Re ̄ection of equatorial Kelvin waves at eastern ocean boundaries Part I: hypothetical boundaries

A baroclinic shallow-water model is developed to investigate the e€ect of the orientation of the eastern ocean boundary on the behavior of equatorial Kelvin waves. The model is formulated in a spherical polar coordinate system and includes dissipation and nonlinear terms, e€ects which have not been previously included in analytical approaches to the problem. Both equatorial and middle latitude response are considered given the large latitudinal extent used in the model. Baroclinic equatorial Kelvin waves of intraseasonal, seasonal and annual periods are introduced into the domain as pulses of ®nite width. Their subsequent re ̄ection, transmission and dissipation are investigated. It is found that dissipation is very important for the transmission of wave energy along the boundary and for re ̄ections from the boundary. The dissipation was found to be dependent not only on the presence of the coastal Kelvin waves in the domain, but also on the period of these coastal waves. In particular the dissipation increases with wave period. It is also shown that the equatorial b-plane approximation can allow an anomalous generation of Rossby waves at higher latitudes. Nonlinearities generally have a small e€ect on the solutions, within the con®nes of this model.