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Dispersion (water waves)
About: Dispersion (water waves) is a research topic. Over the lifetime, 10134 publications have been published within this topic receiving 248462 citations.
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22 Feb 2000
TL;DR: In this paper, the authors present a detailed development of the acoustical wave equation, including propagation in Stratified media and propagation in Dissipative Fluids: Absorption and Dispersion.
Abstract: Detailed Development of the Acoustical Wave Equation. Reflection and Transmission of Normally Incident Plane Waves of Arbitrary Waveform. Normal Incidence Continued: Steady-State Analysis. Transmission Phenomena: Oblique Incidence. Normal Modes in Cartesian Coordinates: Strings, Membranes, Rooms, and Rectangular Waveguides. Horns. Propagation in Stratified Media. Propagation in Dissipative Fluids: Absorption and Dispersion. Spherical Waves. Cylindrical Waves. Waveguides. Radiation from a Baffled Piston. Diffraction. Arrays. Appendices. Index.
920 citations
TL;DR: In this article, a two-dimensional Fourier transform (2D FFT) was used to measure the amplitudes and velocities of the Lamb waves propagating in a plate, the output of the transform being presented using an isometric projection which gives a three-dimensional view of the wave-number dispersion curves.
Abstract: A technique for the analysis of propagating multimode signals is presented. The method involves a two-dimensional Fourier transformation of the time history of the waves received at a series of equally spaced positions along the propagation path. The technique has been used to measure the amplitudes and velocities of the Lamb waves propagating in a plate, the output of the transform being presented using an isometric projection which gives a three-dimensional view of the wave-number dispersion curves. The results of numerical and experimental studies to measure the dispersion curves of Lamb waves propagating in 0.5-, 2.0-, and 3.0-mm-thick steel plates are presented. The results are in good agreement with analytical predictions and show the effectiveness of using the two-dimensional Fourier transform (2-D FFT) method to identify and measure the amplitudes of individual Lamb modes.
889 citations
TL;DR: In this paper, the authors used convectively coupled equatorial waves (CCEWs) to simulate tropical rainfall variability in the equatorial beta plane of a tropical weather system, and found that CCEWs display a large degree of self-similarity over a surprisingly wide range of scales.
Abstract: [1] Convectively coupled equatorial waves (CCEWs) control a substantial fraction of tropical rainfall variability. Their horizontal structures and dispersion characteristics correspond to Matsuno's (1966) solutions of the shallow water equations on an equatorial beta plane, namely, Kelvin, equatorial Rossby, mixed Rossby-gravity, and inertio-gravity waves. Because of moist processes, the tilted vertical structures of CCEWs are complex, and their scales do not correspond to that expected from the linear theory of dry waves. The dynamical structures and cloud morphology of CCEWs display a large degree of self-similarity over a surprisingly wide range of scales, with shallow convection at their leading edge, followed by deep convection and then stratiform precipitation, mirroring that of individual mesoscale convective complexes. CCEWs have broad impacts within the tropics, and their simulation in general circulation models is still problematic, although progress has been made using simpler models. A complete understanding of CCEWs remains a challenge in tropical meteorology.
882 citations
01 Jan 2012
TL;DR: In particular, the linear dispersive term in the Korteweg-de Vries equation prevents this from ever happening in its solution as discussed by the authors, and the instability and subsequent modulation of an initially uniform wave profile can be prevented by including dispersive effects in the shallow water theory.
Abstract: Dispersion and nonlinearity play a fundamental role in wave motions in nature. The nonlinear shallow water equations that neglect dispersion altogether lead to breaking phenomena of the typical hyperbolic kind with the development of a vertical profile. In particular, the linear dispersive term in the Korteweg–de Vries equation prevents this from ever happening in its solution. In general, breaking can be prevented by including dispersive effects in the shallow water theory. The nonlinear theory provides some insight into the question of how nonlinearity affects dispersive wave motions. Another interesting feature is the instability and subsequent modulation of an initially uniform wave profile.
864 citations
TL;DR: The theory of anomalous diffraction gratings, which was developed some years ago, has been reexamined in order to visualize its physical meaning as mentioned in this paper, where each wave diffracted by a grating is identified through the component of its wave vector tangential to the grating.
Abstract: The theory of Wood’s anomalous diffraction gratings, which was developed some years ago, has been reexamined in order to visualize its physical meaning. Each wave diffracted by a grating is identified through the component of its “wave vector” tangential to the grating. Surface waves similar to those found in total internal reflection are included (§2). The amplitudes of these waves can be calculated by successive approximations (§3). One feature of the anomalies is connected with the infinite dispersion of spectra at grazing emergence (§4). Emphasis is put on the existence of polarized quasi-stationary waves which represent an energy current rolling along the surface of a metal (§5). These waves can be strongly excited on the surface of metallic gratings under critical conditions depending also on the profile of the grooves; secondary interference phenomena arise then in the observed spectra (§6). The connection of the quasi-stationary surface waves with the wireless ground waves is discussed (§7). A general formulation is introduced to discuss the significance of the approximation used (Appendix).
838 citations