Revista de Gestão Costeira Integrada
Volume 16, Issue 3, September 2016, Pages 343-355

DOI: 10.5894/rgci660
* Submission: 14 DEC 2015; Peer review: 2 FEB 2016; Revised: 31 MAR 2016; Accepted: 14 APR 2015; Available on-line: 9 MAY 2016

Supporting Information (778KB, PDF)

Nonlinear and dispersive wave effects in coastal processes *  

José Simão Antunes do Carmo ^a

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a - University of Coimbra, Department of Civil Engineering, 3030-788 Coimbra, Portugal. e-mail: jsacarmo@dec.uc.pt

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ABSTRACT
Numerical models are useful instruments for studying complex superposition of wave-wave and wave-current interactions in coastal and estuarine regions, and to investigate the interaction of waves with complex bathymetries or structures built in nearshore areas. The ability of the standard Boussinesq and Serre or Green and Naghdi equations to reproduce these nonlinear processes is well known. However, these models are restricted to shallow water conditions, and addition of other terms of dispersive origin has been considered since the 90’s, particularly for approximations of the Boussinesq-type. Using the general wave theory in shallow water conditions, the different approaches commonly used in hydrodynamics studies in river systems, estuaries and coastal zones are initially addressed. Then, to allow applications in a greater range of shallow waters, namely in intermediate water conditions, a new set of extended Serre equations, with additional terms of dispersive origin, is presented and tested with available data in the literature. The hydrodynamic module, composed of the extended Serre equations, is then used as part of a morphodynamic model, which incorporates two more equations taking into account various processes of sediment transport. The wave velocity-skewness and the acceleration-asymmetry are taken into account and discussed based on numerical results and physical considerations.

Keywords: Wave theory in shallow waters, extended Serre equations, sediment transport, Bailard model, wave accelerationasymmetry,
wave velocity-skewness.

Efeitos não-lineares e dispersivos da onda nos processos costeiros

RESUMO
Os modelos numéricos são instrumentos úteis para estudar a propagação de ondas em meios com diferentes características, desde águas profundas (ao largo) até condições de água pouco profunda, e investigar a interação de ondas com batimetrias complexas ou estruturas construídas em regiões costeiras e estuarinas. As capacidades de modelos do tipo Boussinesq e as equações de Serre, ou de Green e Naghdi, para reproduzir os processos não-lineares de diversas interações são bem conhecidas. No entanto, estas aproximações clássicas restringem-se a condições de águas pouco profundas. Desde meados da década de 90 têm sido desenvolvidas formulações que modificam ou acrescentam termos de origem dispersiva para aplicações mais generalizadas, particularmente em aproximações do tipo Boussinesq. Recorrendo à teoria geral das ondas em condições de águas pouco profundas, são aqui apresentadas, em primeiro lugar, as aproximações comumente usadas em estudos da hidrodinâmica em meios fluviais, estuários e zonas costeiras. Tendo como objetivo alargar o campo de aplicação a outros domínios, em particular a condições de águas intermédias, é em seguida apresentada e testada com dados experimentais uma formulação das equações clássicas de Serre com melhores características dispersivas lineares. Por fim, é proposto um modelo morfodinâmico 1DH composto por um módulo hidrodinâmico, que resolve as equações expandidas de Serre, e por duas equações que incorporam vários processos de transporte sedimentar. Em particular, são avaliados e discutidos termos de transporte induzidos pelo enviesamento (skewness) e pela assimetria da onda.

Palavras-chave: Teoria da onda em água pouco profunda, equações expandidas de Serre, transporte sedimentar, modelo de
Bailard, enviesamento e assimetria da onda.

 

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