The Free Kelvin Wave in Finite-Difference Numerical Models

Abstract

Abstract The effects of viscosity and finite- differencing on free Kelvin waves in numerical models (which employ the Arakawa B- or C-grid difference schemes) are investigated using the f-plane shallow-water equations with offshore finite-difference grids, (assuming alongshore geostrophy). Three nondimensional parameters arise: Δ [=(offshore grid spacing)/(Rossby radius)], ϵ characterizes the offshore lateral viscous effect and α the combined vertical and alongshore viscous effect. This study is more relevant to baroclinic Kelvin waves which tend to suffer poor offshore resolution because of their small Rossby radii. For inviscid models (ϵ = α = 0), as Δ increases (resolution worsens), the alongshore speed increases dramatically in the B-grid, but stays constant at the gravity wave speed in the C-grid. Models with damping only (α > 0, ϵ = 0) behave similarly. With lateral viscosity (ϵ > 0, α > 0), increasing ϵ decreases the speed in both the B- and C-grids—the drop in speed being less severe when the free...