scholarly journals Wave Transmission by Rectangular Submerged Breakwaters

Computation ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 56
Author(s):  
Ikha Magdalena ◽  
Muh Fadhel Atras ◽  
Leo Sembiring ◽  
M. A. Nugroho ◽  
Roi Solomon B. Labay ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Transmission Coefficient ◽  
Numerical Scheme ◽  
Separation Of Variables ◽  
Staggered Grid ◽  
Incoming Wave ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Before And After ◽  
Volume Method

In this paper, we investigate the wave damping mechanism caused by the presence of submerged bars using the Shallow Water Equations (SWEs). We first solve these equations for the single bar case using separation of variables to obtain the analytical solution for the wave elevation over a rectangular bar wave reflector with specific heights and lengths. From the analytical solution, we derive the wave reflection and transmission coefficients and determine the optimal height and length of the bar that would give the smallest transmission coefficient. We also measure the effectiveness of the bar by comparing the amplitude of the incoming wave before and after the wave passes the submerged bar, and extend the result to the case of n-submerged bars. We then construct a numerical scheme for the SWEs based on the finite volume method on a staggered grid to simulate the propagation of a monochromatic wave as it passes over a single submerged rectangular bar. For validation, we compare the transmission coefficient values obtained from the analytical solution, numerical scheme, and experimental data. The result of this paper may be useful in wave reflector engineering and design, particularly that of rectangle-shaped wave reflectors, as it can serve as a basis for designing bar wave reflectors that reduce wave amplitudes optimally.

scholarly journals 1D–2D Numerical Model for Wave Attenuation by Mangroves as a Porous Structure

Computation ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 66
Author(s):  
Ikha Magdalena ◽  
Vivianne Kusnowo ◽  
Moh. Ivan Azis ◽  
Widowati
Keyword(s):  
Porous Media ◽  
Transmission Coefficient ◽  
Numerical Scheme ◽  
Wave Attenuation ◽  
Separation Of Variables ◽  
Coastal Protection ◽  
Diffusion Term ◽  
Central Java ◽  
Friction Term ◽  
Volume Method

In this paper, we investigate wave attenuation caused by mangroves as a porous media. A 1-D mathematical model is derived by modifying the shallow water equations (SWEs). Two approaches are used to involve the existing of mangrove: friction term and diffusion term. The model will be solved analytically using the separation of variables method and numerically using a staggered finite volume method. From both methods, wave transmission coefficient will be obtained and used to observe the damping effect induced by the porous media. Several comparisons are shown to examine the accuracy and robustness of the derived numerical scheme. The results show that the friction coefficient, diffusion coefficient and vegetation’s length have a significant effect on the transmission coefficient. Moreover, numerical observation is extended to a 2-D SWEs, where we conduct a numerical simulation over a real bathymetry profile. The results from the 2-D numerical scheme will be validated using the data obtained from the field measurement which took place in Demak, Central Java, Indonesia. The results from this research will be beneficial to determine the characteristics of porous structures used for coastal protection.

scholarly journals Resonant Periods of Seiches in Semi-Closed Basins with Complex Bottom Topography

Fluids ◽  
2021 ◽  
Vol 6 (5) ◽  
pp. 181
Author(s):  
Ikha Magdalena ◽  
Nadhira Karima ◽  
Hany Qoshirotur Rif’atin
Keyword(s):  
Separation Of Variables ◽  
Bottom Topography ◽  
Small Error ◽  
Staggered Grid ◽  
Resonant Wave ◽  
Wave Elevation ◽  
External Forces ◽  
Volume Method ◽  
Resonant Period ◽  
Wave Induced

Seiches and resonances are two closely related phenomena that can cause damage to coastal areas. Seiches that occur in a basin at a distinct period named the resonant period may generate resonance when a wave induced by external forces enters the basin and has the same period as the seiches. Studying this period has become essential if we want to understand the resonance better. Thus, in this paper, we derive the resonant period in various shapes of semi-closed basin using the shallow water equations. The equations are then solved analytically using the separation of variables method and numerically using the finite volume method on staggered grid to discover the resonant period for each basin. To validate the numerical scheme, we compare its results against the analytical resonant periods, resulting in a very small error for each basin, suggesting that the numerical model is quite reliable in the estimation of the analytical resonant period. Further, resonant wave profiles are also observed. It is revealed that, in the coupled rectangular basin, the maximum wave elevation is disproportionate to the ratio of the length of the basin, while, in the trapezoidal basin, the ratio of the depth of the basin has no significant impact on the maximum wave elevation.

scholarly journals Determining Transmission Coefficient of Propagating Solitary Wave over Trapezoidal Breakwater and Parametric Studies on Different Influential Factors

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Amin Rahimzadeh ◽  
Parviz Ghadimi ◽  
Mohammad A. Feizi Chekab ◽  
Mohammad H. Jabbari
Keyword(s):  
Transmission Coefficient ◽  
Solitary Waves ◽  
Time Integration ◽  
Boussinesq Equations ◽  
Influential Factors ◽  
Width Ratio ◽  
Governing Equations ◽  
Submerged Breakwater ◽  
Transmission Coefficients ◽  
Before And After

The objective of this study is to numerically investigate transmission coefficient of submerged trapezoidal breakwater of various configurations subjected to solitary waves. Boussinesq equations of Madsen and Sorensen are applied as governing equations for simulation purposes. Discretization of governing equations is accomplished using Galerkin finite element method and Adams-Bashforth-Moulton predictor-corrector method is considered for time integration. In order to obtain transmission coefficients, two gauges are considered before and after the submerged breakwater to record initial and transmitted wave heights, respectively. To examine the effect of configuration of breakwaters on their transmission coefficients, submergence ratio and crest width ratio are defined and analyzed. Different submergence ratios and various crest width ratios are considered. Computed results indicate how transmission coefficient decreases with the increase over different ranges of crest width ratio, for all values of submergence ratio. Furthermore, keeping crest width and submergence ratios constant, solitary waves with higher initial heights are simulated. Results of simulation indicate that transmission coefficient becomes higher for the same breakwater characteristics. Finally, a parametric study is conducted on the effect of side slopes of breakwaters. It is shown that side slopes have strong effect on wave transmission.

scholarly journals EVALUATION OF HYDRAULIC PERFORMANCE OF WAVE DISSIPATING BLOCK USING POROSITY

2020 ◽  
pp. 29
Author(s):  
Susumu Araki ◽  
Daiki Watanabe ◽  
Shin-ichi Kubota ◽  
Masaya Hashida
Keyword(s):  
Reflection Coefficient ◽  
Transmission Coefficient ◽  
Hydraulic Performance ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients

The reflection and transmission of wave dissipating work mainly depend on the shape and porosity of wave dissipating block. However, the influence of the shape and porosity of wave dissipating block on the reflection and transmission has not been investigated sufficiently. The purpose of this study is to investigate the influence of the porosity of wave dissipating block on the reflection and transmission coefficients through a series of hydraulic experiments where four kinds of wave dissipating blocks were used. Wave dissipating blocks with smaller porosity provided a larger reflection coefficient and a smaller transmission coefficient as a whole. However, a wave dissipating block provided a smaller reflection coefficient and a smaller transmission coefficient in spite of relatively larger porosity. The measured reflection and transmission coefficients were compared with those estimated by existing equations.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/lqyzabMw66U

Wave Interaction with an Emerged Porous Media

2014 ◽  
Vol 6 (5) ◽  
pp. 680-692 ◽  
Author(s):  
I. Magdalena ◽  
S. R. Pudjaprasetya ◽  
L. H. Wiryanto
Keyword(s):  
Porous Media ◽  
Wave Reflection ◽  
Wave Interaction ◽  
Staggered Grid ◽  
Transmission Curve ◽  
Reflection And Transmission ◽  
Reflection And Transmission Coefficient ◽  
Friction Term ◽  
Horizontal Flux ◽  
Volume Method

AbstractIn this paper, we study wave interaction with an emerged porous media. The governing equation is shallow water equations with a friction term of the linearized Dupuit-Forcheimer’s formula. From the continuity of surface and horizontal flux, we derived the wave reflection and transmission coefficient formulas. They are similar with the corresponding formulas of the submerged solid bar breakwater. We solve the equations numerically using finite volume method on a staggered grid. The numerical wave reduction in the porous media confirms the analytical wave transmission curve.

Single Defect in Finite one Dimensional Photonic Crystals

2012 ◽  
Vol 614-615 ◽  
pp. 1629-1632
Author(s):  
Gang Xu ◽  
Yun Sun
Keyword(s):  
Photonic Crystals ◽  
Transmission Coefficient ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Defect Mode ◽  
Transmission Peak ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Single Defect ◽  
Reflection And Transmission Coefficient

Applying transfer matrix method, we get reflection and transmission coefficient of finite one dimensional photonic crystals. At the same time, we consider the position influence of single defect. We find the frequency of defect mode is same, but the height of transmission peak is not same when single defect is in different position of crystal. The transmission peak is maximum when the defect is in center of finite one dimensional photonic crystals.

An analytical solution of a two-dimensional temperature field in a hollow cylinder under a time periodic boundary condition using Fourier series

2009 ◽  
Vol 223 (8) ◽  
pp. 1889-1901 ◽  
Author(s):  
G Atefi ◽  
M A Abdous ◽  
A Ganjehkaviri ◽  
N Moalemi
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Fourier Series ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Hollow Cylinder ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Separation Of Variables ◽  
Two Dimensional

The objective of this article is to derive an analytical solution for a two-dimensional temperature field in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface, while the inner surface is insulated. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel's theorem is used to solve the problem for a periodic boundary condition. The periodic boundary condition is decomposed using the Fourier series. This condition is simulated with harmonic oscillation; however, there are some differences with the real situation. To solve this problem, first of all the boundary condition is assumed to be steady. By applying the method of separation of variables, the temperature distribution in a hollow cylinder can be obtained. Then, the boundary condition is assumed to be transient. In both these cases, the solutions are separately calculated. By using Duhamel's theorem, the temperature distribution field in a hollow cylinder is obtained. The final result is plotted with respect to the Biot and Fourier numbers. There is good agreement between the results of the proposed method and those reported by others for this geometry under a simple harmonic boundary condition.

Extension of forward modeling phase-screen code in isotropic and anisotropic media up to critical angle

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM107-SM114 ◽  
Author(s):  
James C. White ◽  
Richard W. Hobbs
Keyword(s):  
Critical Angle ◽  
Model Space ◽  
Anisotropic Media ◽  
Forward Modeling ◽  
Phase Screen ◽  
Computationally Efficient ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Phase Corrections ◽  
Converted Phases

The computationally efficient phase-screen forward modeling technique is extended to allow investigation of nonnormal raypaths. The code is developed to accommodate all diffracted and converted phases up to critical angle, building on a geometric construction method. The new approach relies upon prescanning the model space to assess the complexity of each screen. The propagating wavefields are then divided as a function of horizontal wavenumber, and each subset is transformed to the spatial domain separately, carrying with it angular information. This allows both locally accurate 3D phase corrections and Zoeppritz reflection and transmission coefficients to be applied. The phase-screen code is further developed to handle simple anisotropic media. During phase-screen modeling, propagation is undertaken in the wavenumber domain where exact expressions for anisotropic phase velocities are available. Traveltimes and amplitude effects from a range of anisotropic shales are computed and compared with previous published results.

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