Abstract
A theoretical study of the dynamics of long and ultra-long waves in a baroclinic tonal current is made by the use of quasi-geostrophic equations. The stability of the tonal current and the characteristics of wave perturbations are iinvestigated numerically with the finite difference approximation of the linearized perturbation equations applied to a multi-layer model. It is found that the wave solutions are classified into three types : (i) a pair of amplifying and decaying waves, (ii) neutral waves without steering levels in the basic current and (iii) neutral waves with a steering level. They are divided into various regimes in accordance with their vertical structure. The examination of the vertical structure of wave disturbances, as well as of the phase velocity, is made in terms of the wavelength and the vertical shear of the zonal current. Some remarks on the validity of the finite difference approximation by a simple 2-layer model are added in relation to the results obtained by the multi-layer model.
The energy conversion processes are discussed by making a comparison between the unstable waves of the first mode and the higher mode. It is found that the maintenance of the unstable wave of the higher mode is only due to the increase of the eddy available potential energy caused by northward heat transport. Finally a comparison between the characteristics of ultra-long waves obtained by the present study and those of the observation is made.
