A coupled-mode study on weakly viscous Bragg scattering of surface gravity waves

Engineering Applications of Computational Fluid Mechanics

2018

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In this study, a quadtreeadaptive viscous numerical wave tank in which the free surface is resolved by the volume of fluid method is established to solve Bragg resonance caused by Stokes and cnoidal waves. Numerical wavemakers of third-order cnoidal and fifth-order Stokes waves are implemented. Additionally, a numerical damping zone is implemented such that the numerical grid in that area is automatically coarsened under a prescribed low resolution in which the time-matching is more efficient without an excessively small time-step. Furthermore, the areas with intense vorticity, boundary layers, and free surfaces are automatically refined to prescribed high resolutions. The model is shown as stable even when multiple adaptation ( ) criteria are implemented in the computation. With respect to the simulation of Bragg resonance caused by Stokes waves, the obtained reflection and transmission coefficients, velocity in the boundary layers as well as velocity and vorticity fields are compared with other results obtained by extant studies. The model is then applied for solving Bragg resonance caused by cnoidal waves which show stronger scouring on the lee side of the submerged obstacles. The numerical results exhibit higher resolution for examining the secondary eddies compared with the conventional numerical methods. In addition, the computing time of the model with an adaptive grid is at least six times faster than that with a semi-uniform grid while their results are in a good agreement. ARTICLE HISTORY

Section: Validationsmentioning

confidence: 60%

Section: Introductionmentioning

confidence: 99%

Viscous numerical wave tank for Bragg resonance by cnoidal and Stokes waves

Chang

Lin

Engineering Applications of Computational Fluid Mechanics

2018

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“…, M − 1. Additionally, it should be noted that Equations (35) and (36) are valid for all eight cases, as shown in Figure 2.…”

Section: Eigenfunction Matching Methodsmentioning

confidence: 96%

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

Tseng

You

2020

JMSE

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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.

“…Parameters of the problem were set as h 1 = 1.0 m, h s = 0.5h 1 , w b = h 1 , w t = 0.5h 1 , and s = 2π/K = 2h 1 , as shown in Figure 8a. Following Tsai, et al [45], the numbers of shelves and evanescent modes were set to M = 100 and N = 4, respectively. Figure 9a depicts the variation of reflection coefficients |R| against 2k 1,0 /K with the number of breakwaters J equal to 1, 2, and 3, respectively.…”

Section: Water Wave Scattering Over Periodic Breakwatersmentioning

confidence: 99%

“…Parameters of the problem were set as 1 1in Figure8a. Following Tsai, et al[45], the numbers of shelves and evanescent modes were set to 100 M= and 4 N = , respectively.…”

mentioning

confidence: 99%

Bragg Resonance of Water Waves by Multiple Permeable Thin Barriers over Periodic Breakwaters

Tran¹,

Lin

2023

Water

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In this study, the Bragg resonance of water waves scattered by multiple permeable thin barriers over a series of periodic breakwaters was solved by employing the eigenfunction matching method (EMM). The geometrical configuration was divided into multiple shelves separated by steps, on which thin permeable barriers were implemented. The solution was approximated using eigenfunctions with unknown coefficients that were considered as the amplitudes of the water waves for each shelf. The conservations of mass and momentum were then applied to form a system of linear equations, which was sequentially solved by a sparse-matrix solver. The proposed method degenerates to traditional EMM formulations if thin barriers, the permeability of the barrier, or bottom undulations are not considered. The validity of the suggested method was examined based on the results in the literature. Bragg resonances by bottom-standing, surface-piecing, and fully submerged permeable barriers over a series of periodic trapezoidal or half-cosine breakwaters were studied. In addition, the breakwater amplitudes, permeable parameters of the barriers, and incident angles of water wave scattering by different types of periodic breakwaters were discussed.