The effect of friction and topography on coastal internal Kelvin waves at low latitudes

The effects of bottom Ekman layer friction and slope topography on freely propagating coastal internal Kelvin waves in a stratified ocean are examined. Frictional effects are assumed weak and specific slope topographies are chosen so that perturbation methods may be used to obtain solutions. Two models for slope topography are utilized: a steep slope model, which corresponds to the low latitude case where the Rossby radius scale δ_R is assumed large compared to the slope width Ls, and a weak slope model, which corresponds to the case δ_R » L_s. For both cases, internal Kelvin waves are damped by bottom friction, and offshore and vertical phase lags are induced, as well as an onshore flow. However, there are substantial differences between the results obtained with the two different models. For example, vertical phase shifts due to friction for the steep slope case imply that alongshore velocity v at the surface leads v below, while motions at the bottom lead for the weak slope case. For the weak slope, frictional effects are proportional to bottom velocity, implying that, for mid-latitudes, bottom stress effects on barocline modes are minimal. However, results from the steep slope model imply that baroclinic modes are significantly affected by bottom stress at low latitudes. In both cases, the topography changes the frequency and alongshore phase speed of the wave, the modal structure is altered, and an onshore flow is induced. For the weak slope case, the wave speed is proportional to the mean bottom depth averaged over the Rossby radius scale. For the steep slope, changes in wave speed depend on the details of the slope geometry: a slope that is concave downward increases the speed while a slope that is concave upward decreases the speed. Both models are compared with observations from the Peru coast.