In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizi...In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizing the Fourier splitting method, under suitable assumptions on the initial data, for any multi-index α, we show that the solution Ψ satisfies .展开更多
By using the conservation laws and the method of variational principle, an improved Arnol′d′s second nonlinear stability theorem for the two-dimensional multilayer quasi-geostrophic model in periodic channel is obta...By using the conservation laws and the method of variational principle, an improved Arnol′d′s second nonlinear stability theorem for the two-dimensional multilayer quasi-geostrophic model in periodic channel is obtained.展开更多
Based on the barotropic equations including large-scale topography, friction and heat factor, a barotropic quasi-geostrophic model with large-scale topography, friction and heating is obtained by means of scale analys...Based on the barotropic equations including large-scale topography, friction and heat factor, a barotropic quasi-geostrophic model with large-scale topography, friction and heating is obtained by means of scale analysis and small parameter method. It is shown that this equation is a basic one, which is used to study the influence of the Tibetan Plateau on the large-scale flow in the atmosphere. If the friction and heating effect of large-scale topography are neglected, this model will degenerate to the general barotropic quasi-geostrophic one.展开更多
Based on basic equations in isobaric coordinates and the quasi-geostrophic balance,an eddy-flux form budget equation of the divergent wind has been derived. This newly derived budget equation has evident physical sign...Based on basic equations in isobaric coordinates and the quasi-geostrophic balance,an eddy-flux form budget equation of the divergent wind has been derived. This newly derived budget equation has evident physical significance. It can show the intensity of a weather system,the variation of its flow pattern,and the feedback effects from smaller-scale systems(eddy flows). The usefulness of this new budget equation is examined by calculating budgets for the strong divergent-wind centers associated with the South Asian high,and the strong divergence centers over the Tibetan Plateau,during summer(June–August) 2010. The results indicate that the South Asian high significantly interacts with eddy flows. Compared with effects from the mean flow(background circulation),the eddy flows’ feedback influences are of greater importance in determining the flow pattern of the South Asian high. Although the positive divergence centers over the Tibetan Plateau intensify through different mechanisms,certain similarities are also obvious. First,the effects from mean flow are dominant in the rapid intensification process of the positive divergence center. Second,an intense offsetting mechanism exists between the effects associated with the eddy flows’ horizontal component and the effects related to the eddy flows’ convection activities,which weakens the total effects of the eddy flows significantly. Finally,compared with the effects associated with the convection activities of the mean flow,the accumulated effects of the eddy flows’ convection activities may be more favorable for the enhancement of the positive-divergence centers.展开更多
Nonlinear stability criteria for quasi-geostrophic zonally symmetric flow are improved by establishing an optimal Poincard inequality. The inequality is derived by a variational calculation considering the additional ...Nonlinear stability criteria for quasi-geostrophic zonally symmetric flow are improved by establishing an optimal Poincard inequality. The inequality is derived by a variational calculation considering the additional invariant of zonal momentum. When applied to the Eady model in a periodic channel with finite zonal length, the improved nonlinear stability criterion is identical to the linear normal-mode stability criterion provided the channel meridional width is no greater than 0.8605... times its channel length （which is the geophysically relevant case）.展开更多
Starting from a modified barotropic quasi-geostrophic model equation, considering the actual situation of the large-orography of the Tibetan Plateau, neglecting its slope in x direction, and using the reductive pertur...Starting from a modified barotropic quasi-geostrophic model equation, considering the actual situation of the large-orography of the Tibetan Plateau, neglecting its slope in x direction, and using the reductive perturbation method, then the solitary waves are obtained. The results show that the orography is essential factor exciting solitary Rossby waves in a flow without shear.展开更多
From the diabatic quasi-geostrophic equations of motion, the authors analyze the characteristics of diabatic Rossby waves including the thermal effects of the Tibetan Plateau. When the basic zonal flow is barotropic, ...From the diabatic quasi-geostrophic equations of motion, the authors analyze the characteristics of diabatic Rossby waves including the thermal effects of the Tibetan Plateau. When the basic zonal flow is barotropic, it is demonstrated that the cooling of the Tibetan Plateau in winter not only facilitates the meridional propagation of Rossby waves but is an important driving mechanism of the intraseasonal oscillations in middle and high latitudes. When the basic zonal flow is baroclinic, it is found that the cooling of the Tibetan Plateau in winter facilitates the instability of Rossby waves, while in summer there is a threshold for the influence of the heating of the Tibetan Plateau on the stability of Rossby waves.展开更多
A class of large scale geophysical fluid flows are modelled by the quasi-geostrophic equation. An averaging principle for quasi-geostrophic motion under rapidly oscil-lating ( non-autonomous) forcing was obtained, bot...A class of large scale geophysical fluid flows are modelled by the quasi-geostrophic equation. An averaging principle for quasi-geostrophic motion under rapidly oscil-lating ( non-autonomous) forcing was obtained, both on finite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and attractor convergence were also investigated.展开更多
We consider the n-dimensional modified quasi-geostrophic（SQG） equations δtθ ＋ u·△↓θ＋kΛ^αθ=0, u = Λ^α-1R^⊥θ with κ 〉 0, α∈（0, 1] and θ0∈ W^1,∞（R^n）. In this paper, we establish a differen...We consider the n-dimensional modified quasi-geostrophic（SQG） equations δtθ ＋ u·△↓θ＋kΛ^αθ=0, u = Λ^α-1R^⊥θ with κ 〉 0, α∈（0, 1] and θ0∈ W^1,∞（R^n）. In this paper, we establish a different proof for the global regularity of this system. The original proof was given by Constantin, Iyer, and Wu, who employed the approach of Besov space techniques to study the global existence and regularity of strong solutions to modified critical SQG equations for two dimensional case.The proof provided in this paper is based on the nonlinear maximum principle as well as the approach in Constantin and Vicol.展开更多
In this paper, we propose a numerical method based on semi-Lagrangian approach for solving quasi-geostrophic (QG) equations on a sphere. Using potential vorticity and stream-function as prognostic variables, two-...In this paper, we propose a numerical method based on semi-Lagrangian approach for solving quasi-geostrophic (QG) equations on a sphere. Using potential vorticity and stream-function as prognostic variables, two-order centered difference is suggested on the latitude-longitude grid. In our proposed numerical scheme, advection terms are expressed in a Lagrangian frame of reference to circumvent the CFL restriction. The pole singularity associated with the latitude-longitude grid is eliminated by a smoothing technique for the initial flow. Error analysis is provided for the numerical scheme.展开更多
A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic...A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic model and the continuously stratified baroclinic model. Since this system can simulate the baroclinic effect simply, it is widely used to study the large-scale dynamic process in atmosphere and ocean. The present paper is concerned with the linear stability of the multilayer quasi-geostrophic flow, and the associated linear stability criteria are established. Firstly, the nonlinear model is turned into the form of a Hamiltonian system, and a basic flow is defined. But it cannot be an extreme point of the Hamiltonian function since the system is an infinite-dimensional one. Therefore, it is necessary to reconstruct a new Hamiltonian function so that the basic flow becomes an extreme point of it. Secondly, the linearized equations of disturbances in the multilayer quasi-geostrophic flow are derived by introducing infinitesimal disturbances superposed on the basic flows. Finally, the properties of the linearized system are discussed, and the linear stability criteria in the sense of Liapunov are derived under two different conditions with respect to certain norms.展开更多
文摘In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizing the Fourier splitting method, under suitable assumptions on the initial data, for any multi-index α, we show that the solution Ψ satisfies .
文摘By using the conservation laws and the method of variational principle, an improved Arnol′d′s second nonlinear stability theorem for the two-dimensional multilayer quasi-geostrophic model in periodic channel is obtained.
基金RFDP and key national research project "Tibetan Plateau
文摘Based on the barotropic equations including large-scale topography, friction and heat factor, a barotropic quasi-geostrophic model with large-scale topography, friction and heating is obtained by means of scale analysis and small parameter method. It is shown that this equation is a basic one, which is used to study the influence of the Tibetan Plateau on the large-scale flow in the atmosphere. If the friction and heating effect of large-scale topography are neglected, this model will degenerate to the general barotropic quasi-geostrophic one.
基金supported by the National Natural Science Foundation of China (Grant Nos.91637211,41205027 and 41375053)the National Key Basic Research and Development Project of China (Grant No.2012CB417201)
文摘Based on basic equations in isobaric coordinates and the quasi-geostrophic balance,an eddy-flux form budget equation of the divergent wind has been derived. This newly derived budget equation has evident physical significance. It can show the intensity of a weather system,the variation of its flow pattern,and the feedback effects from smaller-scale systems(eddy flows). The usefulness of this new budget equation is examined by calculating budgets for the strong divergent-wind centers associated with the South Asian high,and the strong divergence centers over the Tibetan Plateau,during summer(June–August) 2010. The results indicate that the South Asian high significantly interacts with eddy flows. Compared with effects from the mean flow(background circulation),the eddy flows’ feedback influences are of greater importance in determining the flow pattern of the South Asian high. Although the positive divergence centers over the Tibetan Plateau intensify through different mechanisms,certain similarities are also obvious. First,the effects from mean flow are dominant in the rapid intensification process of the positive divergence center. Second,an intense offsetting mechanism exists between the effects associated with the eddy flows’ horizontal component and the effects related to the eddy flows’ convection activities,which weakens the total effects of the eddy flows significantly. Finally,compared with the effects associated with the convection activities of the mean flow,the accumulated effects of the eddy flows’ convection activities may be more favorable for the enhancement of the positive-divergence centers.
文摘Nonlinear stability criteria for quasi-geostrophic zonally symmetric flow are improved by establishing an optimal Poincard inequality. The inequality is derived by a variational calculation considering the additional invariant of zonal momentum. When applied to the Eady model in a periodic channel with finite zonal length, the improved nonlinear stability criterion is identical to the linear normal-mode stability criterion provided the channel meridional width is no greater than 0.8605... times its channel length （which is the geophysically relevant case）.
文摘Starting from a modified barotropic quasi-geostrophic model equation, considering the actual situation of the large-orography of the Tibetan Plateau, neglecting its slope in x direction, and using the reductive perturbation method, then the solitary waves are obtained. The results show that the orography is essential factor exciting solitary Rossby waves in a flow without shear.
文摘From the diabatic quasi-geostrophic equations of motion, the authors analyze the characteristics of diabatic Rossby waves including the thermal effects of the Tibetan Plateau. When the basic zonal flow is barotropic, it is demonstrated that the cooling of the Tibetan Plateau in winter not only facilitates the meridional propagation of Rossby waves but is an important driving mechanism of the intraseasonal oscillations in middle and high latitudes. When the basic zonal flow is baroclinic, it is found that the cooling of the Tibetan Plateau in winter facilitates the instability of Rossby waves, while in summer there is a threshold for the influence of the heating of the Tibetan Plateau on the stability of Rossby waves.
文摘A class of large scale geophysical fluid flows are modelled by the quasi-geostrophic equation. An averaging principle for quasi-geostrophic motion under rapidly oscil-lating ( non-autonomous) forcing was obtained, both on finite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and attractor convergence were also investigated.
基金supported by Project of Beijing Chang Cheng Xue Zhe(11228102)supported by NSF of China(11171229,11231006)
文摘We consider the n-dimensional modified quasi-geostrophic（SQG） equations δtθ ＋ u·△↓θ＋kΛ^αθ=0, u = Λ^α-1R^⊥θ with κ 〉 0, α∈（0, 1] and θ0∈ W^1,∞（R^n）. In this paper, we establish a different proof for the global regularity of this system. The original proof was given by Constantin, Iyer, and Wu, who employed the approach of Besov space techniques to study the global existence and regularity of strong solutions to modified critical SQG equations for two dimensional case.The proof provided in this paper is based on the nonlinear maximum principle as well as the approach in Constantin and Vicol.
文摘In this paper, we propose a numerical method based on semi-Lagrangian approach for solving quasi-geostrophic (QG) equations on a sphere. Using potential vorticity and stream-function as prognostic variables, two-order centered difference is suggested on the latitude-longitude grid. In our proposed numerical scheme, advection terms are expressed in a Lagrangian frame of reference to circumvent the CFL restriction. The pole singularity associated with the latitude-longitude grid is eliminated by a smoothing technique for the initial flow. Error analysis is provided for the numerical scheme.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.41575026,41275113,and 41475021)
文摘A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic model and the continuously stratified baroclinic model. Since this system can simulate the baroclinic effect simply, it is widely used to study the large-scale dynamic process in atmosphere and ocean. The present paper is concerned with the linear stability of the multilayer quasi-geostrophic flow, and the associated linear stability criteria are established. Firstly, the nonlinear model is turned into the form of a Hamiltonian system, and a basic flow is defined. But it cannot be an extreme point of the Hamiltonian function since the system is an infinite-dimensional one. Therefore, it is necessary to reconstruct a new Hamiltonian function so that the basic flow becomes an extreme point of it. Secondly, the linearized equations of disturbances in the multilayer quasi-geostrophic flow are derived by introducing infinitesimal disturbances superposed on the basic flows. Finally, the properties of the linearized system are discussed, and the linear stability criteria in the sense of Liapunov are derived under two different conditions with respect to certain norms.
