Revista Recursos Hdricos

DOI:10.5894/rh35n1-2
O texto deste artigo foi submetido para reviso e possvel publicao em abril de 2014, tendo sido aceite pela Comisso de Editores Cientficos Associados em abril de 2014. Este artigo parte integrante da Revista Recursos Hdricos, Vol. 35, N 1, 23-35, maio de 2014.

Extenso da teoria de ondas no-lineares at condies de gua profunda

Nonlinear wave theory extended to deep water conditions

Jos S. Antunes do Carmo¹

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1 - IMAR/Universidade de Coimbra, FCTUC, Departamento de Engenharia Civil /// 3030-788 Coimbra /// jsacarmo@dec.uc.pt

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RESUMO
Os modelos numricos so instrumentos teis para estudar a propagao de ondas em meios com diferentes caractersticas, desde guas profundas (ao largo) at condies de gua pouco profunda, e investigar a interao de ondas com batimetrias complexas ou estruturas construdas em regies costeiras e estuarinas.
As capacidades de modelos do tipo Boussinesq e as equaes Serre, ou de Green e Naghdi, para reproduzir os processos no lineares de diversas interaes so bem conhecidas. No entanto, estas aproximaes clssicas restringem-se a condies de guas pouco profundas. Desde meados da dcada de 90 tm sido desenvolvidas formulaes que acrescentam termos de origem dispersiva, em particular para aproximaes do tipo Boussinesq.
Neste trabalho apresentada uma formulao das equaes clssicas de Serre com melhores caractersticas dispersivas lineares. As equaes so resolvidas numericamente por diferenas finitas, aps introduo de uma varivel auxiliar que agrega as derivadas temporais da velocidade na equao da quantidade de movimento.
A discretizao numrica validada por comparao de resultados com a soluo analtica de Serre para uma onda solitria com a/h₀=0.60, e com a soluo de Stokes para guas intermdias. O desempenho do modelo para propagar ondas at condies de guas profundas
(h/L=0.5) e fundos com declives acentuados testado atravs de comparaes com dados experimentais disponveis na literatura.

Palavras-chave: Equaes de Serre, caractersticas dispersivas, guas profundas, soluo numrica, aplicaes.

ABSTRACT
Numerical models are useful tools to study the wave propagation in regions with different characteristics, from deep water (offshore) to shallow water conditions, and to investigate the interaction of waves with complex bathymetries or structures constructed in coastal and estuarine regions.
The ability of Boussinesq-type models and Serre or Green and Naghdi equations to reproduce the nonlinear processes of different interactions is well known. However, these models are restricted to shallow water conditions, and addition of other terms of dispersive origin has been considered since 90’s, particularly for Boussinesq-type approximations.
In this work, a new approximation of the classical Serre equations with improved linear dispersive characteristics is developed and written in a weak quasi-conservative form by introducing a dependent variable that aggregates all time derivatives of momentum equation.
The numerical discretization is validated by comparison with the analytical solution for a highly nonlinear propagating solitary wave (a/h₀=0.60), and with the Stokes solution for intermediate waters. The model performance to propagate waves from deep water conditions (h/L=0.5) and bottoms with large slopes is tested through comparisons with experimental data available in the literature.

Keywords: Serre equations, dispersive characteristics, depth waters, numerical solution, applications.

 

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