Numerical Analyses of Wave Generation and Vortex Formation under the Action of Viscous Fluid Flows over a Depression

Chang, Chih‐Hua

doi:10.3390/jmse7050141

Cited by 3 publications

(1 citation statement)

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“…To the best of our ( 1 ) That is, linear potential theory valid for arbitrary water depth. knowledge, only the latter case has been considered in the existing literature; see (Chang et al 2011(Chang et al , 2012Chu et al 2015;Chang 2019). The emphasis, in the above-mentioned works, lies in the solitary wave transformation by the trench and on the study of the vortical fluid motion induced by the trench.…”

Section: Introductionmentioning

confidence: 99%

A numerical study of the run-up and the force exerted on a vertical wall by a solitary wave propagating over two tandem trenches

Athanassoulis

Mavroeidis

Koutsogiannakis

et al. 2019

J. Ocean Eng. Mar. Energy

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1. Introduction 2. An overview of the fully non-linear Hamiltonian Coupled-Mode Theory 2.1. Classical differential and variational formulation 2.2. The Hamiltonian Coupled-Mode Theory 3. A concise description of the numerical implementation 3.1. Numerical solution of the kinematical substrate problem 3.2. Numerical solution of the Hamiltonian evolution equations 4. Propagation of a solitary wave over some typical bathymetries. Validation and limitations of the present method 4.1. Propagation over a shelf 4.2. Propagation over a step 4.3. Comparison and assessment of the findings of Sec. 4.1 and 4.2 4.4. Propagation over a trench 5. Propagation of a solitary wave over two trenches and reflection at a vertical wall 5.1. Propagation over the trenches 5.2. Run-up on the wall 5.3. Maximum force exerted on the vertical wall Conclusions A numerical study of the run-up and the force exerted on a vertical wall by a solitary wave propagating over two tandem trenches and impinging on the wall AbstractThe propagation and transformation of water waves over varying bathymetries is a subject of fundamental interest to ocean, coastal and harbor engineers. The specific bathymetry considered in this paper consists of one or two, naturally formed or man-made, trenches. The problem we focus on is the transformation of an incoming solitary wave by the trench(es), and the impact of the resulting wave system on a vertical wall located after the trench(es). The maximum run-up and the maximum force exerted on the wall are calculated for various lengths and heights of the trench(es), and are compared with the corresponding quantities in the absence of them. The calculations have been performed by using the fully nonlinear water-wave equations, in the form of the Hamiltonian coupled-mode theory, recently developed in Papoutsellis et al (Eur. J. Mech. B/Fluids, Vol. 72, 2018, pp. 199-224). Comparisons of the calculated free-surface elevation with existing experimental results indicate that the effect of the vortical flow, inevitably developed within and near the trench(es) but not captured by any potential theory, is not important concerning the frontal wave flow regime. This suggests that the predictions of the run-up and the force on the wall by nonlinear potential theory are expected to be nearly realistic.The main conclusion of our investigation is that the presence of two tandem trenches in front of the wall may reduce the run-up from (about) 20% to 45% and the force from 15% to 38%., depending on the trench dimensions and the wave amplitude. The percentage reduction is greater for higher waves. The presence of only one trench leads to reductions 1.4 -1.7 times smaller.Keywords: nonlinear water waves; wave-trench interaction; solitary wave over varying bathymetry; run-up on vertical wall; force on vertical wall; submerged breakwater

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Section: Introductionmentioning

confidence: 99%