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. © 2002 Elsevier Science Ltd. All rights reserved.
All Science Journal Classification (ASJC) codes
- Environmental Engineering
- Ocean Engineering
Beltrami, G. M., Bargagli, A., & Briganti, R. (2003). Gravitational mode calculation of basins discretized by orthogonal curvilinear grids. Ocean Engineering, 30(7), 833 - 853. https://doi.org/10.1016/S0029-8018(02)00079-3