On Breaking Waves and Wave-Current Interaction in Shallow Water: A 2dh Finite Element Model

Carmo, J. S. Antunes Dom; Seabra-Santos, Fernando J.

doi:10.1002/(sici)1097-0363(19960315)22:5<429::aid-fld388>3.0.co;2-8

Cited by 23 publications

(8 citation statements)

References 6 publications

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“…The solution at the wave gauges is presented in Figure . The results can be improved by considering wave breaking mechanisms and Green‐Naghdi models with improved dispersion characteristics such as those proposed in . It is noted that in both cases, only linear terms with second order derivatives are included locally around the regions where the waves become steep.…”

Section: Numerical Experimentsmentioning

confidence: 99%

A modified Galerkin/finite element method for the numerical solution of the Serre‐Green‐Naghdi system

Mitsotakis

Synolakis

McGuinness

2016

Numerical Methods in Fluids

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Abstract. A new modified Galerkin / Finite Element Method is proposed for the numerical solution of the fully nonlinear shallow water wave equations. The new numerical method allows the use of low-order Lagrange finite element spaces, despite the fact that the system contains third order spatial partial derivatives for the depth averaged velocity of the fluid. After studying the efficacy and the conservation properties of the new numerical method, we proceed with the validation of the new numerical model and boundary conditions by comparing the numerical solutions with laboratory experiments and with available theoretical asymptotic results.

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Section: Numerical Experimentsmentioning

confidence: 99%

A modified Galerkin/finite element method for the numerical solution of the Serre‐Green‐Naghdi system

Mitsotakis

Synolakis

McGuinness

2016

Numerical Methods in Fluids

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“…In order to test the robustness of Model (12), several numerical tests were performed. Its good performance is proven through very demanding applications, namely: A1: a solitary wave propagating in a channel 1.0 m depth and 250 m long, with a/h 0 = 0.60; A2: a periodic wave propagating over a submerged bar in shallow-depth (h 0 /λ ≈ 0.03) and intermediate-depth waters (h 0 /λ ≈ 0.11); and A3: periodic wave propagating in quasi-deep-water conditions (h 0 /λ = 0.50).…”

Section: Resultsmentioning

confidence: 99%

“…To validate System (12) and check the accuracy of the numerical method used with α = β = 0 and ξ t = ξ x = ξ xx = ξ xxx = 0, a comparison with a closed-form solitary wave solution of the Serre equations was made, which is expressed as:…”

Section: Solitary Wavementioning

confidence: 99%

“…On the other hand, they have allowed the use of more complete and comprehensive mathematical models. In fact, only models of order σ 2 (σ = h 0 /λ, where h 0 and λ represent, respectively, depth and wavelength characteristics) or greater and of the Boussinesq [9], Serre [10], or Green and Naghdi [11] types are appropriate for describing the dispersive and nonlinear interaction processes of the generation, propagation, and run-up of waves resulting from wave-wave and wave-current interactions [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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Remarks on the Boundary Conditions for a Serre-Type Model Extended to Intermediate-Waters

Carmo¹,

Simão²

2021

Modelling

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Numerical models are useful tools for studying complex wave–wave and wave–current interactions in coastal areas. They are also very useful for assessing the potential risks of flooding, hydrodynamic actions on coastal protection structures, bathymetric changes along the coast, and scour phenomena on structures’ foundations. In the coastal zone, there are shallow-water conditions where several nonlinear processes occur. These processes change the flow patterns and interact with the moving bottom. Only fully nonlinear models with the addition of dispersive terms have the potential to reproduce all phenomena with sufficient accuracy. The Boussinesq and Serre models have such characteristics. However, both standard versions of these models are weakly dispersive, being restricted to shallow-water conditions. The need to extend them to deeper waters has given rise to several works that, essentially, add more or fewer terms of dispersive origin. This approach is followed here, giving rise to a set of extended Serre equations up to kh ≈ π. Based on the wavemaker theory, it is also shown that for kh > π/10, the input boundary condition obtained for shallow-waters within the Airy wave theory for 2D waves is not valid. A better estimate for the input wave that satisfies a desired value of kh can be obtained considering a geometrical modification of the conventional shape of the classic piston wavemaker by a limited depth θh, with θ≤ 1.0.

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“…6. High-tide 4.00 m (ZH); significant wave height H s = 7.0 m; period T = 17.0 sec.These sinusoidal wave characteristics were considered as input boundary conditions for a suitable numerical model, based on Boussinesq type equations (Antunes do Carmo et al[5]; Antunes do Carmo and Seabra-Santos[6]), at a distance of 1450 m from the existing sand dune base, and in a region where the water column is about 14.5 m deep. The results for conditions 2, 5 and 6 are www.witpress.com, ISSN 1743-3541 (on-line)…”

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confidence: 99%

Successful rehabilitation of a sand dune system

Carmo¹,

Reis²,

Freitas³

2006

WIT Transactions on Ecology and the Environment, Vol 88

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The construction of an underwater effluent damaged the continuity of the Leirosa sand dune system, which is located at south of Figueira da Foz, midway along the Portuguese coast. The use of heavy machinery in this fragile area has worsened the erosive effect already caused by an existing groyne one kilometre north of the affected area. The recovery of this system started in 2000, with the artificial reconstruction of the dunes followed by replanting. In February 2001, however, during a storm whose impact was felt all over the central area of Portugal, and especially on the coast, the oceanic front of the Leirosa dune system was destroyed, and alternative hard protection devices have been encouraged. The study carried out showed that a submerged breakwater could be an interesting and efficient strategy, not only to protect the coastal system, but also to increase recreational beach activities. However, the costs involved and the time required to implement this solution have been considered insupportable and, as a consequence, the local industries involved decided on another solution. Geotextiles have been successfully used in hydraulic engineering and more recently also in the construction of artificial dunes and stabilisation of beach nourishment measurements. It is shown that the use of geotextiles can be as effective as any so called "hard engineering protection", with the advantage of being adaptable to the morphology of the dune system and using locally available sand. Keywords: sand dunes, coastal protection, submerged breakwaters, geotextiles. IntroductionIn general, the coasts are nowadays hugely popular places to go for holidays or a day out. Residents and visitors alike are attracted by the sandy beaches, striking scenery and the chance to 'get away from it all'. They provide limitless scope to watch wildlife, pursue outdoor sports such as diving and sailing, or simply walk, contemplate and seek inspiration.Unfortunately, massive tourist use of many beaches has been followed by the destruction of many coastal dune areas in recent decades all over the world. Reconstruction of destroyed dunes is nearly impossible because many of these zones have been taken over by resorts, or in some other cases, the new dunes are smaller and more linear than the natural dunes they have replaced.It is to everyone's benefit to maintain the qualities that make the coasts such special places -their beauty, diversity and wildness. Visitor pressure alone can severely damage the natural environment of these coasts. Too much trampling encourages dune erosion. Beaches may be spoilt by litter and sewage. In general, coastlines are fragile environments and we need to be aware of the impact our own activities may have. This is vital if we are to conserve the quality of our coastlines and ensure that they can be enjoyed by many generations to come.In many coastal zones, it is not uncommon for sand or shingle to be taken from beaches or dunes. This may be used for anything from building to the filling of bunkers on golf cour...

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On Breaking Waves and Wave-Current Interaction in Shallow Water: A 2dh Finite Element Model

Cited by 23 publications

References 6 publications

A modified Galerkin/finite element method for the numerical solution of the Serre‐Green‐Naghdi system

A modified Galerkin/finite element method for the numerical solution of the Serre‐Green‐Naghdi system

Remarks on the Boundary Conditions for a Serre-Type Model Extended to Intermediate-Waters

Successful rehabilitation of a sand dune system

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