Wave refraction

Meyer was known for his researeh in asymptotic analysis, partial differential equations, plasma physics, water waves, meteorology, and in gas dynamics. In the latter field he explored supercritical nozzle flows. In water waves theory, the fundamental hydraulics were studied in collaboration with Joseph B. Keller (1923-), including wave refraction and resonance, extending short wave asymptotics to obtain notable advances in the spatial theory of the classical water waves with applications to both coastal and shelf oceanography. He was a member of the Australian Academy of Sciences. Meyer was an individualist who marched to no one s drum but his own. 

Bay-head beaches are one of the commonest types of coastal deposits, and they tend to straighten a coastline. Wave refraction causes longshore drift to move from headlands to bays where sediments are deposited. Marine deposition also helps straighten coastlines by building beach plains. 

A hot or cold gas layer around a body may significantly influence the distribution of pressure when a shock wave (SW) strikes the surface. Numerical and experimental simulation is used to analyze shock wave refraction at the interface between gases of different density, the pr ures on the bodies are determined, and approximate estimates are provided of the pressure at the front of the body after a re acted shock wave reflects from it. The results for the shock wave refraction on planar and convex cylindrical contact surfaces (CS) are analyzed and compared. 

If the wave vector k forms an angle 0 0 or 90"" with the optical axis, the wave in the crystal splits into an ordinary beam (refractive index n = 2 = o) where the phase velocity is independent of 9, and an extraordinary wave (refractive index Uq) where and therefore the phase velocity does depend on the direction 6 (Fig. 6.1b). 

The actual computation of the longshore transport for determining the long term stability of the shoreline and its stability under severe flood conditions requires data on the heights, periods and directions of breaking waves, which should be evaluated by means of wave refraction diagrams, and the characteristics of beach sediments. 

Fourth Mechanism. In the fourth mechanism, extreme wave events result from the high-order nonlinear interactions specifically, the underlying mechanism is four-wave interactions. Numerical and experimental studies have demonstrated that freak-like waves can be generated frequently in a two-dimensional wave flume, even in the absence of a current, or wave refraction, or wave diffraction " see Fig. 6.2. Further, numerical studies clearly indicate that a freak wave having a single, steep crest can be generated in deep-water by the third-order nonlinear interactions. ... 

When the wave period increases (thus the wavelength increases), the combined effect of wave diffraction, wave refraction, and wave reflection from the harbor boundaries is very significant. In fact, it is possible that for certain semi-enclosed harbor the combined effect of wave diffraction, refraction, and multiple reflections from the boundaries can cause significant increase in the wave amplitude compared with the incident wave amplitude. This is commonly referred to as harbor resonance due to long waves. 

An effective and convenient model equation which has been found to be well suited for combining the effects of wave refraction and diffraction in the coastal region is the two-dimensional elhptic mild slope wave equation first derived by Berkhoff.2... 

Basins are much wider and often larger than flumes, meaning higher construction costs and water usage occur, but the model can be larger and 3D. Waves can be multi-directional and more realistic because the wave transformation mechanisms of wave refraction and diffraction can be simulated. 

Possible nondestructive testing techniques for adhesively bonded structures and composite materials will be introduced along with a literature survey of successes and applications to date. Emphasis on ultrasonic inspection will also be highlighted, including such topics as ultrasonic wave generation, wave velocity, dispersion, reflection factor, wave refraction, attenuation, ultrasonic field analysis, resolution, thickness and defect location measurement, and C-scan testing. 

Wave refraction and reflection are ubiquitous in conservative media [29] however, until recently they had not been studied in excitable reaction-diffusion systems. Refraction was studied theoretically by Momev [30] in a reaction-diffusion system consisting of two regions with different diffusion coefficients and identical local chemical kinetics. Refraction of chemical waves was observed for the first time by Agladze and De Kepper [31] in the ferroin-catalyzed BZ system at the boundary between solution and polyacrylamide gel. In their experiments the jump in wave velocity produced by the difference in diffusion coefficients was small, and the authors were unable to make quantitative measurements. 

The ionosphere has an important effect on a position error. Propagation time differs from a geometric distance between the satelhte and the receiver. This physical phenomena is caused by the wave refraction and the Faraday rotation. These phenomena depend on a number of electrically charged particles in a unit volume of the ionosphere (TEC, Total Electron Content [elections/m ]). Several models are used for this error suppression (Klobuchar for example). These errors could be mitigated with the knowledge of a difference among measurements at two or more frequencies with a help of Equations (2) (3) (Bradford, 2009). 

The resulting change in the extraordinary wave refractive index is thus given by... 

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