Study On The Structure Of Rayleigh-Benard Convection In A Rectangular Box

The research on nonlinear system is one of the subjects, which currently has attracted extensive attention from the research projects all over the world. That is nonlinear system is the most common phenomenon both the natural world and the engineering and technical fields,such as the phenomenon of bifurcation, chaos, fractal and strange attractor and so on, which has drawn increasing interest to the world. It is used in physics, biology, chemistry, meteorology, fluid dynamics (to solve the problem on turbulence), economics, ecology, as well as widely the application of engineering technology, and even has had a far-reaching impact on some social science research and development sector. At the same time, the further deepening of scientific practice promotes the theory of nonlinear dynamics developped in depth in turn.Rayleigh-Benard convection (RBC) is one of the typical models, which are used on open non-equilibrium system, and is one of the basic problems on hydraulics, fluid mechanics. Therefore, the use of RBC model system for studying the stability of convection movement, spatial and temporal structure, pattern formation and the characteristics on nonlinear dynamics has certain representation, very important practical significance and theoretical value.In the experiment, the device of Rayleigh-Benard convection is a closed cavity in the body, whose upper surface temperature is a constant, the surface heated at the bottom. Thus, the forming temperature difference results in the phenomena on fluid movement in the cavity. This experimental system is easy to control and the convection movement is clearly dominated by governing equation. An extremely rich dynamic phenomenon is revealed by the system.In this paper, the basic equations of fluid dynamics are simulated by using the software. Convection movement characteristics and the spatio-temporal structure can be summed up by changing the reduced Rayleigh number(r) and boundary conditions. In the two-dimensional case, RBC system is steady, whose convection track is of cyclical space. With increasing the reduced Rayleigh number, RBC system has two kinds of steady structure. When RBC coupled with lateral flow, the system turns into an unsteady flow. The structure of convection has not only cyclical space, but also cyclical time. Besides, when the critical convection existing, the correspondence between critical lateral flow and critical reduced Rayleigh number has discovered. And the state of local traveling wave(LTW) can be drawn at the same time. When the form of the lateral flow is also periodical, the convectional form of system and the period of the lateral flow are hand in hand. In the three-dimensional case, by the analysis on the pattern of convection along the different coordinate axis direction, it appears the relationship between the regular of convection pattern and the scale of the cell. With the lateral flow in 3D, the degree of nonlinear system increases, and the performance becomes a more complex structure.