A lattice Boltzmann model for the study of advection-diffusion-reaction(ADR)problems is proposed.Via multiscale expansion analysis,we derive from the LB model the resulting macroscopic equations.It is shown that a lin...A lattice Boltzmann model for the study of advection-diffusion-reaction(ADR)problems is proposed.Via multiscale expansion analysis,we derive from the LB model the resulting macroscopic equations.It is shown that a linear equilibrium distribution is sufficient to produce ADR equations within error terms of the order of the Mach number squared.Furthermore,we study spatially varying structures arising from the interaction of advective transport with a cubic autocatalytic reaction-diffusion process under an imposed uniform flow.While advecting all the present species leads to trivial translation of the Turing patterns,differential advection leads to flow induced instability characterized with traveling stripes with a velocity dependent wave vector parallel to the flow direction.Predictions from a linear stability analysis of the model equations are found to be in line with these observations.展开更多
Based on their differences in physical characteristics and time-space scales,the ocean motions have been divided into four types in the present paper：turbulence,wave-like motion,eddy-like motion and circulation.Apply...Based on their differences in physical characteristics and time-space scales,the ocean motions have been divided into four types in the present paper：turbulence,wave-like motion,eddy-like motion and circulation.Applying the three-fold Reynolds averages to the governing equations with Boussinesq approximation,with the averages defined on the former three sub-systems,we derive the governing equation sets of the four sub-systems and refer to their sum as ＂the ocean dynamic system＂.In these equation sets,the interactions among different motions appear in two forms：the first one includes advection transport and shear instability generation of larger scale motions,and the second one is the mixing induced by smaller scale motions in the form of transport flux residue.The governing equation sets are the basis of analytical/numerical descriptions of various ocean processes.展开更多
基金supported by the Max-Planck-Institut fur Eisenforschungby the Interdisciplinary Centre for Advanced Material Simulation(ICAMS),Ruhr Universitat Bochum.
文摘A lattice Boltzmann model for the study of advection-diffusion-reaction(ADR)problems is proposed.Via multiscale expansion analysis,we derive from the LB model the resulting macroscopic equations.It is shown that a linear equilibrium distribution is sufficient to produce ADR equations within error terms of the order of the Mach number squared.Furthermore,we study spatially varying structures arising from the interaction of advective transport with a cubic autocatalytic reaction-diffusion process under an imposed uniform flow.While advecting all the present species leads to trivial translation of the Turing patterns,differential advection leads to flow induced instability characterized with traveling stripes with a velocity dependent wave vector parallel to the flow direction.Predictions from a linear stability analysis of the model equations are found to be in line with these observations.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.40776020,41106032)the National Basic Research Program of China (973 Program,Grant Nos.G1999043800,2006CB403600,2010CB950404 and 2010CB950300)
文摘Based on their differences in physical characteristics and time-space scales,the ocean motions have been divided into four types in the present paper：turbulence,wave-like motion,eddy-like motion and circulation.Applying the three-fold Reynolds averages to the governing equations with Boussinesq approximation,with the averages defined on the former three sub-systems,we derive the governing equation sets of the four sub-systems and refer to their sum as ＂the ocean dynamic system＂.In these equation sets,the interactions among different motions appear in two forms：the first one includes advection transport and shear instability generation of larger scale motions,and the second one is the mixing induced by smaller scale motions in the form of transport flux residue.The governing equation sets are the basis of analytical/numerical descriptions of various ocean processes.
