Natural convection in a two-dimensional horizontal annulus with an internally slotted circle is analyzed with lattice Boltzmann method (LBM). Flow instability is studied with nonlinear dynamic analysis techniques such as phase diagram and power spectrum. It shows that, with the increase of Rayleigh number Ra, the flow field changes from the beginning of a stable equilibrium point to a limit cycle after Hopf bifurcation. And the flow field may exhibit a change from steady-state to periodic oscillation. As the Rayleigh number is further increased, the stable limit cycle change to a two-dimensional torus. As the Rayleigh number Ra is greater than a critical value, chaotic state appears, and the system has a very complicated trajectory structure in the phase space. In general, the nonlinear dynamic characteristics and expressions at different Rayleigh numbers in the system show that the system evolves to chaos through Ruelle-Takens road. It shows evolution from a stable natural convection to chaotic motion with nonlinear characteristics.

A mathematical model was developed to simulate the terrain effect on meterology parameter when cold-air flow passing over a mountain terrain. The solar short-wave radiation, ground and atmolphere long-wave radiation, soil heat flux, the diffusion and transport of water vapor, heat and momentum fluxes in the atmosphere' and the Coriolis parameter change with latitude were considered in the model. The resonable phenomena were obtaioned, such as, wind field change, temperature decrease, the abrupt increase of flux and pressure increase etc. The model provides a method and basis for weather forcast and the reseaech of mesoscale processes over complex terrain.