Long wave reflection from submerged trapezoidal breakwaters

Chang, Han; Liou, Jin Cheng

doi:10.1016/j.oceaneng.2005.11.017

Cited by 70 publications

(10 citation statements)

References 17 publications

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“…The slope method is an extension of Dean's (1964) method that allows a trench and shoals with a linear transition between changes in depth but valid only within the long wave region. Recently, Lin and Liu (2005) and Chang and Liou (2007) conducted analytical studies for the long wave reflection by trapezoidal shape breakwaters by modifying the Dean's (1964) solution.…”

Section: Introductionmentioning

confidence: 99%

Linear wave reflection by trench with various shapes

et al. 2008

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Two types of analytical solutions for waves propagating over an asymmetric trench are derived.One is a long wave solution and the other is a mild-slope solution which is applicable to deeper water. The water depth inside the trench varies in proportion to a power of distance from the center of the trench (where the center means the deepest water depth point and the origin of -coordinate in this study). The mild-slope equation is transformed into a second order ordinary differential equation with variable coefficients based on the longwave assumption or Hunt's (1979) Reply to reviewers' comments on revision of "Linear Wave Reflection by Trench with Various Shapes" by Tae-Hwa Jung, Kyung-Duck Suh, Seung Oh Lee, and Yong-Sik Cho First, we appreciate the reviewers' interest and comments on our manuscript. In the following, we provide responses to the reviewers' comments in a question-answer format. The answers are typed in italic. The page numbers and figure numbers referred to in this reply are those in the revised manuscript in which all numbers of equations were rearranged according to the revision. * Detailed Response to ReviewersAnswer to comments of reviewer 1 I suggest that this paper can be accepted for publication if the following minor modification is made. Minor modification:Please delete all the contents after Eq.(B-8) in Appendix B. The reason is 1) It is unnecessary to expand A(x), B(x), C(x). 2) Even if they need to be expanded, those expansions can be obtained very easily by using the Maple or some other softwares. A) We removed all the contents after Eq. (B-8) as the reviewer suggested.Answer to comments of reviewer 2 1. General comments. The authors have taken care of almost all of my remarks. However, they still want to stick to their extended solutions. They only changed their model into solution. I strongly object to the use of the notation of extended solution to deeper water in this paper. I said it before, the solutions of the mild-slope equation are valid for both deep and shallow water.In the paper two different models are considered:• The long-wave model as such, and Under the condition that the notation and wording of extended is removed from the paper and heed is taken on my previous remarks on this matter, the paper may be published, but only under this condition.We removed the word 'extended' in the paper and replaced following expressions as reviewer suggested. The extended solution  the mild-slope solution The other is a solution extended to deeper water  the other is the mild-slope solution

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Section: Introductionmentioning

confidence: 99%

Linear wave reflection by trench with various shapes

et al. 2008

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“…In dimensionless variables, conditions (2) and (3) To account for the discontinuous changes in the sea-floor depth at each interface between two boundaries (see Fig. 1), the spatial domain is partitioned into n þ 1 regions; the space to the right of the x ¼ 0 boundary, which we will call the right region, and n subdivisions of the space to the left of x ¼ 0.…”

Section: Scale Analysismentioning

confidence: 99%

“…To extend Lamb's result to more realistic situations, many analytical solutions and numerical methods have since been developed. Analytical solutions have been obtained for piecewise linear topographies [2,10,16] and internal waves [21]. Various numerical approaches have used the eigenfunction expansion method for sinusoidal topographies [3], a series of obstacles [4], and permeable structures [17,18], Boussinesq equations [9,19,20], Boundary Element Method [5], nonlinear shallow-water equations [11], and Reynolds equations [15].…”

Section: Introductionmentioning

confidence: 99%

Linear long wave propagation over discontinuous submerged shallow water topography

Shankar

Yan

Golbek

et al. 2015

Applied Mathematics and Computation

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“…But the most difficulty of floating breakwater is to decrease long wave length wave [1] . Bragg resonance was first discovered in crystallography [2]. In coastal and ocean engineering, Heathershaw [3] first published laboratory measurements that significant and large amounts of wave energy be reflected by resonant interactions between surface-water waves and the undulating bedforms while incident surface water wavelengths are approximately twice the bedform wavelengths; Mei [4] explain a theory that strong reflection can be induced by the sandbars themselves, once the so-called Bragg resonance condition is met.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulating of the Interaction of Vertical Fixed Multiple Membranes with Gravity Wave

Tao¹,

Wu²,

Mei³

et al. 2014

Proceedings of the 2014 International Conference on Mechanics and Civil Engineering

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Abstract. In deep sea or temporary application, the floating breakwater should be best used to attenuate the surface wave. But the most difficulty of floating breakwater is to decrease long wave length wave. Bragg resonance condition appears while incident surface water wavelengths are approximately twice the periodic structure wavelengths, and large amounts of incident wave energy are reflected. In recent years, flexible membrane structure, with its numerous advantages, has attracted the attention of the coastal and ocean engineers and researchers. Although Bragg resonance is investigated by using diffirent analytical methods, it is not found by using CFD method. Therefore, in this paper, we use commercial software code FLUENT to numerical simulating the interaction of surface grivaty wave with multiple veitically fixed membranes with constant gaps. At the beginning, we verified the numerical technology by simulating the wave making and the interaction of wave with single membrane; then, we computed 4 diffirent length veitically fixed multiple membranes. The results show that the transmission coefficient is small and decline obviously with the membrane lengthened when incident surface water wavelengths are approximately twice the membrane gap. However, we need to simulate more wave lengthes to find whether there is the strong reflection induced by Bragg resonance. The works in this paper are the base about more studies on Bragg resonance being applied to floating breakwater.

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Long wave reflection from submerged trapezoidal breakwaters

Cited by 70 publications

References 17 publications

Linear wave reflection by trench with various shapes

Linear wave reflection by trench with various shapes

Linear long wave propagation over discontinuous submerged shallow water topography

Numerical Simulating of the Interaction of Vertical Fixed Multiple Membranes with Gravity Wave

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