scholarly journals Bragg Reflections of Oblique Water Waves by Periodic Surface-Piercing and Submerged Breakwaters

2020 ◽  
Vol 8 (7) ◽  
pp. 522
Author(s):  
I-Fan Tseng ◽  
Chi-Shian You ◽  
Chia-Cheng Tsai
Keyword(s):  
Water Waves ◽  
Sparse Matrix ◽  
Linear Equations ◽  
Wave Theory ◽  
Solution Procedure ◽  
Linear Wave ◽  
Matching Method ◽  
Periodic Surface ◽  
Linear Wave Theory ◽  
Small Wave

The Bragg reflections of oblique water waves by periodic surface-piercing structures over periodic bottoms are investigated using the eigenfunction matching method (EMM). Based on the assumption of small wave amplitude, the linear wave theory is employed in the solution procedure. In the step approximation, the surface-piercing structures and the bottom profiles are sliced into shelves separated by abrupt steps. For each shelf, the solution is composed of eigenfunctions with unknown coefficients representing the wave amplitudes. Upon applying the conservations of mass and momentum, a system of linear equations is obtained and is then solved by a sparse-matrix solver. The proposed EMM is validated by several examples in the literature. Then, the method is applied to solve Bragg reflections of oblique water waves by various surface-piercing structures over periodic bottoms. From the numerical experiments, Bragg’s law of oblique waves was used to predict the occurrences of Bragg resonance.

scholarly journals Step Approximation for Water Wave Scattering by Multiple Thin Barriers over Undulated Bottoms

2021 ◽  
Vol 9 (6) ◽  
pp. 629
Author(s):  
Chang-Thi Tran ◽  
Jen-Yi Chang ◽  
Chia-Cheng Tsai
Keyword(s):  
Water Waves ◽  
Water Wave ◽  
Wave Scattering ◽  
Sparse Matrix ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Matching Method ◽  
Water Wave Scattering ◽  
Oblique Wave ◽  
Step Approximation

This paper investigates the scattering of oblique water waves by multiple thin barriers over undulation bottoms using the eigenfunction matching method (EMM). In the solution procedures of the EMM, the bottom topographies are sliced into shelves separated by steps. On each step, surface-piercing or/and bottom-standing barriers can be presented or not. For each shelf, the solution is composed of eigenfunctions with unknown coefficients representing the wave amplitudes. Then applying the conservations of mass and momentum, a system of linear equations is resulted and can be solved by a sparse-matrix solver. If no barriers are presented on the steps, the proposed EMM formulation degenerates to the water wave scattering over undulating bottoms. The effects on the barrier lengths, barrier positions and oblique wave incidences by different undulated bottoms are studied. In addition, the EMM is also applied to solve the Bragg reflections of normal and oblique water waves by periodic barrier over sinusoidal bottoms. The accuracy of the solution is demonstrated by comparing it with the results in the literature.

Kinetic, Dynamic and Energy Characteristics of Vortex Evolution on Bragg Scattering of Water Waves

2010 ◽  
Author(s):  
Tai-Wen Hsu ◽  
Shan-Hwei Ou ◽  
Chin-Yen Tsai ◽  
Jian-Feng Lin
Keyword(s):  
Velocity Field ◽  
Water Waves ◽  
Wave Reflection ◽  
Wave Theory ◽  
Navier Stokes ◽  
Linear Wave ◽  
Bragg Scattering ◽  
Energy Characteristics ◽  
Linear Wave Theory ◽  
Image Velocimetry

The vortex generation and dissipation under Bragg scattering of water wave propagation over a series of submerged rectangular breakwaters are investigated both numerically and experimentally. A Reynolds Averaged Navier-Stokes (RANS) model combined with a k–ε turbulence closure is applied to simulate the entire vortex evolution process as water waves pass over a series of artificial rectangular bars. The Particle Image Velocimetry (PIV) is also used to measure the velocity field in the vicinity of the obstacles. The numerical model is validated through the comparisons of water surface elevations and velocity field with the measurements. The mechanism of vortex evolution and its influence on the interaction of water waves with submerged structures for both cases of resonance and non-resonance were studied. Wave reflection coefficients for both resonant and non-resonant cases were calculated and compared with experiments and solutions based on the linear wave theory. It is also found that the calculated vortex intensity at the last bar is only one third of that at the leading bar for the near-resonant case. The local kinetic energy is also found to attain its minimum value at a place where potential energy became larger in Bragg scattering of water waves.

Nonlinear Waves in Strings: The Barrage Balloon Problem

1998 ◽  
Vol 65 (1) ◽  
pp. 141-149
Author(s):  
J. F. Hall
Keyword(s):  
World War Ii ◽  
Nonlinear Waves ◽  
Wave Reflection ◽  
Wave Theory ◽  
P Wave ◽  
Linear Wave ◽  
Geometrically Nonlinear ◽  
World War ◽  
Linear Wave Theory ◽  
Important Solution

This paper develops a theory for geometrically nonlinear waves in strings and presents analytical solutions for a traveling kink, generation of a geometric wave with its accompanying P wave, reflection of a kink at a fixed support and at a smooth sliding support, and interaction of a P wave and a kink. Conditions that must be satisfied for linear wave theory to hold are derived. The nonlinear theory is demonstrated by extending an historically important solution of the barrage balloon problem that was obtained during World War II.

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