Eigenfunction Expansion Method for Water Wave Scattering by Small Undulation

2011 ◽  
Author(s):  
S. C. Martha ◽  
S. N. Bora ◽  
A. Chakrabarti ◽  
Jiachun Li ◽  
Song Fu
Keyword(s):  
Eigenfunction Expansion ◽  
Water Wave ◽  
Wave Scattering ◽  
Expansion Method ◽  
Water Wave Scattering ◽  
Eigenfunction Expansion Method

Oblique interaction between water waves and a partially submerged rectangular breakwater

2019 ◽  
Vol 234 (1) ◽  
pp. 154-169 ◽  
Author(s):  
R. B. Kaligatla ◽  
N. M. Prasad ◽  
S. Tabssum
Keyword(s):  
Water Waves ◽  
Eigenfunction Expansion ◽  
Wave Scattering ◽  
Wave Reflection ◽  
Expansion Method ◽  
Algebraic Equations ◽  
Eigenfunction Expansion Method ◽  
Balance Relation ◽  
Orthogonal Property ◽  
The One

A problem of oblique wave scattering by a rectangular breakwater floating in water of uneven depth is solved by applying matched eigenfunction expansion method. Three positions of breakwater are considered. The width and draft of breakwater are assumed to be finite, whereas its length is infinite. Breakwater is studied in the settings of without backwall and with a backwall. By using matching conditions at interface boundaries and making use of orthogonal property of eigenfunctions, the problem is converted to a system of algebraic equations. Breakwater’s position is proposed for which wave reflection, transmission, and force on wall are optimized. The breakwater with certain width and draft reflects more wave energy than the one with zero-draft. In the case of absence of wall, breakwater at lee side to the step induces least transmission of waves. In the case of presence of wall, suitable position of breakwater is suggested based on a range of wave frequency to mitigate force on wall. Optimum distances between wall and breakwater are found to attain less force on wall. Using Green’s identity, energy balance relation is derived to check accuracy in results. The findings are likely to be useful to assess the performance of a breakwater in different positions in water of uneven depth.

Time-dependent linear water-wave scattering in two dimensions by a generalized eigenfunction expansion

2009 ◽  
Vol 632 ◽  
pp. 447-455 ◽  
Author(s):  
MICHAEL H. MEYLAN
Keyword(s):  
Eigenfunction Expansion ◽  
Water Wave ◽  
Wave Scattering ◽  
Initial Conditions ◽  
Two Dimensions ◽  
Single Frequency ◽  
Initial Surface ◽  
Water Wave Scattering ◽  
Generalized Eigenfunction ◽  
Generalized Eigenfunction Expansion

We consider the solution in the time domain of the two-dimensional water-wave scattering by fixed bodies, which may or may not intersect with the free surface. We show how the problem with arbitrary initial conditions can be found from the single-frequency solutions using a generalized eigenfunction expansion, required because the operator has a continuous spectrum. From this expansion we derive simple formulas for the evolution in time of the initial surface conditions, and we present some examples of numerical calculations.

The Quasi-Static Analysis for Two-Dimensional Thin Plates

2011 ◽  
Vol 255-260 ◽  
pp. 166-169
Author(s):  
Li Chen ◽  
Yang Bai
Keyword(s):  
Boundary Conditions ◽  
Eigenfunction Expansion ◽  
Solution Space ◽  
Expansion Method ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Elastic Plates ◽  
Various Boundary Conditions ◽  
Eigenfunction Expansion Method ◽  
Concentration Phenomena

The eigenfunction expansion method is introduced into the numerical calculations of elastic plates. Based on the variational method, all the fundamental solutions of the governing equations are obtained directly. Using eigenfunction expansion method, various boundary conditions can be conveniently described by the combination of the eigenfunctions due to the completeness of the solution space. The coefficients of the combination are determined by the boundary conditions. In the numerical example, the stress concentration phenomena produced by the restriction of displacement conditions is discussed in detail.

Water wave scattering by a submerged horizontal semi-circular barrier in a two-layer fluid

2021 ◽  
Vol 33 (12) ◽  
pp. 127102
Author(s):  
Ai-jun Li ◽  
Yong Liu
Keyword(s):  
Water Wave ◽  
Wave Scattering ◽  
Water Wave Scattering

Analysis of water wave scattering by a submerged perforated reef ball using multipole method

Meccanica ◽  
2019 ◽  
Vol 54 (11-12) ◽  
pp. 1747-1765
Author(s):  
Ai-jun Li ◽  
Xiao-lei Sun ◽  
Yong Liu ◽  
Hua-jun Li
Keyword(s):  
Water Wave ◽  
Wave Scattering ◽  
Water Wave Scattering ◽  
Multipole Method
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