Lab Experiment And Theoretical Model For Horizontal Convection

Horizontal convection is a research frontier since it may help understand the mechanism of ocean thermohaline circulation. In this dissertation, lab experiment and theoretical model are combined to make a general discussion about the mechanism and property of the horizontal convection. Series of lab experiments are designed to exhibit the pattern of three-dimensional horizontal convection under the axis symmetric thermal forcing.Exp1 is non-rotating case, while Exp 2 is rotating case.Exp 1 illustrates upper-layer axis-symmetric thermal forcing can produce axis-symmetric shallow overturning circulation in non-rotating frame. The stratification setup by the differential heating tilts the pressure surface, and thus drives the secondary overturning circulation at the bottom of the container domain, even though the strength is much less than the upper overturning circulation. Also, the radial velocity in the upper overturning cell is following 1/R pattern of classic spot source or sink model. The sink on the upper center combines with the source below to form a radial dipole structure, which can be described using a torus. Particularly, the horizontal flow pattern is not totally axis-symmetric but shows a petal pattern, which we speculate that it may be the reflection of standing wave structure of velocity.Exp2 illustrates that in the rotating frame, the differential heating not only produce the overturning circulation and the stratification but also the geostrophic flow. Since the flow partially turns horizontally, the strength of overturning circulation reduces to one quarter; the depth of overturning circulation reduces to three quarters compared to the non-rotating case. The geostrophic flow reaches its maximum at the depth of return flow axes and its vertical pattern satisfies the thermal wind relation. Since the direction of geostrophic flow part is perpendicular to the plane of overturning flow, the combination of the two then shows a spiral structure like Ekman spiral. Also, we may use the spot source and spot vortex model to describe the horizontal flow pattern. The three-dimensional streamline can be analogized with the torus knot of the dipole model.The Exp1 and Exp2 illuminate that previous theory and lab experiment results in the non-rotating frame are still good reference. The lab experiment in this paper not only discovers new phenomena but also make a detailed depiction for the three-dimensional rotating horizontal convection.Exp3 and Exp4 are designed to diagnose the real ocean basin. Four axis-symmetric closed basins are separated in the domain and then we can estimate the basin-scale flow pattern, especially how the geostrophic flow adjusts when it is blocked by the boundary.Exp 3 exhibits the overturning circulation can still exist in the closed basin, moreover, the stratification generate the baroclinic beta effect, which results in the asymmetric phenomena in the horizontal flow. Also, the blocked geostrophic flow turns to the basin gyre.Exp4 is the half-closed basin case. We aim to evaluate how geostrophic flow adjusts in the run-through passage. The result shows that the overturning circulation is strengthened compared with closed case and multi-gyres are triggered by the run-through flow across each basin.Exp3 and Exp4 mainly show that pure surface thermal forcing can produce overturning circulation as well as the basin gyre. The baroclinic beta effect also results in the western intensification of flow in the basin.Based on the phenomena of the experiment, theoretical model are applied to discuss the thermodynamic property of horizontal convection. The horizontal convection belongs to the irreversible non-equilibrium open system. We speculate that when the differential heating is fixed, the circulation starts to adjust the temperature gradient and then transfer the internal energy to kinetic energy of the circulation. Thus, the structure of the circulation should reflect its thermodynamic property. Here, we aim to explain why the circulation stays at a particular depth at the steady state? Is this the intrinsic depth for the system? Simply, we apply a one-dimensional tube model in the non-rotating frame to characterize the motion of fluid parcel from the hot source to the cold source. This process is not the circulation itself but also the thermal cycle of the pure heat engine. According to the maximum entropy production principle in thermodynamics, the circulation will choose a particular depth at the steady state which can maximize the entropy production rate of the system. Thus, following this principle in our tube model, we diagnose the intrinsic depth in the fixed thermal forcing by picking out the depth of maximum entropy production rate, which depth is also indentified as the maximum velocity depth and maximum heat transport depth. After that, we also give the trend of the variation of the intrinsic depth and the strength of the circulation changing with the external thermal forcing. We discover that mixing can both deepen and strengthen the overturning circulation.We don't measure the temperature field in our lab experiment, thus we use a vertical-plane model to set up a theoretical description for the thermocline pattern. After that, we make an inference for the real ocean situation. The experiment result at some degree illustrates that the surface differential heating may engender the ocean stratification and also the meridional overturning circulation. Wind stirring and turbulent mixing may deepen the thermocline and overturning circulation. Meanwhile, the pressure gradient companied with the thermal forcing may help drive the basin-scale gyre.In summary, lab experiment and theoretical model are combined in this paper to successfully explain some property of three-dimensional rotating horizontal convection. Petal shape phenomena are discovered and intrinsic depth is diagnosed as well as analyzed.