【摘要】 建立了求解准地转相当正压涡度方程的格子Boltzmann(LB)模型.该模型将准地转相当正压涡度方程作为一个平流-扩散-反应方程来加以处理,在整体二阶精度下,通过Chapman_Enskog多尺度分析法,可将格子Boltzmann方程还原到相当正压涡度方程.在不同Reynolds数、不同边界条件以及不同风应力驱动下的数值解表明,该模型正确反映了风生环流的基本结构和不同边界的耗散特征,并得到风生环流的多平衡态解等非线性特征.此外,不同Rossby变形半径下的实验证明,小Rossby变形半径更容易激发环流的非线性模态.通过与同等类型有限差方案的比较,表明本文的LB模型具有稳定性好、精度高等优点.更多还原

【Abstract】 A lattice Boltzmann(LB) model is created to solve the quasi-geostrophic equivalent barotropic vorticity equation numerically. In this numerical scheme,the quasi-geostrophic barotropic equivalent vorticity equation is considered as a convection-diffusion-reaction equation.Under overall second-order accuracy,the quasi-geostrophic barotropic equivalent vorticity equation is recovered from the LB equation by Chapman-Enskog asymptotic technique.From the numerical results under different Reynolds numbers,different boundary conditions and different types of wind-stress,the LB model shows correct basic structure and dissipation features of the wind-driven ocean circulation.The nonlinear feature,such as multiple-equilibrium solutions,is also obtained by this LB model. It is also found that the nonlinear mode is more obvious under relatively small Rossby deformation radius.With contrast to the result of the equal finite difference model,this LB model shows higher-order accuracy and better numerical stability.更多还原