Time-Dependent Ventilated Thermocline

In this thesis, I study the time-varying behavior of a ventilated thermocline with basin scales at annual and decadal time scales. The variability is forced by three external forcings: the wind stress (chapter 3), the surface heat flux (chapter 4) and the upwelling along the eastern boundary (chapter 5). It is found that the thermocline variability is forced mainly by wind in a shadow zone while mainly by surface buoyancy flux in a ventilated zone. A two-layer planetary geostrophic model is developed (chapter 2) to simulate a thermocline. The model includes some novel physical mechanisms. Most importantly, it captures the essential feature of subduction; it also is able to account for a time-varying surface temperature. The equation for the interface is a quasi-linear equation, which can be solved analytically by the method of characteristics. The effect of a varying Ekman pumping is investigated. In a shadow zone, it is found that the driving due to the Ekman pumping is mainly balanced by the propagation of planetary waves. However, in a ventilated zone, the cold advection of subducted water plays the essential role in opposing the Ekman pumping. The different dynamics also results in different thermocline variability between the two zones. After a change of Ekman pumping, in the shadow zone, since the baroclinic Rossby wave responds to a changing Ekman pumping slowly (in years to decades), an imbalance arises between the Rossby wave and the Ekman pumping, which then excites thermocline variability. However, in the ventilated zone, both the advection and the Ekman pumping vary rapidly after a barotropic process (about one week) to reach a new steady balance, leaving little thermocline variability. In addition, the evolution of the thermocline and circulation are also discussed. Furthermore, with a periodic Ekman pumping, it is found that linear solutions are approximate the fully nonlinear solution well, particularly for annual forcings. However, the linear disturbance is strongly affected by the basic thermocline structure and circulation. The divergent group velocity field, which is mainly caused by the divergent Sverdrup flow field, produces a decay effect on disturbances. The mean thermocline structure also strongly affects the relative importance of the local Ekman pumping and remote Rossby waves. As a result, in a shadow zone, local response dominates for a shallow interface while the remote Rossby wave dominates for a deep interface. With a strong decadal forcing, the nonlinearity becomes important in the shadow zone, particularly in the western part. The time-mean thermocline which results, becomes shallower than the steady thermocline under the mean Ekman pumping. Then, we investigate the effect on the permanent thermocline by a moving outcrop line, which simulates the effect of a varying surface heat flux. The two layer model is modified by adding an (essentially passive) mixed layer atop. The outcrop line and the mixed layer depth are specified. It is found that, opposite to a surface wind stress, a surface buoyancy flux causes strong variability in the ventilated zone through subducted water while it affects the shadow zone very little. Furthermore, two regimes of buoyancy-forced solution are found. When the outcrop line moves slowly, the solutions are non-entrainment solutions. For these solutions, the surface heat flux is mainly balanced by the horizontal advection. The mixed layer is never entrained. The time-mean thermocline is close to the steady thermocline with the time-mean outcrop line. When the outcrop line moves southward rapidly during the cooling season, the solutions become entrainment solutions. Now, deep vertical convection must occur, because the horizontal advection in the permanent thermocline is no longer strong enough to balance the surface cooling. The mixed layer penetrates rapidly such that water mass is entrained into the mixed layer through the bottom. The time-mean thermocline resembles the steady thermocline with the early spring mixed layer, as suggested by Stommel (1979). The local variability in the permanent thermocline is most efficiently produced by decadal forcings. Finally, two issues about the waves radiating from the eastern boundary are discussed. The first is the penetration of planetary waves across the southern boundary of a subtropical gyre. We find that the wave penetration across the southern boundary is substantially changed by the zonal variation of the thermocline structure. The zonal variation alters both the effective P and the wave front orientation. As a result, the wave penetration differs for interfaces at different depths. For an interface near the surface, part of the waves penetrate into the equatorial region. For middle depths, most waves will be trapped within the subtropical gyre. In contrast, for deep depths, all waves penetrate southward. The second issue of the eastern boundary waves mainly concerns with the breaking of planetary waves in the presence of an Ekman pumping and the associated two-dimensional mean flow. It is found that the breaking is affected significantly by an Ekman pumping and the associated mean flow. With an Ekman pumping, downwelling breaking is suppressed and the breaking time is delayed; upwelling breaking is enhanced and their times are shortened. The breaking times and positions are mainly determined by the maximum vertical perturbation speed while the intensity of the breaking front mainly depends on the amplitude of the perturbation. The intensity of a breaking front increases with the amplitude of the forcing, but decreases with the distance from the eastern boundary. The orientation of a breaking front is overall in northeast-southwest ( x , -1/f2).