A numerical model of mixing and convection driven by surface buoyancy flux

Abstract

This thesis studies mixing and convection in a rectangular basin driven by a specified heat flux at the surface. A numerical model is constructed for this purpose. The main focus of the study is on the density and circulation structure resulting from the thermal forcing. In chapter two, a simple vertical one-dimensional model is developed to examine the mixing processes under a given surface heat flux. In order to simulate strong vertical mixing in the region where stratification is unstable, turbulent processes are modeled by a convective overturning parameterization of eddy viscosity and diffusivity. The results show that the density structure is strongly affected by the convective overturning adjustment as surface cooling prevails, and the resulting density field is nearly depth independent. In chapter three, a more complicated two-dimensional model is constructed to simulate mixing and circulation in a vertical rectangular basin with rigid boundaries. The aspect ratio of the basin ranges from 1 to 0.001 and Rayleigh number from 104 to 2 x 1012. It is found that the circulation pattern is dominated by these two important numbers. The roles of density overturning and density-momentum overturning mixing are further investigated. The results show that the convective overturning not only homogenizes the density field in the unstably stratified region but also contributes to increase the circulation. A crude scale analysis of the system shows that the characteristics of the density and momentum fields from the analysis agree well with the numerical results.