Propagation of Kelvin waves along irregular coastlines in finite-difference models

In this paper, we examine the behavior of internal Kelvin waves on anf-plan e in finite-difference models using the Arakawa C-grid. The dependence of K elvin wave phase speed on offshore grid resolution and propagation directio n relative to the numerical grid is illustrated by numerical experiments fo r three different geometries: (1) Kelvin wave propagating along a straight coastline; (2) Kelvin wave propagating at a 45 degrees angle to the numeric al grid along a stairstep coastline with stairstep size equal to the grid s pacing; (3) Kelvin wave propagating at a 45 degrees angle to the numerical grid along a coarse resolution stairstep coastline with stairstep size grea ter than the grid spacing. It can be shown theoretically that the phase spe ed of a Kelvin wave propagating along a straight coastline on an Arakawa C- grid is equal to the analytical inviscid wave speed and is not dependent on offshore grid resolution. However, we found that finite-difference models considerably underestimate the Kelvin wave phase speed when the wave is pro pagating at an angle to the grid and the grid spacing is comparable with th e Rossby deformation radius. In this case, the phase speed converges toward the correct value only as grid spacing decreases well below the Rossby rad ius. A grid spacing of one-fifth the Rossby radius was required to produce results for the stairstep boundary case comparable with the straight coast case. This effect does not appear to depend on the resolution of the coastl ine, but rather on the direction of wave propagation relative to the grid. This behavior is important for modeling internal Kelvin waves in realistic geometries where the Rossby radius is often comparable with the grid spacin g, and the waves propagate along irregular coastlines. (C) 1998 Published b y Elsevier Science Limited. All rights reserved.