Diffraction Of Short Waves Research Articles

Diffraction of short waves modelled using new mapped wave envelope finite and infinite elements

We consider a two-dimensional wave diffraction problem from a closed body such that the complex progressive wave potential satisfies the Sommerfield condition and the Helmholtz equation. We are interested in the case where the wavelength is much smaller than any other length dimensions of the problem. We introduce new mapped wave envelope infinite elements to model the potential in the far field, and test them for some simple Dirichlet boundary condition problems. They are used in conjuction with wave envelope finite elements developed earlier [1] to model the potential in the near field. An iterative procedure is used in which an initial estimate of the phase is iteratively improved. The iteration scheme, by which the wave envelope and phase are recovered, is described in detail. Copyright © 1999 John Wiley & Sons, Ltd.

The effect of coastal currents on diffraction of short waves and their impact upon a vertical wall

In terms of linear theory, a solution is derived to the problem on diffraction of a short wave running at an arbitrary angle toward an area of long-shore flows, bounded by a vertical wall. Dependencies of the wave field parameters and of the impact upon the wall on the magnitude and direction of flows, on the angle of incidence of the wave, and on the width of the near-shore flow are examined.

A universal law for HF field behavior near the surface of a moving perfectly conducting cylinder in the penumbra region

Asymptotic methods in the problems of diffraction of short waves from motionless objects are developed in detail. Much less attention has been paid to the theory for moving interfaces. In particular, of principal interest are phenomena that occur at relativistic velocities of the interface motion. The heuristic principles of locality and apparent location of the interface indicate that the universal Fock’s law for the field behavior in the penumbra region holds true for a convex perfectly conducting body, which travels in free space. The emerging new parameter (cylinder travel velocity) does not influence the description of kinematic phenomena if the apparent location of the interface is used instead of its instantaneous location.

Combined refraction and diffraction of short waves using the dual-reciprocity boundary-element method

Short waves are those with a wavelength-to-depth ratio of less than approximately 20; they play an important role in coastal sediment transport as well as the harbour oscillations with which coastal engineers are concerned. It is usually much more difficult to numerically model the combined effects of the refraction and diffraction of short waves in coastal regions, due to the fact that a large number of grid points is usually required if the computational domain itself must be discretized. In this paper, the dual-reciprocity boundary-element method (DRBEM) model developed by Zhu [ Eng. Anal. with Boundary Elements, 12 (1993) 261–74] is further applied to the case of waves with short wavelengths. The model's excellent accuracy and efficiency in modelling short waves is further established after some of our preliminary results are compared with corresponding previously published numerical and experimental data.

Diffraction properties of a defocusing ionospheric lens

The problem of short-wave signal diffraction by a defocusing lens induced by powerful short-wave radiation in the ionosphere has been solved. It is shown that the received signal is subject both to a noticeable attenuation and a significant increase in the local caustic areas at the terrestrial surface. The results of calculations are compared with the experimental data. The basic characteristics of an artificial ionospheric lens are presented.

Surface Waves and Coastal Dynamics

This review covers theoretical advances made during the past decade for predicting or understanding wind-induced waves and associated coastal processes. First, the offshore propagation over many wavelengths is discussed. An effective approximation which permits practical calculations of both refraction and diffraction over a mildly sloping bottom is given. For still longer distances nonlinear effects accumulate to become important; recent progress in the parabolic approximation for the refraction and diffraction of short waves is also reviewed. The nearshore region is discussed and the infragravity waves which are caused by nonlinear interactions of short waves within a narrow frequency band are surveyed. The effects of a gradual or sudden change of depth or a steady current on the modulation of short waves and the generation of long infragravity waves is also discussed. A discussion of infragravity waves which resonate in harbours and the strong resonance of edge waves on beaches is made. The final topics are concerned with the causes and effects of bars and ripples on the seabed.

Uniform and local asymptotic behavior of the penumbral wave field for diffraction of short waves on a smooth convex contour

Green's formula is applied to construct the asymptotic behavior of the penumbral wave field uniform in angles and in distances for the case of diffraction on a smooth convex contour.

Diffraction of short waves by a segment

The shortwave asymptotics of the Green function for a segment is investigated in the case of the Neumann boundary condition. In the shadow zone and the light zone terms describing the diffracted waves issuing from the end points of the segment are separated out from the solution in the form of a contour integral. The corresponding single integrals are then reduced to expressions coinciding with the formulas of the geometric theory of diffraction. It is here found, that the primary diffracted waves are described by series of residues having the same order with respect to the large parameter of the problem; for the series describing multiple diffracted waves it suffices to restrict attention to a single residue.

Diffraction of short waves on a screen of variable transparency

A model problem of a point source in the field of which there is a screen of variable transparency is considered. The character of the change of transparency of the screen makes it possible to construct an exact solution of the problem by the method of separation of variables. A shortwave asymptotic expression for the wave field is obtained.

Combined refraction and diffraction of short waves using the finite element method

A two-dimensional finite element numerical model is presented that calculates combined refraction and diffraction of short waves. The wave equation solved governs the propagation of periodic, small amplitude surface gravity waves over a variable depth seabed of mild slope. An efficient computational scheme is employed that allows the solution of practical problems that typically require large computational grids. Comparisons are presented between the finite element model calculations and an analytical solution, a two-dimensional numerical solution, a three-dimensional numerical solution, and measurements from a hydraulic model.

Diffraction by a nonplanar screen

This paper is concerned with diffraction of short waves by a nonplanar screen (two-dimensional case, Dirichlet boundary condition). The high-frequency asymptotic approximation to the solution is obtained. First the wave field of the primary wave is found in a neighbourhood of the screen edge and then this field is continued along the boundary. Secondary waves arise here as the consequence of interaction between the edge and the primary wave. The secondary wave is diffracted by another edge of the screen, and a third order wave arises, and so on. This process gives the formulas for the wave field in a neighbourhood of the screen. Green's formula is used to continue the solution outside of this neighbourhood.

Shortwave diffraction by an oblate spheroid

The diffraction of shortwaves emitted by a point source located on the equator on an oblate spheroid is investigated by a three-dimensional analog of Watson's method. The zone of deep shadow is considered under the assumption that the point of observation is near the source and is either on the surface of the spheroid or near this surface.

The integral equations of stationary problems on the diffraction of short waves at obstacles of the segment type

A METHOD is described for reducing two-dimensional stationary problems of the diffraction of short acoustic and elastic waves at obstacles of the segment type to integral equations of the second kind. It is shown that the principle of contractive mappings is applicable to these equations when the wavelength is sufficiently short. We investigate at the same time integral equations in which the kernel depends on the absolute value of the difference between two arguments, and when the arguments vary over a finite interval, under the assumption that the Fourier transform of the kernel has a finite number of zeros and cuts in the complex plane.

Some Theoretical Results on Diffraction of Short Waves by Thin Obstacles

Diffraction of short acoustic waves (plane or otherwise) may be treated by methods akin to geometrical optics provided that the lateral dimensions of the diffracting obstacle are large as compared with a wavelength. On the other hand, it is possible to construct thin- or slender-body theories that are directly analogous to corresponding aerodynamic theories only if the wavelength is large as compared with the lateral dimensions. The present theory is an attempt to explore the hazy middle ground where the wavelength and lateral dimensions are comparably small. Diffraction of a plane wave by a two-dimensional thin wing at zero incidence to the oncoming wave is considered as a model for this class of problems, and a method is given for finding the scattering into the region near the plane of the wing. In particular, we find a 45° phase shift and an asymptotic “x−3/2” decay of the scattered disturbance in the shadow region directly behind the wing. A corresponding result for a slender, sharply pointed, three-dimensional obstacle indicates a 90° phase shift and an “x−2” decay with distance.

XVII. On the diffraction of short waves by a rigid sphere

XVII. <i>On the diffraction of short waves by a rigid sphere</i>