Explicit Representation for the Infinite-Depth Two-Dimensional Free-Surface Green's Function in Linear Water-Wave Theory

2010 ◽  
Vol 70 (7) ◽  
pp. 2353-2372 ◽  
Author(s):  
Ricardo Hein ◽  
Mario Durán ◽  
Jean-Claude Nédélec
Keyword(s):  
Free Surface ◽  
Green’S Function ◽  
Green's Function ◽  
Water Wave ◽  
Wave Theory ◽  
Explicit Representation ◽  
Two Dimensional ◽  
Infinite Depth ◽  
Linear Water Wave Theory

scholarly journals METHOD OF ANALYSES FOR TWO-DIMENSIONAL WATER WAVE PROBLEMS

1976 ◽  
Vol 1 (15) ◽  
pp. 155 ◽  
Author(s):  
Takeshi Ijima ◽  
Chung Ren Chou ◽  
Akinori Yoshida
Keyword(s):  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Water Wave ◽  
Boundary Value ◽  
Wave Transformation ◽  
Two Dimensional ◽  
Simple Method ◽  
Dimensional Boundary ◽  
Horizontal Cylinders

One of the most powerful tools to analyze the boundary-value problems in water wave motion is the Green's function. However, to derive the Green's function which satisfies the imposed boundary conditions is sometimes difficult or impossible, especially in variable water depth. In this paper, a simple method of numerical analyses for two-dimensional boundary-value problems of small amplitude waves is proposed, and the wave transformation by fixed horizontal cylinders as an example of fixed boundaries, the wave transformation by and the motion of a cylinder floating on water surface as example of oscillating boundaries and the wave transformation by permeable seawall and breakwater as example of permeable boundaries are calculated and compared with experimental results.

scholarly journals Green’s function for the semi-infinite strip in terms of an improper integral

2020 ◽  
Vol 17 (2) ◽  
pp. 235-246
Author(s):  
Dragan Filipovic ◽  
Tatijana Dlabac
Keyword(s):  
Green’S Function ◽  
Closed Form ◽  
Green's Function ◽  
Infinite Strip ◽  
Two Dimensional ◽  
Infinite Depth ◽  
Improper Integral

In this paper Green?s function for the semi-infinite strip (which is the two-dimensional Green?s function for a groove of infinite depth and length) is determined in the form of an improper integral, as opposed to the standard summation form. The integral itself, although rather complex, is found in a closed form. By using the derived Green?s function simple formulas are obtained for a single and two-wire line configurations inside the groove.

A note on uniqueness in the linearized water-wave problem

1999 ◽  
Vol 386 ◽  
pp. 5-14 ◽  
Author(s):  
N. G. KUZNETSOV ◽  
M. J. SIMON
Keyword(s):  
Free Surface ◽  
Finite Number ◽  
Water Wave ◽  
Axisymmetric Problem ◽  
Two Dimensional ◽  
Plane Region ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Infinite Depth ◽  
The Uniqueness Theorem

The uniqueness theorem of Simon & Ursell (1984), concerning the linearized two-dimensional water-wave problem in a fluid of infinite depth, is extended in two directions. First, we consider a two-dimensional geometry involving two submerged symmetric bodies placed sufficiently far apart that they are not confined in the vertical right angle having its vertex on the free surface as the theorem of Simon & Ursell requires. A condition is obtained guaranteeing the uniqueness outside a finite number of bounded frequency intervals. Secondly, the method of Simon & Ursell is generalized to prove uniqueness in the axisymmetric problem for bodies violating John's condition provided the free surface is a connected plane region.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

scholarly journals Unified double- and single-sided homogeneous Green’s function representations

2016 ◽  
Vol 472 (2190) ◽  
pp. 20160162 ◽  
Author(s):  
Kees Wapenaar ◽  
Joost van der Neut ◽  
Evert Slob
Keyword(s):  
Green’S Function ◽  
Multiple Scattering ◽  
Green's Function ◽  
Time Reversal ◽  
Wave Theory ◽  
Boundary Integral ◽  
Open Boundary ◽  
Quantum Mechanical ◽  
Holographic Imaging ◽  
Scattering Time

In wave theory, the homogeneous Green’s function consists of the impulse response to a point source, minus its time-reversal. It can be represented by a closed boundary integral. In many practical situations, the closed boundary integral needs to be approximated by an open boundary integral because the medium of interest is often accessible from one side only. The inherent approximations are acceptable as long as the effects of multiple scattering are negligible. However, in case of strongly inhomogeneous media, the effects of multiple scattering can be severe. We derive double- and single-sided homogeneous Green’s function representations. The single-sided representation applies to situations where the medium can be accessed from one side only. It correctly handles multiple scattering. It employs a focusing function instead of the backward propagating Green’s function in the classical (double-sided) representation. When reflection measurements are available at the accessible boundary of the medium, the focusing function can be retrieved from these measurements. Throughout the paper, we use a unified notation which applies to acoustic, quantum-mechanical, electromagnetic and elastodynamic waves. We foresee many interesting applications of the unified single-sided homogeneous Green’s function representation in holographic imaging and inverse scattering, time-reversed wave field propagation and interferometric Green’s function retrieval.

scholarly journals Chemical Source Inversion Using Assimilated Constituent Observations in an Idealized Two-Dimensional System

2009 ◽  
Vol 137 (9) ◽  
pp. 3013-3025
Author(s):  
Andrew Tangborn ◽  
Robert Cooper ◽  
Steven Pawson ◽  
Zhibin Sun
Keyword(s):  
Kalman Filter ◽  
Green’S Function ◽  
Green's Function ◽  
Transport Model ◽  
Chemical Constituents ◽  
Gaussian Model ◽  
Satellite Observation ◽  
Dimensional System ◽  
Two Dimensional ◽  
Source Inversion

Abstract A source inversion technique for chemical constituents is presented that uses assimilated constituent observations rather than directly using the observations. The method is tested with a simple model problem, which is a two-dimensional Fourier–Galerkin transport model combined with a Kalman filter for data assimilation. Inversion is carried out using a Green’s function method and observations are simulated from a true state with added Gaussian noise. The forecast state uses the same spectral model but differs by an unbiased Gaussian model error and emissions models with constant errors. The numerical experiments employ both simulated in situ and satellite observation networks. Source inversion was carried out either by directly using synthetically generated observations with added noise or by first assimilating the observations and using the analyses to extract observations. Twenty identical twin experiments were conducted for each set of source and observation configurations, and it was found that in the limiting cases of a very few localized observations or an extremely large observation network there is little advantage to carrying out assimilation first. For intermediate observation densities, the source inversion error standard deviation is decreased by 50% to 90% when the observations are assimilated with the Kalman filter before carrying out the Green’s function inversion.

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