On the radiation and scattering of short surface waves. Part 2

1973 ◽  
Vol 59 (1) ◽  
pp. 129-146 ◽  
Author(s):  
F. G. Leppington
Keyword(s):  
Surface Waves ◽  
Simple Wave ◽  
Finite Depth ◽  
Short Wave ◽  
Asymptotic Estimates ◽  
Radiation Problem ◽  
Expansion Technique ◽  
Wave Trains ◽  
Intersection Points ◽  
Scattering And Radiation

A short-wave asymptotic analysis is undertaken for problems concerned with the radiation and scattering of surface waves by a cylinder whose cross-section S intersects the free surface normally. It is assumed that S is locally smooth and convex at the two intersection points with the fluid, which may be of infinite or finite depth. For both the scattering and radiation problem, a matched expansion technique is used to provide asymptotic estimates, in terms of relatively simple wave-free limit potentials, for the amplitudes of the surface wave trains that propagate from S. Explicit details are given for some particular geometries, confirming and extending earlier results. The method can, in principle, be extended to deal with other geometries.

An explicit Hamiltonian formulation of surface waves in water of finite depth

1992 ◽  
Vol 237 ◽  
pp. 435-455 ◽  
Author(s):  
A. C. Radder
Keyword(s):  
Surface Waves ◽  
Water Waves ◽  
Hamiltonian Formulation ◽  
Vertical Plane ◽  
Finite Depth ◽  
Short Wave ◽  
Linear Dispersion ◽  
Energy Functionals ◽  
Canonical Variables ◽  
Wave Nonlinearity

A variational formulation of water waves is developed, based on the Hamiltonian theory of surface waves. An exact and unified description of the two-dimensional problem in the vertical plane is obtained in the form of a Hamiltonian functional, expressed in terms of surface quantities as canonical variables. The stability of the corresponding canonical equations can be ensured by using positive definite approximate energy functionals. While preserving full linear dispersion, the method distinguishes between short-wave nonlinearity, allowing the description of Stokes waves in deep water, and long-wave nonlinearity, applying to long waves in shallow water. Both types of nonlinearity are found necessary to describe accurately large-amplitude solitary waves.

On the radiation and scattering of short surface waves. Part 1

1972 ◽  
Vol 56 (1) ◽  
pp. 101-119 ◽  
Author(s):  
F. G. Leppington
Keyword(s):  
Surface Waves ◽  
Surface Condition ◽  
Short Wave ◽  
The Body ◽  
Finite Width ◽  
Two Dimensional ◽  
Scattering Problems ◽  
Periodic Surface ◽  
Wave Trains ◽  
Formal Limit

The radiation and scattering of time-periodic surface waves by partially immersed objects is investigated in the short-wave asymptotic limit ε → 0, where ε is a non-dimensional wavelength. Details are given for the prototype radiation and scattering problems in which the fluid has infinite depth and the body is a two-dimensional dock of finite width and zero thickness. The solutions are then generalized to deal with other two-dimensional geometries, with the restriction that the ends of the obstacle are horizontal for a distance of many wavelengths. The method of matched expansions is used. A first approximation ϕ0, presumed to be a good estimate for the potential throughout most of the fluid region, is obtained by replacing the free-surface condition by its formal limit ϕ0 = 0. In the vicinity of the ends of the obstacle, the correct surface condition is used but the geometry of the problem is simplified. The remaining surface layers are dealt with by superimposing on the function ϕ0 regular wave trains of the appropriate amplitude.

Theory of Short Wave Excitation

1986 ◽  
Vol 30 (03) ◽  
pp. 147-152
Author(s):  
Yong Kwun Chung
Keyword(s):  
Incident Wave ◽  
Characteristic Length ◽  
Finite Depth ◽  
Short Wave ◽  
The Body ◽  
Wave Number ◽  
Floating Body ◽  
Wave Excitation ◽  
Exciting Forces ◽  
Wave Exciting Forces

When the wavelength of the incident wave is short, the total surface potential on a floating body is found to be 2∅ i & O (m-l∅ i) on the lit surface and O (m-l∅ j) on the shadow surface where ~b i is the potential of the incident wave and m the wave number in water of finite depth. The present approximation for wave exciting forces and moments is reasonably good up to X/L ∅ 1 where h is the wavelength and L the characteristic length of the body.

Short-period Rayleigh-wave dispersion across the Tibetan Plateau

1975 ◽  
Vol 65 (5) ◽  
pp. 1051-1057 ◽  
Author(s):  
W. P. Chen ◽  
P. Molnar
Keyword(s):  
Tibetan Plateau ◽  
Simple Wave ◽  
Wave Dispersion ◽  
New Delhi ◽  
The Tibetan Plateau ◽  
Period Range ◽  
Short Period ◽  
Wave Forms ◽  
Wave Trains ◽  
Rayleigh Wave Dispersion

Abstract Well-dispersed Rayleigh waves within the period range of 4 to 11 sec are observed at New Delhi (NDI) and Shillong (SHL), India, for seven earthquakes near and in the Tibetan Plateau from 1963 to 1971. The dispersion curves and the simply dispersed wave forms suggest a prominent overlying wave guide, probably sediments, in the Tibetan area. The thickness of such sediments is most likely between 2.5 and 7.0 km. The simple wave trains, without much distortion due to multipathing, are consistent with a relatively inert, recent tectonism in Tibet.

Shear-coupled higher mode seismic surface waves

1967 ◽  
Vol 57 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Stuart Crampin
Keyword(s):  
Surface Waves ◽  
Wave Motion ◽  
S Wave ◽  
Higher Modes ◽  
Mode Wave ◽  
Mode Dispersion ◽  
Seismic Surface Waves ◽  
Wave Trains ◽  
Group Velocities

abstract Some higher mode wave trains with irregular dispersion, and some anomalies in the S-wave motion at epicentral distances less than 30°, are shown to be shear-coupled higher modes. The group velocities along the higher mode portions of the paths agree well with observations of direct higher mode dispersion in Scandinavia.

scholarly journals A NOVEL ASYMPTOTIC SOLUTION TO THE SOMMERFELD RADIATION PROBLEM: ANALYTIC FIELD EXPRESSIONS AND THE EMERGENCE OF THE SURFACE WAVES

2018 ◽  
Vol 64 ◽  
pp. 9-22 ◽  
Author(s):  
Seil S. Sautbekov ◽  
Sotirios Bourgiotis ◽  
Ariadni Chrysostomou ◽  
Panayiotis V. Frangos
Keyword(s):  
Asymptotic Solution ◽  
Surface Waves ◽  
Radiation Problem
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