Wave propagation through a gap in a thin vertical wall indeep wáter

• Autores: B. C. Das, Soumen De, B. N. Mandal
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 21, Nº. 3, 2019, págs. 93-105
• Idioma: inglés
• DOI: 10.4067/S0719-06462019000300093
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• Resumen
  • español

    Resumen En este artículo re-investigamos el problema de dispersión oblicua de ondas superficiales de agua por una pared vertical con una abertura sumergida en agua infinitamente profunda. Se formula en términos de dos ecuaciones integrales de primera especie, una involucrando la diferencia de potencial a través de la parte mojada de la pared y la otra involucrando la componente horizontal de la velocidad a través de la apertura. Las ecuaciones integrales son resueltas aproximadamente usando aproximaciones de Galerkin de un término involucrando constantes multiplicadas por funciones peso apropiadas, cuyas formas son dictadas por la física del problema. Esto se contrapone con lo complicado de soluciones conocidas para las correspondientes ecuaciones integrales de agua profunda para el caso de incidencia normal, usadas anteriormente en la literatura como aproximaciones de Galerkin de un término. Últimamente esto lleva a cotas superiores e inferiores muy cercanas (numéricamente) para los coeficientes de reflexión y transmisión de tal suerte que sus promedios producen estimaciones numéricas razonablemente precisas para estos coeficientes. Se recuperan resultados numéricos conocidos en la literatura para la incidencia normal y para una apertura delgada, confirmando que los métodos empleados son correctos.

  • English

    Abstract The problem of oblique scattering of surface water waves by a vertical wall with a gap submerged in infinitely deep water is re-investigated in this paper. It is formulated in terms of two first kind integral equations, one involving the difference of potential across the wetted part of the wall and the other involving the horizontal component of velocity across the gap. The integral equations are solved approximately using one-term Galerkin approximations involving constants multiplied by appropriate weight functions whose forms are dictated by the physics of the problem. This is in contrast with somewhat complicated but known solutions of corresponding deep water integral equations for the case of normal incidence, used earlier in the literature as one-term Galerkin approximation. Ultimately this leads to very closed (numerically) upper and lower bounds of the reflection and transmission coefficients so that their averages produce fairly accurate numerical estimates for these coefficients. Known numerical results for normal incidence and for a narrow gap obtained by other methods in the literatura are recovered, thereby confirming the correctness of the method employed here.

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