Complementary approximations to wave scattering by vertical barriers

1995 ◽  
Vol 294 ◽  
pp. 155-180 ◽  
Author(s):  
R. Porter ◽  
D. V. Evans
Keyword(s):  
Wave Scattering ◽  
Galerkin Approximation ◽  
Finite Depth ◽  
Accurate Method ◽  
Scattering Problems ◽  
Relative Ease ◽  
Infinite Depth ◽  
Vertical Barrier ◽  
Vertical Barriers ◽  
Depth Water

Scattering of waves by vertical barriers in infinite-depth water has received much attention due to the ability to solve many of these problems exactly. However, the same problems in finite depth require the use of approximation methods. In this paper we present an accurate method of solving these problems based on a Galerkin approximation. We will show how highly accurate complementary bounds can be computed with relative ease for many scattering problems involving vertical barriers in finite depth and also for a sloshing problem involving a vertical barrier in a rectangular tank.

Oblique Wave-Scattering by Thick Horizontal Barriers

1999 ◽  
Vol 122 (2) ◽  
pp. 100-108 ◽  
Author(s):  
B. N. Mandal ◽  
Mridula Kanoria
Keyword(s):  
Water Wave ◽  
Wave Scattering ◽  
Rectangular Cross Section ◽  
Wave Train ◽  
Finite Depth ◽  
Wave Number ◽  
Thick Wall ◽  
Galerkin Approximations ◽  
Thick Barrier ◽  
Depth Water

This paper is concerned with scattering of an obliquely incident surface water wave train by an obstacle in the form of a thick horizontal barrier of rectangular cross section present in finite depth water. Four different geometrical configurations of the obstacle are considered. It may be surface-piercing or bottom-standing, or in the form of a submerged block not extending down to the bottom, or in the form of a thick wall with a submerged gap. Multi-term Galerkin approximations involving ultraspherical Gegenbauer polynomials for solving first-kind integral equations are utilized in the mathematical analysis to obtain very accurate numerical estimates for the reflection coefficient, which are depicted graphically against the wave number for each configurations of the thick barrier. [S0892-7219(00)00701-9]

scholarly journals Water Wave Scattering by an Infinite Step in the Presence of an Ice-Cover

2019 ◽  
Vol 24 (4) ◽  
pp. 157-168
Author(s):  
S. Ray ◽  
S. De ◽  
B.N. Mandal
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Water Wave ◽  
Wave Scattering ◽  
Fluid Velocity ◽  
Galerkin Approximation ◽  
Classical Problem ◽  
Finite Depth ◽  
Ice Cover ◽  
Water Wave Scattering

Abstract The classical problem of water wave scattering by an infinite step in deep water with a free surface is extended here with an ice-cover modelled as a thin uniform elastic plate. The step exists between regions of finite and infinite depths and waves are incident either from the infinite or from the finite depth water region. Each problem is reduced to an integral equation involving the horizontal component of velocity across the cut above the step. The integral equation is solved numerically using the Galerkin approximation in terms of simple polynomial multiplied by an appropriate weight function whose form is dictated by the behaviour of the fluid velocity near the edge of the step. The reflection and transmission coefficients are obtained approximately and their numerical estimates are seen to satisfy the energy identity. These are also depicted graphically against thenon-dimensional frequency parameter for various ice-cover parameters in a number of figures. In the absence of ice-cover, the results for the free surface are recovered.

Oblique wave scattering by submerged thin wall with gap in finite-depth water

1996 ◽  
Vol 18 (6) ◽  
pp. 319-327 ◽  
Author(s):  
Sudeshna Banerjea ◽  
Mridula Kanoria ◽  
D.P. Dolai ◽  
B.N. Mandal
Keyword(s):  
Wave Scattering ◽  
Finite Depth ◽  
Thin Wall ◽  
Oblique Wave ◽  
Depth Water

Approximate analysis of the containment of contaminated sites prior to remediation

2000 ◽  
Vol 42 (1-2) ◽  
pp. 319-324 ◽  
Author(s):  
H. Rubin ◽  
A. Rabideau
Keyword(s):  
Steady State ◽  
Peclet Number ◽  
Dimensionless Parameter ◽  
Contaminated Sites ◽  
Unsteady State ◽  
Péclet Number ◽  
Vertical Barrier ◽  
Time Period ◽  
Barrier Performance ◽  
Vertical Barriers

This study presents an approximate analytical model, which can be useful for the prediction and requirement of vertical barrier efficiencies. A previous study by the authors has indicated that a single dimensionless parameter determines the performance of a vertical barrier. This parameter is termed the barrier Peclet number. The evaluation of barrier performance concerns operation under steady state conditions, as well as estimates of unsteady state conditions and calculation of the time period requires arriving at steady state conditions. This study refers to high values of the barrier Peclet number. The modeling approach refers to the development of several types of boundary layers. Comparisons were made between simulation results of the present study and some analytical and numerical results. These comparisons indicate that the models developed in this study could be useful in the design and prediction of the performance of vertical barriers operating under conditions of high values of the barrier Peclet number.

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