Studying nonlinear equatorial dynamics with a spectral element shallow water equation model and internal gravity wave guide in boundary current.

Abstract

A spectral element shallow water equation model has been built in the first part of this dissertation. Applying it in the simulation of the equatorial ocean response to a Rossby wave vortex pair, we find that the cyclonic equatorial Rossby wave vortex pair can cause significant nonlinear instabilities in the western boundary region while it is reflected from there. As a result, the dynamic and kinetic structures in the western part of the ocean are totally different from those in the cases dominated by linear dynamics. Moreover, an extra amount of the energy flux carried by the long waves is permanently lost to the high order short Rossby waves due to the long-short wave interactions in the western boundary region. Therefore, the strong nonlinearity has further reduced the effectiveness of the western boundary in reflecting the long Rossby wave signals. The simulation results also show that the phase speeds of the equatorial long Rossby wave and the equatorial Kelvin wave of depression, which correspond to the thermocline shoaling, are smaller in the nonlinear simulations than those in the linear case. The simulation with low Reynolds number shows that high horizontal eddy viscosity can severely suppress the nonlinear instability. The simulation results with $R\sb e$ = 200 are largely explainable by the linear theory. In the second part of this dissertation, we have found that it is possible for internal gravity wave guides to exist in the eastern boundary currents. The phase speeds of the internal gravity waves trapped in these guides are close to that of the baroclinic Kelvin wave, and the waves in the same wave guide, i.e., they have the same turning longitudes, travel at the same phase speed. These internal gravity waves have wavelengths shorter than the Rossby radius of deformation. They can propagate both following and against the mean current. In the northern hemisphere, the northward propagating waves are more likely to be observed in the vicinities of the coastal area, while the southward propagating waves tend to be trapped in the wave guides which are farther away from the eastern boundary.