The Free Kelvin Wave with Lateral and Vertical Viscosity

Abstract

Free Kelvin wave solutions of the linear shallow-water equations are described, for an f-plane. Lateral and vertical viscous effects are represented by terms ??2u and du, respectively, where (u,v) is the (onshore, longshore) velocity. Both no-slip and free-slip boundary conditions are considered. When ? = 0 and d = 0, the lognshore phase speed decreases as longshore wavelength increases. Decay time is independent of wavelength, so the shorter waves are more efficient at sending information alongshore. For ? = 0 and d = 0, speed still decreases with increasing wavelength, but ht longer waves decay more slowly, and the longshore decay distance is now largest for long waves. Several examples are given. The wave properties are much less dependent on ? when free-slip rather than no-slip conditions are used. The onshore velocity is nonzero when ? > 0. This property is used to estimate ? = 103?104 m102 s?1, from previous observations of free baroclinic coastally-trapped waves off Peru. Longshore geostrophy is a good approximation unless ? is large and wavelength is small. With longshore geostrophy wave properties can be found in terms of just two nondimensional parameters: ?, related to offshore viscous effects, and α, which combines vertical and alongshore viscous effects. Wave properties for a wide range of values of ? and α are given. Effects of lateral and vertical diffusion can be added. With longshore geostrophy, the wave properties can be deduced by simply reinterpreting the parameter α.