak was highest for the system containing PS nanoparticles. Finally, ultrasonic attenuation enhanced by the PS particle size to wavelength ratio increase according to α_sca ～ (d/λ)^0.38 scaling law and declined by replacing the dense particles with larger hollow PS particles. Comparison of the normalized attenuation of the PS particle filled SBR in various mechanical wave attenuation regimes implied low sensitivity to particle size in vibration, mild differentiation in the sound, and finally severe differentiation in the ultrasound regimes. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 82–88, 2010     

Growing crack as superposition of surface Rayleigh waves

A crack, symmetrically propagating in elastic material, was considered as superposition of surface Rayleigh waves. The self-similar growth of face loaded crack was considered in detail. Exact expressions of deformation and stress fields in the crack’s surrounding were found and asymptotic behavior of stress near crack’s tips was also obtained. A condition that determines the crack’s velocity of self-similar propagation was found.     

Coherent structures in presence of dust charge fluctuations

This paper shows the formation of nonlinear coherent structures in a dusty plasma in presence of dust charge fluctuations. Using the typical plasma parameters the potential of the nonlinear coherent structures is derived.     

Symmetry Analysis of Nonlinear Incompressible Non-Hydrostatic Boussinesq Equations

The symmetries of the （2＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq （INHB） equations, which describe the atmospheric gravity waves （GWs）, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. Calculation shows the INHB equations are invariant under some Galilean transformations, scaling transformations, and space-time translations. The symmetry reduction equations and similar solutions of the INHB equations are proposed.     

Influence of nonlinearly induced diffraction on spatial solitary waves

Spatial solitary waves carried by a TE mode in planar optical waveguides with Kerr-type of nonlinearity are investigated based on a modified nonlinear (1 + 1) Schrödinger equation. Looking for effects instigated by the spatial inhomogeneity of the nonlinear polarization, the nonzero divE-term is taken into account in the nonlinear guided wave equation together with the nonparaxial approach and vector model. It is shown that, at self-focusing of beams in a (1 + 1) geometry, the effect coming out from the divergence term predominates over modifications related to the nonparaxial vector model. This term is interpreted as nonlinearly induced diffraction which plays the role of an effective saturation. Analytical solutions supported by numerical results are found.     

Electromagnetically induced transparency in a non-uniform plasma

Electromagnetically induced transparency in a non-uniform plasma is investigated. We discuss the possible frequency ranges in which a weak beam below cutoff can propagate transparently in this plasma with the presence of a strong high frequency field. We also analyze the effect of driving intensity on the frequency range of the probe. Received 3 March 2000 and Received in final form 21 April 2000