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Gravitational mode calculation of basins discretized by orthogonal curvilinear grids |
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| Authors: | Gian Mario BeltramiRiccardo Briganti |
| Institution: | a Department of DISAT, University of L’Aquila, Monteluco di Roio, 67040 L’Aquila, Italy b Department of the Environment, ENEA ‘Casaccia’, Via Angullarese 301, 00060 Roma, Italy c Department DSIC, University Roma Tre, Via Volterra 62-00146 Roma, Italy |
| Abstract: | 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. |
| Keywords: | Gravitational modes Shallow-water equations Adiabatic boundary conditions Orthogonal curvilinear coordinates Staggered grids |
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