Lattice Boltzmann Modeling For Mechanistic Models Of Wind-driven Ocean Circulation

Lattice Boltzmann method (LBM) is a newly developed computational fluid numerical method, which is originated from lattice gas cellular automata (LGCA) at the end of 1980's last centrury. LBM simulates the fluid movement at the microscopic particle level that is absolutely different from the conventional numerical methods. Single particle distribution satisfying classic Boltzmann equation is the is variable described by LBM. The so-called LB equation is a special discrete form of continuum Boltzmann equation in discrete particle velocity, discrete spatial and temporal spaces By use of the Chapman-Enskog multi-scale analysis technique and the conservations of physical variables, the LB equation can be recovered to the fluid dynamical equation at macroscopic level with the low Knudsen number and low Mach number assumptions. As a result of it, we can obtain the macroscopic fluid movement through calculating the particle distribution numerically.As an attempt to simulate ocean circulation by LBM, it is necessary to investigate the features of the LB models for the mechanistic models, which have relative simple forms but obvious physical senses. Based on LBM, several wind-driven ocean circulation mechanistic models, the quasi-geostrophic equivalent barotropic vorticity equation model, the single-layer shallow water model, the multi-layer shallow water model, are discussed here.A simple LB model is present to numerically solve the quasi-geostrophic barotropic equivalent vorticity equation at first. In this numerical scheme, the quasi-geostrophic barotropic equivalent vorticity equation is considered as a convetion-diffusion-reaction equation, which is easily treated by LBM. Under second-order accuracy, the quasi-geostrophic barotropic equivalent vorticity equationis recovered from the LB equation by Chapman-Enskog expansion. With contrast to the conventional numerical method (Byran, 1963), this LB model shows higher-order accuracy and better numerical stability. From the numerical results under different Reynolds numbers and different boundary conditions, the model shows basic structure and dissipation mechanism of wind-driven circulation. The transition from weak-nonlinearity solution, to strong-nonlineary, and then to inertial runaway is also found in the experiments. As the conventional methods, the multiple-equlibirum feature is also found in the double-gyre wind-driven circulation based on the LB model.On the other hand, we reconstruct the reduced gravity, shallow water LB model that is firstly present by Salmon (1999a). By including second-order integral approximation to collision operator, this new shallow water LB model has overall second-order accuracy with fully explicit feature even when the macroscopic-related external forces are introduced. Any implicit iterative technique that is massive computer time consuming is not needed. The numerical experiments are performed under different Reynolds numbers, different spatial resolutions and different boundary conditions, which include the non-slip, free-slip and partial-slip boundary conditions. The multiple equilibria solution feature and low-frequency oscillations are found in the numerical results with different model conditions. The periods of different circulation patterns are given by the results in different. The periods of the oscillations shows multiple time scale feature ranged from subannual to interannual. Through the analysis of the anomaly fields, it is found that the modes responsible for the oscillations change with not only the Reynolds number, but also the boundary condition.Based on the single layer shallow water LB model, a coupled LB model with overall second-order accuracy and fully explicit feature is present to simulate the wind-driven, reduced gravity, 2.5-layer shallow water system. The simple stratification in vertical direction is included in this new model. We put emphasis on the investigations of multiple-equilibrium feature and low-frequency variability of wind-driven circulation with stratification based on this model. Two attractors arefound in the results. It is obvious that one attractor is subtropical solution and the other is subpolar solution. Under some parameter set, the transition between these two attractors is also found and the anti-symmetric solution is seemly an intermediate state during the course of the transition. The time-dependent variability is analyzed by use of the singular spectral analysis and multi-channel singular spectral analysis. The oscillations with different periods that range from 9 months to about 4 years are found. The spatio-temporal structures of the statistical oscillation modes are obtained from the spectral analysis. The barotropic Rossby basin mode, barotropic gyre mode and batroclinic gyre mode are found to be responsible for the oscillations under different parameter sets.