Gravitational mode calculation of basins discretized by orthogonal curvilinear grids

✍ Scribed by Gian Mario Beltrami; Andrea Bargagli; Riccardo Briganti

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 346 KB
• Volume: 30
• Category: Article
• ISSN: 0029-8018
• DOI: 10.1016/s0029-8018(02)00079-3

✦ Synopsis

This paper presents a simple and straightforward method for carrying out the direct numerical solution of the eigenvalue problem associated to the homogeneous linear shallow-water equations expressed using orthogonal curvilinear coordinates, when 'adiabatic' boundary conditions apply. These equations, together with the boundary conditions, define a self-adjoint problem in the continuum. The method presented here, which is thought for calculating the 2-D theoretical gravity modes of both natural and artificial basins, relies on a change of basis of the dependent variable vector. This preliminary transformation makes it, in fact, possible to formulate two different numerical approaches which guarantee the self-adjoint property of the discrete form of the system consisting of the governing equations and the boundary conditions. The method is tested using a square and a fully circular domain, both of which allow comparisons with well-known analytical and numerical solutions. Discretizing the physical domain of a fully circular basin by a cylindrical coordinate grid makes it possible to show the actual efficiency of the method in calculating the theoretical gravity modes of basins discretized by a boundary-following coordinate grid which allows laterally variable resolution.