Showing papers on "Wave propagation published in 2009"

Theory of Reflectance and Emittance Spectroscopy

Abstract: Acknowledgements 1. Introduction 2. Electromagnetic wave propagation 3. The absorption of light 4. Specular reflection 5. Single particle scattering: perfect spheres 6. Single particle scattering: irregular particles 7. Propagation in a nonuniform medium: the equation of radiative transfer 8. The bidirectional reflectance of a semi-infinite medium 9. The opposition effect 10. A miscellany of bidirectional reflectances and related quantities 11. Integrated reflectances and planetary photometry 12. Photometric effects of large scale roughness 13. Polarization 14. Reflectance spectroscopy 15. Thermal emission and emittance spectroscopy 16. Simultaneous transport of energy by radiation and conduction Appendix A. A brief review of vector calculus Appendix B. Functions of a complex variable Appendix C. The wave equation in spherical coordinates Appendix D. Fraunhoffer diffraction by a circular hole Appendix E. Table of symbols Bibliography Index.

Eikonal tomography: surface wave tomography by phase front tracking across a regional broad‐band seismic array

Abstract: SUMMARY We present a new method of surface wave tomography based on applying the eikonal equation to observed phase traveltime surfaces computed from seismic ambient noise. The source–receiver reciprocity in the ambient noise method implies that each station can be considered to be an effective source and the phase traveltime between that source and all other stations is used to track the phase front and construct the phase traveltime surface. Assuming that the amplitude of the waveform varies smoothly, the eikonal equation states that the gradient of the phase traveltime surface can be used to estimate both the local phase speed and the direction of wave propagation. For each location, we statistically summarize the distribution of azimuthally dependent phase speed measurements based on the phase traveltime surfaces centred on different effective source locations to estimate both the isotropic and azimuthally anisotropic phase speeds and their uncertainties. Examples are presented for the 12 and 24 s Rayleigh waves for the EarthScope/USArray Transportable Array stations in the western USA. We show that (1) the major resulting tomographic features are consistent with traditional inversion methods, (2) reliable uncertainties can be estimated for both the isotropic and anisotropic phase speeds, (3) ‘resolution’ can be approximated by the coherence length of the phase speed measurements and is about equal to the station spacing, (4) no explicit regularization is required in the inversion process and (5) azimuthally dependent phase speed anisotropy can be observed directly without assuming its functional form.

Depth‐integrated, non‐hydrostatic model for wave breaking and run‐up

Abstract: This paper describes the formulation, verification, and validation of a depth-integrated, non-hydrostatic model with a semi-implicit, finite difference scheme. The formulation builds on the nonlinear shallow-water equations and utilizes a non-hydrostatic pressure term to describe weakly dispersive waves. A momentum-conserved advection scheme enables modeling of breaking waves without the aid of analytical solutions for bore approximation or empirical equations for energy dissipation. An upwind scheme extrapolates the free-surface elevation instead of the flow depth to provide the flux in the momentum and continuity equations. This greatly improves the model stability, which is essential for computation of energetic breaking waves and run-up. The computed results show very good agreement with laboratory data for wave propagation, transformation, breaking, and run-up. Since the numerical scheme to the momentum and continuity equations remains explicit, the implicit non-hydrostatic solution is directly applicable to existing nonlinear shallow-water models. Copyright © 2008 John Wiley & Sons, Ltd.

Streamwise-travelling waves of spanwise wall velocity for turbulent drag reduction

Abstract: Waves of spanwise velocity imposed at the walls of a plane turbulent channel flow are studied by direct numerical simulations. We consider sinusoidal waves of spanwise velocity which vary in time and are modulated in space along the streamwise direction. The phase speed may be null, positive or negative, so that the waves may be either stationary or travelling forward or backward in the direction of the mean flow. Such a forcing includes as particular cases two known techniques for reducing friction drag: the oscillating wall technique (a travelling wave with infinite phase speed) and the recently proposed steady distribution of spanwise velocity (a wave with zero phase speed). The travelling waves alter the friction drag significantly. Waves which slowly travel forward produce a large reduction of drag that can relaminarize the flow at low values of the Reynolds number. Faster waves yield a totally different outcome, i.e. drag increase (DI). Even faster waves produce a drag reduction (DR) effect again. Backward-travelling waves instead lead to DR at any speed. The travelling waves, when they reduce drag, operate in similar fashion to the oscillating wall, with an improved energetic efficiency. DI is observed when the waves travel at a speed comparable with that of the convecting near-wall turbulence structures. A diagram illustrating the different flow behaviours is presented.

Propagation of vector vortex beams through a turbulent atmosphere

Abstract: We numerically study the propagation properties of vector vortex beams through a turbulent atmosphere. The irradiance pattern, degree of polarization, and scintillation index of radially polarized beam are computed for different propagation distances in an atmosphere with weak and strong turbulences. Corresponding properties of a fundamental Gaussian beam and a scalar vortex beam with topological charge of + 1 propagating through the same atmospheric turbulence conditions are calculated for comparison. With the same initial intensity profile, the vector vortex beam shows substantially lower scintillation than the scalar vortex. The existence of the vectorial vortex can be identified with longer propagation distance than the scalar vortex even with vanishing characteristic vortex structure in the irradiance images. This indicates the potential advantages of using a vector vortex beam to mitigate atmospheric effects and enable a more robust free space communication channel with longer link distance.

Statistical properties of directional ocean waves: the role of the modulational instability in the formation of extreme events.

Abstract: We discuss two independent, large scale experiments performed in two wave basins of different dimensions in which the statistics of the surface wave elevation are addressed. Both facilities are equipped with a wave maker capable of generating waves with prescribed frequency and directional properties. The experimental results show that the probability of the formation of large amplitude waves strongly depends on the directional properties of the waves. Sea states characterized by long-crested and steep waves are more likely to be populated by freak waves with respect to those characterized by a large directional spreading.

Evaluation of fatigue damage using nonlinear guided waves

Abstract: This research develops an experimental procedure for characterizing fatigue damage in metallic plates using nonlinear guided waves. The work first considers the propagation of nonlinear waves in a dispersive medium and determines the theoretical and practical considerations for the generation of higher order harmonics in guided waves. By using results from the nonlinear optics literature, it is possible to demonstrate that both phase and group velocity matching are essential for the practical generation of nonlinear guided elastic waves. Next, the normalized acoustic nonlinearity of low cycle fatigue damaged aluminum specimens is measured with Lamb waves. A pair of wedge transducers is used to generate and detect the fundamental and second harmonic Lamb waves. The results show that the normalized acoustic nonlinearity measured with Lamb waves is directly related to fatigue damage in a fashion that is similar to the behavior of longitudinal and Rayleigh waves. This normalized acoustic nonlinearity is then compared with the measured cumulative plastic strain to confirm that these two parameters are related, and to reinforce the notion that Lamb waves can be used to quantitatively assess plasticity driven fatigue damage using established higher harmonic generation techniques.

PLANE WAVE DISCONTINUOUS GALERKIN METHODS: ANALYSIS OF THE h-VERSION ∗, ∗∗

Abstract: We are concerned with a finite element approximation for time-harmonic wave propagation governed by the Helmholtz equation. The usually oscillatory behavior of solutions, along with numerical dispersion, render standard finite element methods grossly inefficient already in medium-frequency regimes. As an alternative, methods that incorporate information about the solution in the form of plane waves have been proposed. We focus on a class of Trefftz-type discontinuous Galerkin methods that employs trial and test spaces spanned by local plane waves. In this paper we give ap riori convergence estimates for the h-version of these plane wave discontinuous Galerkin methods in two dimensions. To that end, we develop new inverse and approximation estimates for plane waves and use these in the context of duality techniques. Asymptotic optimality of the method in a mesh dependent norm can be established. However, the estimates require a minimal resolution of the mesh beyond what it takes to resolve the wavelength. We give numerical evidence that this requirement cannot be dispensed with. It reflects the presence of numerical dispersion.

Statistical properties of mechanically generated surface gravity waves: a laboratory experiment in a three-dimensional wave basin

Abstract: A wave basin experiment has been performed in the MARINTEK laboratories, in one of the largest existing three-dimensional wave tanks in the world. The aim of the experiment is to investigate the effects of directional energy distribution on the statistical properties of surface gravity waves. Different degrees of directionality have been considered, starting from long-crested waves up to directional distributions with a spread of ±30° at the spectral peak. Particular attention is given to the tails of the distribution function of the surface elevation, wave heights and wave crests. Comparison with a simplified model based on second-order theory is reported. The results show that for long-crested, steep and narrow-banded waves, the second-order theory underestimates the probability of occurrence of large waves. As directional effects are included, the departure from second-order theory becomes less accentuated and the surface elevation is characterized by weak deviations from Gaussian statistics.

Waveguiding and frequency selection of Lamb waves in a plate with a periodic stubbed surface

Abstract: In this paper, we numerically and experimentally study the waveguiding of Lamb modes in a thin plate with a periodic stubbed surface and propose a frequency-selection method based on the found complete band gaps of Lamb waves in the periodic structure In the numerical simulations, we employ finite-element method to analyze the waveguiding effect of a line defect created in the periodic plate structure; and on the experimental side, we utilize a pulsed laser to generate broadband elastic-wave energy and a laser interferometer to receive the wave signals inside the line-defect waveguide In the experiment, well-confined acoustic energy in the acoustic band gaps is observed Furthermore, a polyline sharply bent waveguide is designed and used for the frequency selection of Lamb waves Measurements show that acoustic energy with frequencies in the band gaps can be separated out and guided by the bent waveguiding route The characteristics of deaf bands found in the experiment are discussed as well

Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation

Abstract: A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on the surface elevation and the velocity potential at the free surface. These equations involve a Dirichlet-Neumann operator and we show that all the asymptotic models can be recovered by a simple asymptotic expansion of this operator, in function of the shallowness parameter (shallow water limit) or the steepness parameter (deep water limit). Based on this method, a new two-dimensional fully dispersive model for small wave steepness is also derived, which extends to uneven bottom the approach developed by Matsuno \cite{matsuno3} and Choi \cite{choi}. This model is still valid in shallow water but with less precision than what can be achieved with Green-Naghdi model, when fully nonlinear waves are considered. The combination, or the coupling, of the new fully dispersive equations with the fully nonlinear shallow water Green-Naghdi equations represents a relevant model for describing ocean wave propagation from deep to shallow waters.

Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium

Abstract: We review the geometrical-optics evolution of an electromagnetic wave propagating along a curved ray trajectory in a gradient-index dielectric medium. A Coriolis-type term appears in Maxwell equations under transition to the rotating coordinate system accompanying the ray. This term describes the spin–orbit coupling of light which consists of (i) the Berry phase responsible for trajectory-dependent polarization variations and (ii) the spin Hall effect representing polarization-dependent trajectory perturbations. These mutual phenomena are described within universal geometrical structures underlying the problem and are explained by the dynamics of the intrinsic angular momentum carried by the wave. Such close geometrodynamical interrelations illuminate a dual physical nature of the phenomena.

Optical anisotropic metamaterials: Negative refraction and focusing

Abstract: We design three-dimensional (3D) metallic nanowire media with different structures and numerically demonstrate that they can be homogeneous effective indefinite anisotropic media by showing that their dispersion relations are hyperbolic. For a finite slab, a nice fitting procedure is exploited to obtain the dispersion relations from which we retrieve the effective permittivities. The pseudo focusing for the real 3D wire medium agrees very well with the homogeneous medium having the effective permittivity tensor of the wire medium. Studies also show that in the long-wavelength limit, the hyperbolic dispersion relation of the 3D wire medium can be valid even for evanescent modes.

Observation of electronic structure minima in high-harmonic generation.

Abstract: We report detailed measurements of the high-harmonic spectra generated from argon atoms. The spectra exhibit a deep minimum that is shown to be independent of the laser intensity, and is thus a clear measure of the electronic structure of the atom. We show that exact field-free continuum wave functions reproduce the minimum, but plane wave and Coulomb wave functions do not. This remarkable observation suggests that electronic structure can be accurately determined in high-harmonic experiments despite the presence of the strong laser field. Our results clarify the relation between high-harmonic generation and photoelectron spectroscopy. The use of exact continuum functions also resolves the ambiguity associated with the choice of the dispersion relation.

An investigation of the lowest-order transverse-electric (TE_1) mode of the parallel-plate waveguide for THz pulse propagation

Abstract: We experimentally and theoretically investigate the lowest-order transverse-electric (TE1) mode of the parallel-plate waveguide (PPWG) for the propagation of broadband THz pulses. We demonstrate undistorted THz pulse propagation via the single TE1 mode, solving the group-velocity-dispersion and spectral-filtering problems caused by the mode's low-frequency cutoff. We observe a remarkable counterintuitive property of the TE1 mode: its attenuation decreases with increasing frequency for all frequencies above cutoff. This phenomenon has not been observed with any other THz waveguide to date, and it can enable extremely low-loss propagation. We present a physical interpretation of this frequency-dependent behavior using a simple plane-wave description of the TE1 mode propagation. We also find that it is possible to achieve almost 100% coupling to the TE1 mode from a focused free-space Gaussian beam. In addition, using the above plane-wave analysis, we show how to mitigate the diffraction losses inherent to long path-length PPWGs via the use of transverse-concave plates.

An unsplit convolutional perfectly matched layer technique improved at grazing incidence for the viscoelastic wave equation

Abstract: SUMMARY In the context of the simulation of wave propagation, the perfectly matched layer (PML) absorbing boundary layer has proven to be efficient to absorb non-grazing incidence waves. However, the classical discrete PML cannot efficiently absorb waves reaching the absorbing layer at grazing incidence. This is observed, for instance, in the case of thin mesh slices, or in the case of sources located close to the absorbing boundaries or receivers located at large offset. In order to improve the PML efficiency at grazing incidence we derive an unsplit convolutional PML (CPML) for a fourth-order staggered finite-difference numerical scheme applied to the 3-D viscoelastic seismic wave equation. The time marching equations of the standard linear solid mechanisms used do not need to be split and only the memory variables associated with velocity derivatives are stored at each time step. This is important in the case of more than one damping mechanism. Memory storage is reduced by more than 70 per cent in the PML regions in 3-D simulations compared to split PMLs optimized at grazing incidence. We validate the technique based on a benchmark performed in a thin mesh slice.

The Pseudo-analytical Method: Application of Pseudo-Laplacians to Acoustic And Acoustic Anisotropic Wave Propagation

Abstract: Summary We generalize the pseudo-spectral method for the acoustic wave equation to create analytical solutions to the constant velocity acoustic wave equation in an arbitrary number of space dimensions. We accomplish this by modifying the Fourier Transform of the Laplacian operator so that it compensates exactly for the error due to the second-order finite-difference time marching scheme used in the conventional pseudo-spectral method. Of more practical interest, we show that this modified or pseudo-Laplacian is a smoothly varying function of the parameters of the acoustic wave equation (velocity most importantly) and thus can be further generalized to create near-analyticallyaccurate solutions for the variable velocity case. We call this new method the pseudo-analytical method. We further show that by applying this approach to the concept of acoustic anisotropic wave propagation, we can create scalar-mode VTI and TTI wave equations that overcome the disadvantages of previously published methods for acoustic anisotropic wave propagation. These methods should be ideal for forward modeling and reverse time migration applications.

The Dynamics of Modulated Wave Trains

Abstract: The authors of this title investigate the dynamics of weakly-modulated nonlinear wave trains. For reaction-diffusion systems and for the complex Ginzburg - Landau equation, they establish rigorously that slowly varying modulations of wave trains are well approximated by solutions to the Burgers equation over the natural time scale. In addition to the validity of the Burgers equation, they show that the viscous shock profiles in the Burgers equation for the wave number can be found as genuine modulated waves in the underlying reaction-diffusion system. In other words, they establish the existence and stability of waves that are time-periodic in appropriately moving coordinate frames which separate regions in physical space that are occupied by wave trains of different, but almost identical, wave number. The speed of these shocks is determined by the Rankine - Hugoniot condition where the flux is given by the nonlinear dispersion relation of the wave trains. The group velocities of the wave trains in a frame moving with the interface are directed toward the interface. Using pulse-interaction theory, the authors also consider similar shock profiles for wave trains with large wave number, that is, for an infinite sequence of widely separated pulses. The results presented here are applied to the FitzHugh - Nagumo equation and to hydrodynamic stability problems.

Oblique propagation of whistler mode waves in the chorus source region

Abstract: [1] Whistler mode chorus has been shown to play a role in the process of local acceleration of electrons in the outer Van Allen radiation belt. Most of the quasi-linear and nonlinear theoretical studies assume that the waves propagate parallel to the terrestrial magnetic field. We show a case where this assumption is invalid. We use data from the Cluster spacecraft to characterize propagation and spectral properties of chorus. The recorded high-resolution waveforms show that chorus in the source region can be formed by a succession of discrete wave packets with decreasing frequency that sometimes change into shapeless hiss. These changes occur at the same time in the entire source region. Multicomponent measurements show that waves in both these regimes can be found at large angles to the terrestrial magnetic field. The hiss intervals contain waves propagating less than one tenth of a degree from the resonance cone. In the regime of discrete wave packets the peak of the wave energy density is found at a few degrees from the resonance cone in a broad interval of azimuth angles. The wave intensity increases with the distance from the magnetic field minimum along a given field line, indicating a gradual amplification of chorus in the source region.

Nonlinear fast magnetoacoustic wave propagation in the neighbourhood of a 2D magnetic X-point: oscillatory reconnection

Abstract: Context. This paper extends the models of Craig & McClymont ( 1991, ApJ, 371, L41) and McLaughlin & Hood ( 2004, A& A, 420, 1129) to include finite beta and nonlinear effects. Aims. We investigate the nature of nonlinear fast magnetoacoustic waves about a 2D magnetic X-point. Methods. We solve the compressible and resistive MHD equations using a Lagrangian remap, shock capturing code (Arber et al. 2001, J. Comp. Phys., 171, 151) and consider an initial condition in v x B . (z) over cap (a natural variable of the system). Results. We observe the formation of both fast and slow oblique magnetic shocks. The nonlinear wave deforms the X-point into a "cusp-like" point which in turn collapses to a current sheet. The system then evolves through a series of horizontal and vertical current sheets, with associated changes in connectivity, i.e. the system exhibits oscillatory reconnection. Our final state is non-potential (but in force balance) due to asymmetric heating from the shocks. Larger amplitudes in our initial condition correspond to larger values of the final current density left in the system. Conclusions. The inclusion of nonlinear terms introduces several new features to the system that were absent from the linear regime.

Photonic band gap structures of obliquely incident electromagnetic wave propagation in a one-dimension absorptive plasma photonic crystal

Abstract: The photonic band gap structures of obliquely incident electromagnetic waves propagating in a one-dimension plasma photonic crystal with collision have been studied on the basis of electromagnetic theory and transfer matrix approach. The dispersion relations for both the transverse electric wave case and the transverse magnetic wave case are deduced. And the photonic band gap structures, with their function dependence on the microplasma layer density, microplasma width, collision frequency, background material dielectric constant, and incident angle, are computed. The results show that there exist two photonic band gap structures in an adsorptive plasma photonic crystal: one is a normal photonic band gap structure and the other is an absorption photonic band gap structure. Parameter dependence of the effects is calculated and discussed.