In this paper, a climate dynamics model with the effects of topography and a non-constant external force, which consists of the Navier-Stokes equations and a temperature equation arising from the evolution process of ...In this paper, a climate dynamics model with the effects of topography and a non-constant external force, which consists of the Navier-Stokes equations and a temperature equation arising from the evolution process of the atmosphere, was considered.Under certain assumptions imposed on the initial data and by using some delicate estimates and compactness arguments, we proved the L^1-stability of weak solutions to the atmospheric equations.展开更多
This study looks at the mathematical model of internal atmospheric waves,often known as gravity waves,occurring inside a fluid rather than on the surface.Under the shallow-fluid assumption,internal atmospheric waves m...This study looks at the mathematical model of internal atmospheric waves,often known as gravity waves,occurring inside a fluid rather than on the surface.Under the shallow-fluid assumption,internal atmospheric waves may be described by a nonlinear partial differential equation system.The shallow flow model’s primary concept is that the waves are spread out across a large horizontal area before rising vertically.The Fractional Reduced Differential Transform Method(FRDTM)is applied to provide approximate solutions for any given model.This aids in the modelling of the global atmosphere,which has applications in weather and climate forecasting.For the integer-order value(α=1),the FRDTM solution is compared to the precise solution,EADM,and HAM to assess the correctness and efficacy of the proposed technique.展开更多
From the controlling equations of atmosphere motion, Prandtl's mixing length theory is used to derive the atmospheric turbulence models, such as Burgers equation model and Burgers-KdV equation model. And then the ...From the controlling equations of atmosphere motion, Prandtl's mixing length theory is used to derive the atmospheric turbulence models, such as Burgers equation model and Burgers-KdV equation model. And then the projective Riccati equations are applied to solve these atmospheric turbulence models, where much more patterns are obtained, including solitary wave pattern, singular pattern, and so on.展开更多
This paper reviews the three-pattern decomposition of global atmospheric circulation(3P-DGAC)developed in recent years,including the decomposition model and the dynamical equations of global horizontal,meridional,and ...This paper reviews the three-pattern decomposition of global atmospheric circulation(3P-DGAC)developed in recent years,including the decomposition model and the dynamical equations of global horizontal,meridional,and zonal circulations.Compared with the traditional two-dimensional(2D)circulation decomposition method,the 3P-DGAC can effectively decompose the actual vertical vorticity into two components that are caused by the horizontal circulation and convergent/divergent movement(associated with the meridional and zonal circulations).It also decomposes the vertical velocity into the components of the meridional vertical circulation and the zonal vertical circulation,thus providing a new method to study the dynamical influences of convergent/divergent motions on the evolution of actual vertical vorticity and an accurate description of local vertical circulations.The 3P-DGAC is a three-dimensional(3D)circulation decomposition method based on the main characteristics of the actual atmospheric movements.The horizontal,meridional,and zonal circulations after the 3P-DGAC are the global generalization of Rossby waves in the middle-high latitudes and Hadley and Walker circulations in low latitudes.Therefore,the three-pattern decomposition model and its dynamical equations provide novel theoretical tools for studying complex interactions between middle-high and low latitude circulations as well as the physical mechanisms of the abnormal evolution of large-scale atmospheric circulations under the background of global warming.展开更多
In this paper, an attempt is made to study some interesting results of the coupled nonlinear equations in the atmosphere. By introducing a phase angle function ζ, it is shown that the atmospheric equations in the pr... In this paper, an attempt is made to study some interesting results of the coupled nonlinear equations in the atmosphere. By introducing a phase angle function ζ, it is shown that the atmospheric equations in the presence of specific forcing exhibit the exact and explicit solitary wave solutions under certain conditions.展开更多
This article involves the study of atmospheric internal waves phenomenon,also referred to as gravity waves.This phenomenon occurs inside the fluid,not on the surface.The model is based on a shallow fluid hypothesis re...This article involves the study of atmospheric internal waves phenomenon,also referred to as gravity waves.This phenomenon occurs inside the fluid,not on the surface.The model is based on a shallow fluid hypothesis represented by a system of nonlinear partial differential equations.The basic assumption of the shallow flow model is that the horizontal size is much larger than the vertical size.Atmospheric internal waves can be perfectly represented by this model as the waves are spread over a large horizontal area.Here we used the Elzaki Adomian Decomposition Method(EADM)to obtain the solution for the considered model along with its convergence analysis.The Adomian decomposition method together with the Elzaki transform gives the solution in a convergent series without any linearization or perturbation.Comparisons are built between the results obtained by EADM and HAM to examine the accuracy of the proposed method.展开更多
The kinetic energy variations of mean flow and turbulence at three levels in the surface layer were calculated by using eddy covariance data from observations at Jinta oasis in 2005 summer. It is found that when the m...The kinetic energy variations of mean flow and turbulence at three levels in the surface layer were calculated by using eddy covariance data from observations at Jinta oasis in 2005 summer. It is found that when the mean horizontal flow was stronger, the turbulent kinetic energy was increased at all levels, as well as the downward mean wind at the middle level. Since the mean vertical flow on the top and bottom were both negligible at that time, there was a secondary circulation with convergence in the upper half and divergence in the lower half of the column. After consideration of energy conversion, it was found that the interaction between turbulence and the secondary circulation caused the intensification of each other. The interaction reflected positive feedback between turbulence and the vertical shear of the mean flow. Turbulent sensible and latent heat flux anomaly were also analyzed. The results show that in both daytime and at night, when the surface layer turbulence was intensified as a result of strengthened mean flow, the sensible heat flux was decreased while the latent heat flux was increased. Both anomalous fluxes contributed to the cold island effect and the moisture island effect of the oasis.展开更多
This paper establishes the kinetic equations in atmospheric chemistry that describe the macroscopic mechanisms of secondary fine particle pollution generated by precursors during atmospheric self-purification.The dyna...This paper establishes the kinetic equations in atmospheric chemistry that describe the macroscopic mechanisms of secondary fine particle pollution generated by precursors during atmospheric self-purification.The dynamic and static solutions of these equations can be applied to calculate quantitative relationships between the concentration ratio of precursors and secondary fine particles as well as the physical clearance power of the atmosphere,chemical reaction rate,and the scale of a contaminated area.The dynamic solution presented here therefore corresponds with a theoretical formula for calculating the overall rate constant for the oxidation reaction of reducing pollutants in the actual atmosphere based on their local concentrations and meteorological monitoring data.In addition,the static solution presented in this paper reveals the functional relationship between the concentration of secondary fine particles and precursor emission rate as well as atmospheric self-purification capacity.This result can be applied to determine the atmospheric environmental capacity of a precursor.Hourly records collected over the last 40 years from 378 weather stations in China's Mainland as well as the spatiotemporal distribution sequence of overall oxidation reaction rates from precursors show that when the reference concentration limit of secondary fine particles is100μmol m-3,the atmospheric environmental capacity of total precursors canbe calculated as 24890×1010 mol yr-1.Thus,when the annual average concentration limit of given fine particles is 35μg m-3 and the ratio of sulfate and nitrate to 30%and 20%of the total amount of fine particles,the capacities of SO2,NOx and NH3 are 1255,1344,and 832(1010g yr-1),respectively.The clearance density of precursors for different return periods across China's Mainland under above conditions are also provided in this study.展开更多
The long-term behavior of the atmospheric evolution, which cannot be answered and solvedby the numerical experiments, must be undrstood before we design the numerical forecastmodels of the long-range weather and clima...The long-term behavior of the atmospheric evolution, which cannot be answered and solvedby the numerical experiments, must be undrstood before we design the numerical forecastmodels of the long-range weather and climate. It is necessary to carry out some studiesof basic theory. Based on the stationary external forcings, Chou studied the adjustment of the nonlinear atmospheric system tending to forcings in R^n. Then these resultswere extended to the infinite dimensional Hilbert space. For the real atmospheric system,展开更多
The topological characteristics for the basic system of equations of atmospheric motion were analyzed with the help of method provided by stratification theory. It was proved that in the local rectangular coordinate s...The topological characteristics for the basic system of equations of atmospheric motion were analyzed with the help of method provided by stratification theory. It was proved that in the local rectangular coordinate system the basic system of equations of atmospheric motion is stable in infinitely differentiable function class. In the sense of local solution, the necessary and sufficient conditions by which the typical problem for determining solution is well posed were also given. Such problems as something about "speculating future from past" in atmospheric dynamics and how to amend the conditions for determining solution as well as the choice of underlying surface when involving the practical application were further discussed. It is also pointed out that under the usual conditions, three motion equations and continuity equation in the basic system of equations determine entirely the property of this system of equations.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 41630530, 41575109 & 91230202)
文摘In this paper, a climate dynamics model with the effects of topography and a non-constant external force, which consists of the Navier-Stokes equations and a temperature equation arising from the evolution process of the atmosphere, was considered.Under certain assumptions imposed on the initial data and by using some delicate estimates and compactness arguments, we proved the L^1-stability of weak solutions to the atmospheric equations.
文摘This study looks at the mathematical model of internal atmospheric waves,often known as gravity waves,occurring inside a fluid rather than on the surface.Under the shallow-fluid assumption,internal atmospheric waves may be described by a nonlinear partial differential equation system.The shallow flow model’s primary concept is that the waves are spread out across a large horizontal area before rising vertically.The Fractional Reduced Differential Transform Method(FRDTM)is applied to provide approximate solutions for any given model.This aids in the modelling of the global atmosphere,which has applications in weather and climate forecasting.For the integer-order value(α=1),the FRDTM solution is compared to the precise solution,EADM,and HAM to assess the correctness and efficacy of the proposed technique.
文摘From the controlling equations of atmosphere motion, Prandtl's mixing length theory is used to derive the atmospheric turbulence models, such as Burgers equation model and Burgers-KdV equation model. And then the projective Riccati equations are applied to solve these atmospheric turbulence models, where much more patterns are obtained, including solitary wave pattern, singular pattern, and so on.
基金supported by the National Key R&D Program of China(Grant No.2017YFC1502305)the National Natural Science Foundation of China(Grant Nos.41775069&41975076)。
文摘This paper reviews the three-pattern decomposition of global atmospheric circulation(3P-DGAC)developed in recent years,including the decomposition model and the dynamical equations of global horizontal,meridional,and zonal circulations.Compared with the traditional two-dimensional(2D)circulation decomposition method,the 3P-DGAC can effectively decompose the actual vertical vorticity into two components that are caused by the horizontal circulation and convergent/divergent movement(associated with the meridional and zonal circulations).It also decomposes the vertical velocity into the components of the meridional vertical circulation and the zonal vertical circulation,thus providing a new method to study the dynamical influences of convergent/divergent motions on the evolution of actual vertical vorticity and an accurate description of local vertical circulations.The 3P-DGAC is a three-dimensional(3D)circulation decomposition method based on the main characteristics of the actual atmospheric movements.The horizontal,meridional,and zonal circulations after the 3P-DGAC are the global generalization of Rossby waves in the middle-high latitudes and Hadley and Walker circulations in low latitudes.Therefore,the three-pattern decomposition model and its dynamical equations provide novel theoretical tools for studying complex interactions between middle-high and low latitude circulations as well as the physical mechanisms of the abnormal evolution of large-scale atmospheric circulations under the background of global warming.
文摘 In this paper, an attempt is made to study some interesting results of the coupled nonlinear equations in the atmosphere. By introducing a phase angle function ζ, it is shown that the atmospheric equations in the presence of specific forcing exhibit the exact and explicit solitary wave solutions under certain conditions.
文摘This article involves the study of atmospheric internal waves phenomenon,also referred to as gravity waves.This phenomenon occurs inside the fluid,not on the surface.The model is based on a shallow fluid hypothesis represented by a system of nonlinear partial differential equations.The basic assumption of the shallow flow model is that the horizontal size is much larger than the vertical size.Atmospheric internal waves can be perfectly represented by this model as the waves are spread over a large horizontal area.Here we used the Elzaki Adomian Decomposition Method(EADM)to obtain the solution for the considered model along with its convergence analysis.The Adomian decomposition method together with the Elzaki transform gives the solution in a convergent series without any linearization or perturbation.Comparisons are built between the results obtained by EADM and HAM to examine the accuracy of the proposed method.
基金supported by the State Key Program of National Natural Science of China(Grant Nos.40233035 and 40633014)funded by one of National Basic Research Program of China(Grant No.2009CB421402)
文摘The kinetic energy variations of mean flow and turbulence at three levels in the surface layer were calculated by using eddy covariance data from observations at Jinta oasis in 2005 summer. It is found that when the mean horizontal flow was stronger, the turbulent kinetic energy was increased at all levels, as well as the downward mean wind at the middle level. Since the mean vertical flow on the top and bottom were both negligible at that time, there was a secondary circulation with convergence in the upper half and divergence in the lower half of the column. After consideration of energy conversion, it was found that the interaction between turbulence and the secondary circulation caused the intensification of each other. The interaction reflected positive feedback between turbulence and the vertical shear of the mean flow. Turbulent sensible and latent heat flux anomaly were also analyzed. The results show that in both daytime and at night, when the surface layer turbulence was intensified as a result of strengthened mean flow, the sensible heat flux was decreased while the latent heat flux was increased. Both anomalous fluxes contributed to the cold island effect and the moisture island effect of the oasis.
基金supported by S & T Development Program (Grant No. CAMS 2018KJ026)
文摘This paper establishes the kinetic equations in atmospheric chemistry that describe the macroscopic mechanisms of secondary fine particle pollution generated by precursors during atmospheric self-purification.The dynamic and static solutions of these equations can be applied to calculate quantitative relationships between the concentration ratio of precursors and secondary fine particles as well as the physical clearance power of the atmosphere,chemical reaction rate,and the scale of a contaminated area.The dynamic solution presented here therefore corresponds with a theoretical formula for calculating the overall rate constant for the oxidation reaction of reducing pollutants in the actual atmosphere based on their local concentrations and meteorological monitoring data.In addition,the static solution presented in this paper reveals the functional relationship between the concentration of secondary fine particles and precursor emission rate as well as atmospheric self-purification capacity.This result can be applied to determine the atmospheric environmental capacity of a precursor.Hourly records collected over the last 40 years from 378 weather stations in China's Mainland as well as the spatiotemporal distribution sequence of overall oxidation reaction rates from precursors show that when the reference concentration limit of secondary fine particles is100μmol m-3,the atmospheric environmental capacity of total precursors canbe calculated as 24890×1010 mol yr-1.Thus,when the annual average concentration limit of given fine particles is 35μg m-3 and the ratio of sulfate and nitrate to 30%and 20%of the total amount of fine particles,the capacities of SO2,NOx and NH3 are 1255,1344,and 832(1010g yr-1),respectively.The clearance density of precursors for different return periods across China's Mainland under above conditions are also provided in this study.
基金State Key Research Project on Dynamics and Predictive Theory of the Climate and the Doctor's Foundation of State Education Committee.
文摘The long-term behavior of the atmospheric evolution, which cannot be answered and solvedby the numerical experiments, must be undrstood before we design the numerical forecastmodels of the long-range weather and climate. It is necessary to carry out some studiesof basic theory. Based on the stationary external forcings, Chou studied the adjustment of the nonlinear atmospheric system tending to forcings in R^n. Then these resultswere extended to the infinite dimensional Hilbert space. For the real atmospheric system,
基金Project supported by the National Natural Science Foundation of China(Nos.40175014,90411006)
文摘The topological characteristics for the basic system of equations of atmospheric motion were analyzed with the help of method provided by stratification theory. It was proved that in the local rectangular coordinate system the basic system of equations of atmospheric motion is stable in infinitely differentiable function class. In the sense of local solution, the necessary and sufficient conditions by which the typical problem for determining solution is well posed were also given. Such problems as something about "speculating future from past" in atmospheric dynamics and how to amend the conditions for determining solution as well as the choice of underlying surface when involving the practical application were further discussed. It is also pointed out that under the usual conditions, three motion equations and continuity equation in the basic system of equations determine entirely the property of this system of equations.