The solution of the equations of motion shows several vertical baroclinic modes that are established according to the pycnocline, i.e. the distribution of the density of seawater as a function of depth. In a stratified ocean, the interface between two layers is subjected to an oscillation phenomenon whose natural (normal) frequency depends on the difference in buoyancy between the two layers. Each interface corresponds to a phase velocity of baroclinic waves travelling horizontally.
The density increases with depth, the densest water naturally being in the ocean depths. However, the evolution of density with depth is not uniform. In equatorial and tropical regions, there is a layer of water near the surface of almost constant density, then a transition zone through which the density increases very rapidly with depth. This layer so-called pycnocline generally coincides with the thermocline. To larger depths the density changes slowly. At high latitudes, the density of the layer near the surface is high because of the low temperature of seawater; the vertical profile is less contrasted and pycnocline less easy to discern.
The distinction between different normal modes is therefore at low latitudes. For the first baroclinic mode, the interface is at the base of the pycnocline, which at the equator is in average at 255 m in the Pacific Ocean, 220 m in the Atlantic Ocean and 180 m in the Indian Ocean. The phase velocity measured in the Pacific is about 2.8 m/s; so an equatorial Kelvin wave takes two months to cross the Pacific from New Guinea to South America. The phase velocities are measured to 2.35 m/s and 2.30 m/s in the Atlantic and Indian Oceans. The surface height perturbation η corresponding to this mode of propagation reflects changes in depth of the thermocline, but opposite in sign and approximately 300 times lower: an elevation of 5 cm of the surface corresponds to a deepening of the thermocline of about 15 m.
The interface of another important mode is at the top of the pycnocline, i.e. in average at 125 m, 30 m and 50 m in the Pacific, Atlantic and Indian oceans, respectively, with phase velocities of 1.0 m/s in the Pacific and 0.28 m/s in the other two oceans. Other intermediate modes can be identified, probably resulting from coupling with the two main modes.
[i] In a homogeneous medium, propagation in a given direction of a monochromatic wave (or sine) results in a simple translation of the sinusoid at a speed called phase velocity or celerity. In a non-dispersive medium, the speed does not depend on the frequency (or wavelength). In this case every complex wave is the sum of several monochromatic waves that also undergo an overall translation of its profile, this without deformation. In contrast, in a dispersive medium the phase velocity depends on the frequency and the energy transported by the wave moves at a speed lower than the phase velocity, said group velocity.