Diffraction Of Kelvin Waves Research Articles

The diffraction of Kelvin wave due to an island

This paper describes a numerical method to determine the diffraction effect of an oceanographic Kelvin wave system by an island. A standard shallow water approximation theory is assumed for the oceanographic equation. The problem is solved in two cases, when the island is elliptic and circular in shape and when it is far or near to the coastline, also when the island becomes narrow and perpendicular to an infinitely long coastline. Numerical computation of diffraction of the Kelvin waves has been calculated and plotted.

The Diffraction of Kelvin Waves and Bores at Coastal Bends

Abstract Bends in coastal mountain ranges may diffract propagating atmospheric Kelvin waves and trapped coastal currents. Analytic solutions exist for the diffraction of both linear Kelvin waves and linear nonrotating gravity waves. Within the context of the single-layer shallow-water equations, we examine the diffraction of nonlinear gravity waves and bores in a nonrotating reference frame and nonlinear Kelvin waves and coastally trapped bores in a rotating reference frame. The diffraction process can significantly decrease the amplitude of linear and nonlinear waves and bores in the nonrotating reference frame. Unlike for their linear counterpart, however, the diffraction-related amplitude decay for the nonrotating nonlinear waves takes place entirely within the region of the bend and does not produce a continuous decay after the bend. Moreover, theory predicts a critical bend angle at which bore amplitudes will be zero at the wall after propagation around the bend, but shallow-water model simulations d...

The diffraction of Kelvin wave due to a narrow headland normal to an infinite coastline

This paper describes an analytic method to determine the diffraction of an oceanographic Kelvin wave system by a narrow headland with the headland being perpendicular to an infinitely long coastline.

Diffraction of kelvin waves in a rotating semibounded basin containing a semi-infinite wall

The Wiener-Hopf method is used to obtain the exact solution of the problem of Kelvin wave diffraction in a rotating semibounded basin containing a semi-infinite wall. The solution is analysed asymptotically and numerically. The nature of the waves propagated in the basin is discussed.

Diffraction of Kelvin waves by a finite barrier

The diffraction of Kelvin waves by a finite barrier and depth discontinuities is considered using Wiener-Hopf technique. Diffracted wave and generation of double Kelvin wave are studied and comparison has been made with the case of semi-infinite barrier and depth discontinuity.

Diffraction of kelvin waves in a channel with a semi-infinite wall

The Wiener-Hopf method is used to derive an exact solution of the problem of diffraction of Kelvin waves in a rotating channel containing a semi-infinite wall. A numerical analysis of the solution is carried out. The nature of the waves propagating in the channel is considered.

Propagation of kelvin waves from a channel into a semibounded tank

The problem of propagation of Kelvin waves from a channel into a semibounded tank is considered. An exact solution of the problem is constructed using the Wiener — Hopf method. The solution is analyzed asymptotically and numerically. The Wiener — Hopf method was used in /1,2/ to solve the problem of diffraction of the Kelvin waves in tanks bounded by the infinite and semiinfinite parallel walls. Below a generalized method of matching /3/ is used to solve the problem of diffraction of Kelvin waves in the case when the walls confining the fluid meet at the right angles.

Diffraction of Kelvin waves at the open end of a plane-parallel channel

The Wiener-Hopf method is used for solving the problem of surface wave diffraction at the end of a plane parallel channel in a tank rotating at constant velocity. Asymptotic and numerical analysis of the obtained solution is carried out.

Diffraction of Kelvin waves from a rotating channel with an infinite and a semi-infinite barrier

The diffraction of long waves in a rotating channel of constant depth, consisting of an infinite and a semi-infinite parallel barrier of zero thickness, is investigated. The excitation is due to a Kelvin wave travelling towards the open end from inside the channel. An exact solution is given for the region inside the semi-infinite channel, consisting of a 'reflected' Kelvin wave and the various travelling modes, which become attenuated waves when the width of the channel is less than a certain value. MOreover it is shown that there is a resonance effect for some critical values of the channel width. In the remaining region an asymptotic expression for the far field is obtained. This expression involves a Kelvin wave travelling along the infinite barrier and also an outgoing cylindrical wave (Poincare wave) coming from the edge of the semi-infinite barrier of the channel.

Diffraction of kelvin waves by a half-infinite wall in a semi-bounded basin

Diffraction of kelvin waves by a half-infinite wall in a semi-bounded basin

Diffraction of Kelvin waves at a sharp bend

A closed form solution is obtained for the linearized problem of the diffraction of Kelvin waves by a sharp bend on a rotating earth. It is shown that for the frequency ω of the incoming wave less than f, where ½f is the angular velocity of rotation, the wave is transmitted around the bend without change of amplitude. For ω > f the amplitude is in general reduced but is unaltered for the special angles π/(2n + 1). For these special angles the solution is obtained in elementary terms.

The diffraction of Kelvin waves at a corner

In a uniform rotating liquid of uniform depth, Kelvin waves may be propagated in one direction along a straight boundary of the liquid. The Wiener-Hopf technique is used to obtain the wave field due to Kelvin waves incident at a rightangle corner. An asymptotic solution is obtained for the field far from the corner. It is shown that for low frequencies the Kelvin waves are propagated round the corner without change of amplitude, but that for high frequencies cylindrical waves of the ‘Poincaré’ type are generated at the corner, so that the amplitudes of the Kelvin waves propagated round the corner are reduced.