The wide-spacing approximation applied to multiple scattering and sloshing problems

1990 ◽  
Vol 210 ◽  
pp. 647-658 ◽  
Author(s):  
D. V. Evans
Keyword(s):  
Plane Wave ◽  
Closed Form ◽  
Multiple Scattering ◽  
Water Wave ◽  
Wave Incident ◽  
Reflection And Transmission ◽  
Wide Spacing ◽  
Plane Wave Incident ◽  
Rigid Walls

Linear water-wave theor is used in conjuctin with a wide-spacing approximation to develop closed-form expressions for the reflection and transmission coeffcients appropriate to a plane wave incident upon any number of identical equally spaced obstacles in two dimensins, and also to derive a real expressin from which the sloshing requencies, which occur when the bodies are bounded by rigid walls, can be determined. In each case the solutin is in terms of known properties of radiation problems associated with any one of the bodies in isolation.

REPLY BY D. RANKIN TO THE DISCUSSION BY J. T. WEAVER

Geophysics ◽  
1963 ◽  
Vol 28 (3) ◽  
pp. 490-490
Author(s):  
D. Rankin
Keyword(s):  
Electromagnetic Field ◽  
Plane Wave ◽  
Radiation Field ◽  
Free Space ◽  
Wave Incident ◽  
Induction Field ◽  
The Earth ◽  
Plane Wave Incident

I am indebted to Weaver if he has indeed clarified certain points which I had previously considered to be obvious. Cagniard (1953) states explicitly the magnitude of the wavelengths in free space and it is further implicit in the work of Rankin (1962) that it is indeed this same electromagnetic field which is being considered. The plane wave aspect of the problem arises from the extent of and not the distance from the source so that truly it is the induction field and not the radiation field that is under discussion. I had believed, until this note by Weaver, that d’Erceville and Kunetz (1962) also considered a plane wave incident on the earth and in fact that I was merely following both Cagniard and d’Erceville and Kunetz in this matter. The consistency of the results would tend to confirm this belief.

REFLECTION FROM A WIRE GRID PARALLEL TO A CONDUCTING PLANE

1954 ◽  
Vol 32 (9) ◽  
pp. 571-579 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Plane Wave ◽  
Transmission Line ◽  
Incident Wave ◽  
Electric Vector ◽  
Wave Incident ◽  
Conducting Surface ◽  
Conducting Plane ◽  
Wire Grid ◽  
Parallel Wire ◽  
Plane Wave Incident

A solution is outlined for the problem of a plane wave incident obliquely on a parallel-wire grid which is backed by a plane conducting surface. The electric vector of the incident wave is taken to be parallel to the grid wires. The equivalent transmission line problem is pointed out. It is shown that, in certain cases, a resistive wire grid will absorb all the energy in the incident wave.

Island Rays

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Plane Wave ◽  
Deep Water ◽  
Wave Incident ◽  
Windward Side ◽  
Leeward Side ◽  
Wave Trapping ◽  
Wave Refraction ◽  
Plane Wave Incident ◽  
Waves And Currents ◽  
The Way

This chapter deals with the mathematics of rays that develop around islands. Island rays follow strange trajectories. On the windward side of the island, rays converge slightly, resulting in high waves. Because waves curving around each side of the island converge, waves are lower on the leeward side. Rays that curve around the protected side of the island and spin off into deep water again after turning more than 270 degrees [cross] others on the way. This is an example of how wave refraction around islands can contribute to confused seas. The chapter describes calculations relating to straight and parallel depth contours, focusing on plane wave incident and wave trapping on a ridge, as well as circular depth contours and constant phase lines. It also considers the case of waves and currents moving in exactly opposite directions, asking whether waves can be stopped by opposing streams.

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