Reflection and transmission from porous structures under oblique wave attack

1991 ◽  
Vol 224 ◽  
pp. 625-644 ◽  
Author(s):  
Robert A. Dalrymple ◽  
Miguel A. Losada ◽  
P. A. Martin
Keyword(s):  
Porous Medium ◽  
Plane Wave ◽  
Water Waves ◽  
Normal Wave ◽  
Eigenfunction Expansions ◽  
Reflection And Transmission ◽  
Oblique Wave ◽  
Water Region ◽  
Wave Incidence ◽  
Wave Modes

The linear theory for water waves impinging obliquely on a vertically sided porous structure is examined. For normal wave incidence, the reflection and transmission from a porous breakwater has been studied many times using eigenfunction expansions in the water region in front of the structure, within the porous medium, and behind the structure in the down-wave water region. For oblique wave incidence, the reflection and transmission coefficients are significantly altered and they are calculated here.Using a plane-wave assumption, which involves neglecting the evanescent eigenmodes that exist near the structure boundaries (to satisfy matching conditions), the problem can be reduced from a matrix problem to one which is analytic. The plane-wave approximation provides an adequate solution for the case where the damping within the structure is not too great.An important parameter in this problem is Γ2= ω2h(s- if)/g, where ω is the wave angular frequency,hthe constant water depth,gthe acceleration due to gravity, andsandfare parameters describing the porous medium. As the friction in the porous medium,f, becomes non-zero, the eigenfunctions differ from those in the fluid regions, largely owing to the change in the modal wavenumbers, which depend on Γ2.For an infinite number of values of ΓF2, there are no eigenfunction expansions in the porous medium, owing to the coalescence of two of the wavenumbers. These cases are shown to result in a non-separable mathematical problem and the appropriate wave modes are determined. As the two wavenumbers approach the critical value of Γ2, it is shown that the wave modes can swap their identity.

Wave transformation by a vertical barrier between a single-layer fluid and a two-layer fluid

2000 ◽  
Vol 214 (6) ◽  
pp. 759-769
Author(s):  
M M Lee ◽  
A T Chwang
Keyword(s):  
Water Waves ◽  
Lower Layer ◽  
Wave Transformation ◽  
Linear Wave ◽  
Type I ◽  
Type Ii ◽  
Homogeneous Fluid ◽  
Reflection And Transmission ◽  
Vertical Barrier ◽  
Wave Modes

The reflection and transmission of water waves by a vertical barrier between a homogeneous fluid and a two-layer fluid are investigated for two different types of barrier: type I is a surface-piercing barrier and type II a bottom-standing barrier. For a type I barrier, the lower-layer fluid is the same as the homogeneous fluid and has a higher density than that of the upper-layer fluid. For a type II barrier, the upper layer fluid is the same as the homogeneous fluid and has a lower density than that of the lower-layer fluid. For any given finite thickness of the fluid layers, a hydrostatic equilibrium state exists. Incident progressive waves can then be transmitted through the gap beneath or above the barrier. By using the linear wave theory and eigenfunction expansions, these boundary value problems are solved by a suitable application of the least-squares method. The definitions of the corresponding reflection and transmission coefficients are introduced in each case. For the two-layer fluid, there are two different wave modes: the surface (barotropic) and interfacial (baroclinic) wave modes. It is found that water waves, propagating either from the homogeneous or from the two-layer fluid, are partially reflected or transmitted and produce simultaneously both modes of water waves in the two-layer fluid.

OBLIQUE WAVE SCATTERING BY A RECTANGULAR SUBMARINE TRENCH

2015 ◽  
Vol 56 (3) ◽  
pp. 286-298 ◽  
Author(s):  
RUMPA CHAKRABORTY ◽  
B. N. MANDAL
Keyword(s):  
Water Waves ◽  
Wave Scattering ◽  
Wave Train ◽  
Galerkin Approximation ◽  
Central Line ◽  
Wave Number ◽  
Reflection And Transmission ◽  
Oblique Wave ◽  
Transmission Coefficients ◽  
Linearized Theory

The problem of oblique wave scattering by a rectangular submarine trench is investigated assuming a linearized theory of water waves. Due to the geometrical symmetry of the rectangular trench about the central line $x=0$, the boundary value problem is split into two separate problems involving the symmetric and antisymmetric potential functions. A multi-term Galerkin approximation involving ultra-spherical Gegenbauer polynomials is employed to solve the first-kind integral equations arising in the mathematical analysis of the problem. The reflection and transmission coefficients are computed numerically for various values of different parameters and different angles of incidence of the wave train. The coefficients are depicted graphically against the wave number for different situations. Some curves for these coefficients available in the literature and obtained by different methods are recovered.

High frequency diffraction by a soft circular disc

1972 ◽  
Vol 71 (3) ◽  
pp. 545-565
Author(s):  
J. C. Newby
Keyword(s):  
Integral Equation ◽  
Plane Wave ◽  
Infinite Number ◽  
High Frequency ◽  
Normal Wave ◽  
Incident Field ◽  
Fourier Component ◽  
Incident Plane Wave ◽  
Oblique Wave ◽  
Incident Plane

AbstractInitially a general incident field is considered and the equations are split into Fourier components. Each Fourier component gives rise to an integral equation similar to that obtained when investigating diffraction of a normally incident plane wave. After the oblique wave has been specified an analysis similar to that used for the normal wave leads to a solution of the problem containing an infinite number of constants. It is shown, however, that these constants do not affect the leading terms of the high frequency scattering coefficient.

Reflection and Transmission of a Plane Wave by an Array of Cavities in the Interface of Two Solids

1992 ◽  
Vol 59 (1) ◽  
pp. 102-108 ◽  
Author(s):  
Yonglin Xu
Keyword(s):  
Plane Wave ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Singular Integral Equations ◽  
Boundary Integral ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Typical Cell ◽  
Wave States ◽  
Doubly Periodic Array

The reflection and transmission of a plane wave by a distribution of cavities in the interface of two solids of different mechanical properties are investigated. For the calculation of the reflection and transmission coefficients by a distribution of cavities, six auxiliary wave states are used in conjunction with the reciprocal identity. Specific results are presented for scattering by a doubly periodic array of cavities in the interface of solids of different elastic moduli and mass densities. For a typical cell, the boundary integral equations for scattering by a cavity at the interface of two solids are derived on the basis of continuity of displacements and tractions across the interface and by taking advantage of the geometrical periodicity. Solutions to the system of singular integral equations have been obtained by the boundary element method. Numerical results are presented as functions of the frequency for two angles of incidence.

scholarly journals MACH-REFLECTION AS A DIFFRACTION PROBLEM

1976 ◽  
Vol 1 (15) ◽  
pp. 45 ◽  
Author(s):  
Udo Berger ◽  
Soren Kohlhase
Keyword(s):  
Wave Height ◽  
Incident Wave ◽  
Water Waves ◽  
Gas Dynamics ◽  
Mach Reflection ◽  
Diffraction Problem ◽  
Vertical Wall ◽  
Oblique Wave ◽  
Wave Heights ◽  
The Waves

As under oblique wave approach water waves are reflected by a vertical wall, a wave branching effect (stem) develops normal to the reflecting wall. The waves progressing along the wall will steep up. The wave heights increase up to more than twice the incident wave height. The £jtudy has pointed out that this effect, which is usually called MACH-REFLECTION, is not to be taken as an analogy to gas dynamics, but should be interpreted as a diffraction problem.

Oblique wave-free potentials for water waves in constant finite depth

2015 ◽  
Vol 14 (2) ◽  
pp. 126-137
Author(s):  
Rajdeep Maiti ◽  
Uma Basu ◽  
B. N. Mandal
Keyword(s):  
Water Waves ◽  
Finite Depth ◽  
Oblique Wave
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