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

Abstract

Abstract. A baroclinic shallow-water model is developed to investigate the eect 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, eects 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 eect on the solutions, within the con®nes of this model.

Reflection of equatorial Kelvin waves at eastern ocean boundaries Part II: Pacific and Atlantic Oceans

“…2). This is consistent with the northern Paci®c boundary being more nonmeridional (see Soares et al, 1998). The Paci®c energy dissipation is roughly similar in both hemispheres.…”

“…For an inclined boundary, it would be expected from inviscid theory, that the poleward propagation of coastal waves would be enhanced compared with the meridional boundary. However, as discussed in Soares et al (1998), the dissipation induced by the inclined boundary is larger than that induced by the meridional one (see Fig. 2c).…”

“…Three dierent wave period (as in Soares et al, 1998) are considered: intraseasonal (T = 60 days), seasonal (T = 180 days) and annual (T = 360 days).…”

“…(Grimshaw and Allen, 1988;Clarke and Shi, 1991). Soares et al (1998) using a viscous baroclinic shallow water model, have investigated the eects of viscosity, non-linearity, angle of coastline inclination and incident wave period on the baroclinic equatorial Kelvin waves at eastern ocean boundaries. They have found, by energy¯ux considerations, that the impact of viscosity is greater than the eect of non-linearities.…”

“…2 Numerical model Non linear, 1/2 layer, shallow-water equations are used as the basis of the numerical model. The model is described in detail in Soares (1994) and Soares et al (1998). Spherical coordinates with k (longitude) increasing eastward and h (latitude) increasing northward are used in the model because of its large latitudinal extent.…”