A heavy rainfall event that occurred over the middle and lower reaches of the Yangtze River Basin （YRB） during July 11-13 2000 is explored in this study. The potential/stream function is used to analyze the upstream...A heavy rainfall event that occurred over the middle and lower reaches of the Yangtze River Basin （YRB） during July 11-13 2000 is explored in this study. The potential/stream function is used to analyze the upstream ＂strong signals＂ of the water vapor transport in the Tibetan Plateau （TP）. The studied time period covers from 2000 LST 5 July to 2000 LST 15 July （temporal resolution： 6 hours）. By analyzing the three-dimensional structure of the water vapor flux, vorticity and divergence prior to and during the heavy rainfall event, the upstream ＂strong signals＂ related to this heavy rainfall event are revealed. A strong correlation exists between the heavy rainfall event in the YRB and the convective clouds over the TE The ＂convergence zone＂ of the water vapor transport is also identified, based on correlation analysis of the water vapor flux two days and one day prior to, and on the day of, the heavy rainfall. And this ＂convergence zone＂ coincides with the migration of the maximum rainfall over the YRB. This specific coupled structure actually plays a key role in generating heavy rainfall over the YRB. The eastward movement of the coupled system with a divergence]convergence center of the potential function at the upper/lower level resembles the spatiotemporal evolution of the heavy rainfall event over the YRB. These upstream ＂strong signals＂ are clearly traced in this study through analyzing the three-dimensional structure of the potential/stream function of upstream water vapor transport.展开更多
In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinea...In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems （with same stiffness matrix but different right-hand side） on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.展开更多
Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid...Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid.Moreover,the scaling between these two grid sizes is super-linear.Approximation,stability and convergence aspects of a fully discrete scheme are analyzed.At last a numrical example is given whose results show that the algorithm proposed in this paper is effcient.展开更多
The stream function and the velocity potential can be easily computed by solving the Poisson equations in a unique way for the global domain. Because of the var- ious assumptions for handling the boundary conditions, ...The stream function and the velocity potential can be easily computed by solving the Poisson equations in a unique way for the global domain. Because of the var- ious assumptions for handling the boundary conditions, the solution is not unique when a limited domain is concerned. Therefore, it is very important to reduce or eliminate the effects caused by the uncertain boundary condition. In this paper, an iterative and ad- justing method based on the Endlich iteration method is presented to compute the stream function and the velocity potential in limited domains. This method does not need an explicitly specifying boundary condition when used to obtain the effective solution, and it is proved to be successful in decomposing and reconstructing the horizontal wind field with very small errors. The convergence of the method depends on the relative value for the distances of grids in two different directions and the value of the adjusting factor. It is shown that applying the method in Arakawa grids and irregular domains can obtain the accurate vorticity and divergence and accurately decompose and reconstruct the original wind field. Hence, the iterative and adjusting method is accurate and reliable.展开更多
Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level met...Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.展开更多
Based on the linear wave, solitary wave and fifth order stokes wave derived by use of the Unified Variational Principle of Water Gravity Wave (UVPWGW), this paper derives stream function wave theory by using UVPWGW. T...Based on the linear wave, solitary wave and fifth order stokes wave derived by use of the Unified Variational Principle of Water Gravity Wave (UVPWGW), this paper derives stream function wave theory by using UVPWGW. This paper will handle the Kinematic Free Surface Boundary Condition (KFSBC) and Dynamic Free Surface Boundary Condition (DFSBC) directly and give the optimum solution, instead of the conditions Sigma(Q(av) - Q(i))(2) = min, and the related equations of stational condition. When the wave height H, period T and water depth D are given, the original stream function wave will be determined, and can not be adjusted if it does not agree with the real case; in the present method, the adjustment can be done by adding several constraint conditions, for example, the wave profile can be adjusted according to the condition of accurate peak position. The examples given in this paper show that for the original stream function wave, the DFSBC can be fairly well satisfied, but the KFSBC can not; however, the stream function wave derived by UVPWGW is better than the original one in the sense of minimum error squares in the aspect of the level at which KFSBC and DFSBC are satisfied.展开更多
A 2-dimensional global free surface diagnostic model, combined with dynamic calculation, is used to investigate the world ocean circulation; the model has a horizontal resolution of 1/4°×1/4°. The simul...A 2-dimensional global free surface diagnostic model, combined with dynamic calculation, is used to investigate the world ocean circulation; the model has a horizontal resolution of 1/4°×1/4°. The simulated results agree well with the results of other modesl and observations. The distribution of Stream Function suggests that the main circulation systems in the wodd ocean have been represented, including oceanic currents strengthened in the oceanic western. Be close to the observed results, the net mass transport of the Kuroshio axes is estimated about 54Sv; The distribution of the horizontal circulation in each layer shows that the main circulation systems in the world ocean are well simulated, for example, the Kuroshio and the Antarctic Circumpolar Current can go down to the bottom layer, but the Gulf Stream cannot, and its direction reverses at the depths of 1000 to 2 000 m.展开更多
Two basic hypothesises of Taylor-Galerkin Finite Element Method are studied in this paper. One of them which is unreasonable is redefined. The only hypothesis becomes the standpoint of Generalized Finite Element. We u...Two basic hypothesises of Taylor-Galerkin Finite Element Method are studied in this paper. One of them which is unreasonable is redefined. The only hypothesis becomes the standpoint of Generalized Finite Element. We use this idea to analysis stream function-vorticity equations with Modified Taylor-Galerkin Finite Element Method, and give the two-step solving method, which makes the solving process more reasonable than ever before. Several computational examples reveal that the results of this new method are satisfied.展开更多
This study compares the climatology and long-term trend of northern winter stratospheric residual mean meridional circulation(RMMC), as well as its responses to El Ni?o-Southern Oscillation(ENSO), stratospheric Quasi ...This study compares the climatology and long-term trend of northern winter stratospheric residual mean meridional circulation(RMMC), as well as its responses to El Ni?o-Southern Oscillation(ENSO), stratospheric Quasi Biennial Oscillation(QBO), and solar cycle in ten reanalyses and a stratosphere-resolving model, CESM1-WACCM. The RMMC is a large-scale meridional circulation cell in the stratosphere, usually referred to as the estimate of the Brewer Dobson circulation(BDC). The distribution of the BDC is generally consistent among multiple reanalyses except that the NOAA twentieth century reanalysis(20RC) largely underestimates it. Most reanalyses(except ERA40 and ERA-Interim) show a strengthening trend for the BDC during 1979–2010. All reanalyses and CESM1-WACCM consistently reveal that the deep branch of the BDC is significantly enhanced in El Ni?o winters as more waves from the troposphere dissipate in the stratospheric polar vortex region. A secondary circulation cell is coupled to the temperature anomalies below the QBO easterly center at 50 hPa with tropical upwelling/cooling and midlatitude downwelling/warming, and similar secondary circulation cells also appear between 50–10 hPa and above 10 hPa to balance the temperature anomalies. The direct BDC response to QBO in the upper stratosphere creates a barrier near 30°N to prevent waves from propagating to midlatitudes, contributing to the weakening of the polar vortex. The shallow branch of the BDC in the lower stratosphere is intensified during solar minima, and the downwelling warms the Arctic lower stratosphere. The stratospheric responses to QBO and solar cycle in most reanalyses are generally consistent except in the two 20 CRs.展开更多
The seasonal and interannual variability of zonal mean Hadley circulation are analyzed, and the important effects of sea surface temperature(SST), especially the tropical Pacific SST, on the meridional circulation are...The seasonal and interannual variability of zonal mean Hadley circulation are analyzed, and the important effects of sea surface temperature(SST), especially the tropical Pacific SST, on the meridional circulation are discussed. Following results are obtained: 1) the Hadley circulation presents a single clockwise(anticlockwise) cross-equator circulation in the Northern(Southern) Hemisphere winter,while it is a double-ring-shaped circulation quasi-symmetric about the equator in spring and autumn. The annual mean state just indicates the residual of the Hadley cell in winter and summer. 2) The first mode of interannual anomalies shows a single cell crossing the equator like the climatology in winter and summer but with narrower width. The second mode shows a double ring-shaped cell quasi-symmetric about the equator which is similar to the Hadley cell in spring or autumn. 3) Vertical motion of the Hadley circulation is driven by sea surface temperature(SST) through latent and sensible heat in the tropics, and the interannual anomalies are mainly driven by the SST anomaly(SSTa) in the tropical Pacific. 4) The meridional gradient of SSTa is well consistent with the lower meridional wind of Hadley circulation in the interannual part. For the spatial distribution, the meridional gradient of SSTa in the Pacific plays a major role for the first two modes while the effects of the Indian Ocean and the Atlantic Ocean can be ignored.展开更多
Taking the distributing calculation of velocity and concentration as an example, the paper established a series of governing equations by the vorticity stream function method, and dispersed the equations by the finit...Taking the distributing calculation of velocity and concentration as an example, the paper established a series of governing equations by the vorticity stream function method, and dispersed the equations by the finite differencing method. After figuring out the distribution field of velocity, the paper also calculated the concentration distribution in sedimentation tank by using the two dimensional concentration transport equation. The validity and feasibility of the numerical method was verified through comparing with experimental data. Furthermore, the paper carried out a tentative exploration into the application of numerical simulation of sedimentation tanks.展开更多
This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center...This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center of the spherical container is studied. Stream function solutions for the flow fields are obtained in terms of modified Bessel functions and Gegenbauer functions. The pressure fields, the micro-rotation components, the drag experienced by a permeable sphere, the wall correction factor, and the flow rate through the permeable surface are obtained for the frictionless impermeable spherical container and the zero shear stress at the impermeable spherical container. Variations of the drag force and the wall correction factor with respect to different fluid parameters are studied. It is observed that the drag force, the wall correction factor, and the flow rate are greater for the frictionless impermeable spherical container than the zero shear stress at the impermeable spherical container. Several cases of interest are deduced from the present analysis.展开更多
For some special flows, especially the potential flow in a plane, using the hodograph method has obvious advantages. Realistic flows have a stream surface, namely, a two-dimensional manifold, on which the velocity vec...For some special flows, especially the potential flow in a plane, using the hodograph method has obvious advantages. Realistic flows have a stream surface, namely, a two-dimensional manifold, on which the velocity vector of the flow lies on its tangent space. By introducing a stream function and a potential function, we establish the hodo- graph method for potential flows on a surface using the tensor analysis. For the derived hodograph equation, we obtain a characteristic equation and its characteristic roots, from which we can classify the type of the second-order hodograph equation. Moreover, we give some examples for special surfaces.展开更多
Some new results of the modeling of mean free surface of waves or wave set-up are presented. The stream function wave theory is applied to incident short waves. The limiting wave steepness is adopted as the wave break...Some new results of the modeling of mean free surface of waves or wave set-up are presented. The stream function wave theory is applied to incident short waves. The limiting wave steepness is adopted as the wave breaker index in the calculation of wave breaking dissipation. The model is based on Roelvink (1993), but the numerical techniques used in the solution are based on the Weighted-Average Flux (WAF) method (Watson et al., 1992), with Time-Operator-Splitting (TOS) used for the treatment of the source terms. This method allows a small number of computational points to be used, and is particularly efficient in modeling wave set-up. The short wave (or incident primary wave) energy equation is solved by use of a traditional Lax-Wendroff technique. The present model is found to be satisfactory compared with the measurements conducted by Stive (1983).展开更多
This paper gives the detailed mathematical expression of the flow in the spherical coordinates system. Applying the law of conservation of mass, movement theorem of steady flow, and applying the mathematical method of...This paper gives the detailed mathematical expression of the flow in the spherical coordinates system. Applying the law of conservation of mass, movement theorem of steady flow, and applying the mathematical method of stream function with consideration of the axis symmetry, the three components of velocity quantum of the flow are deduced in detail. Here the overall analysis of the flow is presented in the view of the concept of whole, and the paper gives the necessary corrections of some results of Ref.[1]展开更多
A general theorem for the Stokes flow over a plane boundary with mixed stick-slip boundary conditions is established. This is done by using a representation for the velocity and pressure fields in the three-dimensiona...A general theorem for the Stokes flow over a plane boundary with mixed stick-slip boundary conditions is established. This is done by using a representation for the velocity and pressure fields in the three-dimensional Stokes flow in terms of a biharmonic function and a harmonic function. The earlier theorem for the Stokes flow due to fundamental singularities before a no-slip plane boundary is shown to be a special case of the present theorem. Furthermore, in terms of the Stokes stream function, a corollary of the theorem is also derived, providing a solution to the problem of the axisymmetric Stokes flow along a rigid plane with stick-slip boundary conditions. The formulae for the drag and torque exerted by the fluid on the boundary are established. An illustrative example is given.展开更多
The unsteady axisymmetric incompressible flow between two concentric spheres was discussed in this paper. It is useful to most astrophysical, geophysical and engineering applications. In order to get the existence and...The unsteady axisymmetric incompressible flow between two concentric spheres was discussed in this paper. It is useful to most astrophysical, geophysical and engineering applications. In order to get the existence and uniqueness of weak solution of this flow with the stream_velocity form, firstly, the relations among the nonlinear terms in this equation is found; then, the existence is proved by an auxiliary semi_discrete scheme and a compactness argument.展开更多
In this paper, problems of the flow over a fat plate in the large Reynolds numbercase are studied by using the method of multiple scales￣[1,2].We have obtained N-orderuniformly valid asymptotic solutions of the Naver...In this paper, problems of the flow over a fat plate in the large Reynolds numbercase are studied by using the method of multiple scales￣[1,2].We have obtained N-orderuniformly valid asymptotic solutions of the Naver-Stodes equations.展开更多
The design methods for gradient coils are mostly based on discrete extrinsic methods(e.g.,the BioteSavart integration calculation),for which the surface normal vector strongly influences any numerical calculation of t...The design methods for gradient coils are mostly based on discrete extrinsic methods(e.g.,the BioteSavart integration calculation),for which the surface normal vector strongly influences any numerical calculation of the discretized surface.Previous studies are mostly based on regular or analytical surfaces,which allow normal vectors to be expressed analytically.For certain applications,design methods for extending currentcarrying surfaces from developable or analytic geometries to arbitrary surfaces generated from a scanned point cloud are required.The key task is to correctly express the discretized normal vectors to ensure geometrical accuracy of the designed coils.Mathematically,it has been proven that applying a Delaunay triangulation to approximate a smooth surface can result in the discrete elemental normal vectors converging to those of the original surface.Accordingly,this article uses Delaunay triangulation to expand upon previous design methods so that they encompass arbitrary piecewise continuous surfaces.Two design methods,the stream function and the so-called solid isotropic material with penalization(SIMP)method,are used to design circumvolute and noncircumvolute gradient coils on general surfaces.展开更多
文摘A heavy rainfall event that occurred over the middle and lower reaches of the Yangtze River Basin （YRB） during July 11-13 2000 is explored in this study. The potential/stream function is used to analyze the upstream ＂strong signals＂ of the water vapor transport in the Tibetan Plateau （TP）. The studied time period covers from 2000 LST 5 July to 2000 LST 15 July （temporal resolution： 6 hours）. By analyzing the three-dimensional structure of the water vapor flux, vorticity and divergence prior to and during the heavy rainfall event, the upstream ＂strong signals＂ related to this heavy rainfall event are revealed. A strong correlation exists between the heavy rainfall event in the YRB and the convective clouds over the TE The ＂convergence zone＂ of the water vapor transport is also identified, based on correlation analysis of the water vapor flux two days and one day prior to, and on the day of, the heavy rainfall. And this ＂convergence zone＂ coincides with the migration of the maximum rainfall over the YRB. This specific coupled structure actually plays a key role in generating heavy rainfall over the YRB. The eastward movement of the coupled system with a divergence]convergence center of the potential function at the upper/lower level resembles the spatiotemporal evolution of the heavy rainfall event over the YRB. These upstream ＂strong signals＂ are clearly traced in this study through analyzing the three-dimensional structure of the potential/stream function of upstream water vapor transport.
基金supported by National Foundation of Natural Science under the Grant 11071216
文摘In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems （with same stiffness matrix but different right-hand side） on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.
文摘Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is studied.This algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine grid.Moreover,the scaling between these two grid sizes is super-linear.Approximation,stability and convergence aspects of a fully discrete scheme are analyzed.At last a numrical example is given whose results show that the algorithm proposed in this paper is effcient.
基金Project supported by the National Natural Science Foundation of China (No.40975031)
文摘The stream function and the velocity potential can be easily computed by solving the Poisson equations in a unique way for the global domain. Because of the var- ious assumptions for handling the boundary conditions, the solution is not unique when a limited domain is concerned. Therefore, it is very important to reduce or eliminate the effects caused by the uncertain boundary condition. In this paper, an iterative and ad- justing method based on the Endlich iteration method is presented to compute the stream function and the velocity potential in limited domains. This method does not need an explicitly specifying boundary condition when used to obtain the effective solution, and it is proved to be successful in decomposing and reconstructing the horizontal wind field with very small errors. The convergence of the method depends on the relative value for the distances of grids in two different directions and the value of the adjusting factor. It is shown that applying the method in Arakawa grids and irregular domains can obtain the accurate vorticity and divergence and accurately decompose and reconstruct the original wind field. Hence, the iterative and adjusting method is accurate and reliable.
文摘Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.
文摘Based on the linear wave, solitary wave and fifth order stokes wave derived by use of the Unified Variational Principle of Water Gravity Wave (UVPWGW), this paper derives stream function wave theory by using UVPWGW. This paper will handle the Kinematic Free Surface Boundary Condition (KFSBC) and Dynamic Free Surface Boundary Condition (DFSBC) directly and give the optimum solution, instead of the conditions Sigma(Q(av) - Q(i))(2) = min, and the related equations of stational condition. When the wave height H, period T and water depth D are given, the original stream function wave will be determined, and can not be adjusted if it does not agree with the real case; in the present method, the adjustment can be done by adding several constraint conditions, for example, the wave profile can be adjusted according to the condition of accurate peak position. The examples given in this paper show that for the original stream function wave, the DFSBC can be fairly well satisfied, but the KFSBC can not; however, the stream function wave derived by UVPWGW is better than the original one in the sense of minimum error squares in the aspect of the level at which KFSBC and DFSBC are satisfied.
基金supported by the Project Funding of the Fund Committee of Science Department (No.40346029)National Natural Science Foundation (40346029)the offing comprehensive evaluation of our country (908-02-01-03)
文摘A 2-dimensional global free surface diagnostic model, combined with dynamic calculation, is used to investigate the world ocean circulation; the model has a horizontal resolution of 1/4°×1/4°. The simulated results agree well with the results of other modesl and observations. The distribution of Stream Function suggests that the main circulation systems in the wodd ocean have been represented, including oceanic currents strengthened in the oceanic western. Be close to the observed results, the net mass transport of the Kuroshio axes is estimated about 54Sv; The distribution of the horizontal circulation in each layer shows that the main circulation systems in the world ocean are well simulated, for example, the Kuroshio and the Antarctic Circumpolar Current can go down to the bottom layer, but the Gulf Stream cannot, and its direction reverses at the depths of 1000 to 2 000 m.
文摘Two basic hypothesises of Taylor-Galerkin Finite Element Method are studied in this paper. One of them which is unreasonable is redefined. The only hypothesis becomes the standpoint of Generalized Finite Element. We use this idea to analysis stream function-vorticity equations with Modified Taylor-Galerkin Finite Element Method, and give the two-step solving method, which makes the solving process more reasonable than ever before. Several computational examples reveal that the results of this new method are satisfied.
基金supported by grants from the National Natural Science Foundation of China(41705024,41875048)the National Key R&D Program of China(2016YFA0602104)+1 种基金the Planning and Budgeting Committee of the Council for Higher Education in Israelthe Startup Foundation for Introducing Talent of NUIST(2016r060)
文摘This study compares the climatology and long-term trend of northern winter stratospheric residual mean meridional circulation(RMMC), as well as its responses to El Ni?o-Southern Oscillation(ENSO), stratospheric Quasi Biennial Oscillation(QBO), and solar cycle in ten reanalyses and a stratosphere-resolving model, CESM1-WACCM. The RMMC is a large-scale meridional circulation cell in the stratosphere, usually referred to as the estimate of the Brewer Dobson circulation(BDC). The distribution of the BDC is generally consistent among multiple reanalyses except that the NOAA twentieth century reanalysis(20RC) largely underestimates it. Most reanalyses(except ERA40 and ERA-Interim) show a strengthening trend for the BDC during 1979–2010. All reanalyses and CESM1-WACCM consistently reveal that the deep branch of the BDC is significantly enhanced in El Ni?o winters as more waves from the troposphere dissipate in the stratospheric polar vortex region. A secondary circulation cell is coupled to the temperature anomalies below the QBO easterly center at 50 hPa with tropical upwelling/cooling and midlatitude downwelling/warming, and similar secondary circulation cells also appear between 50–10 hPa and above 10 hPa to balance the temperature anomalies. The direct BDC response to QBO in the upper stratosphere creates a barrier near 30°N to prevent waves from propagating to midlatitudes, contributing to the weakening of the polar vortex. The shallow branch of the BDC in the lower stratosphere is intensified during solar minima, and the downwelling warms the Arctic lower stratosphere. The stratospheric responses to QBO and solar cycle in most reanalyses are generally consistent except in the two 20 CRs.
基金jointly supported by the National Basic Research Program(973 ProgramNos.2012CB417402 and 2013CB956201)
文摘The seasonal and interannual variability of zonal mean Hadley circulation are analyzed, and the important effects of sea surface temperature(SST), especially the tropical Pacific SST, on the meridional circulation are discussed. Following results are obtained: 1) the Hadley circulation presents a single clockwise(anticlockwise) cross-equator circulation in the Northern(Southern) Hemisphere winter,while it is a double-ring-shaped circulation quasi-symmetric about the equator in spring and autumn. The annual mean state just indicates the residual of the Hadley cell in winter and summer. 2) The first mode of interannual anomalies shows a single cell crossing the equator like the climatology in winter and summer but with narrower width. The second mode shows a double ring-shaped cell quasi-symmetric about the equator which is similar to the Hadley cell in spring or autumn. 3) Vertical motion of the Hadley circulation is driven by sea surface temperature(SST) through latent and sensible heat in the tropics, and the interannual anomalies are mainly driven by the SST anomaly(SSTa) in the tropical Pacific. 4) The meridional gradient of SSTa is well consistent with the lower meridional wind of Hadley circulation in the interannual part. For the spatial distribution, the meridional gradient of SSTa in the Pacific plays a major role for the first two modes while the effects of the Indian Ocean and the Atlantic Ocean can be ignored.
文摘Taking the distributing calculation of velocity and concentration as an example, the paper established a series of governing equations by the vorticity stream function method, and dispersed the equations by the finite differencing method. After figuring out the distribution field of velocity, the paper also calculated the concentration distribution in sedimentation tank by using the two dimensional concentration transport equation. The validity and feasibility of the numerical method was verified through comparing with experimental data. Furthermore, the paper carried out a tentative exploration into the application of numerical simulation of sedimentation tanks.
文摘This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center of the spherical container is studied. Stream function solutions for the flow fields are obtained in terms of modified Bessel functions and Gegenbauer functions. The pressure fields, the micro-rotation components, the drag experienced by a permeable sphere, the wall correction factor, and the flow rate through the permeable surface are obtained for the frictionless impermeable spherical container and the zero shear stress at the impermeable spherical container. Variations of the drag force and the wall correction factor with respect to different fluid parameters are studied. It is observed that the drag force, the wall correction factor, and the flow rate are greater for the frictionless impermeable spherical container than the zero shear stress at the impermeable spherical container. Several cases of interest are deduced from the present analysis.
基金Project supported by the National Natural Science Foundation of China (Nos. 10971165, 10771167,and 10926080)
文摘For some special flows, especially the potential flow in a plane, using the hodograph method has obvious advantages. Realistic flows have a stream surface, namely, a two-dimensional manifold, on which the velocity vector of the flow lies on its tangent space. By introducing a stream function and a potential function, we establish the hodo- graph method for potential flows on a surface using the tensor analysis. For the derived hodograph equation, we obtain a characteristic equation and its characteristic roots, from which we can classify the type of the second-order hodograph equation. Moreover, we give some examples for special surfaces.
基金This project was supported by the Fok Ying Tung Education Foundation(Grant No.81068)and the China-Australia Institutional Links Project.
文摘Some new results of the modeling of mean free surface of waves or wave set-up are presented. The stream function wave theory is applied to incident short waves. The limiting wave steepness is adopted as the wave breaker index in the calculation of wave breaking dissipation. The model is based on Roelvink (1993), but the numerical techniques used in the solution are based on the Weighted-Average Flux (WAF) method (Watson et al., 1992), with Time-Operator-Splitting (TOS) used for the treatment of the source terms. This method allows a small number of computational points to be used, and is particularly efficient in modeling wave set-up. The short wave (or incident primary wave) energy equation is solved by use of a traditional Lax-Wendroff technique. The present model is found to be satisfactory compared with the measurements conducted by Stive (1983).
文摘This paper gives the detailed mathematical expression of the flow in the spherical coordinates system. Applying the law of conservation of mass, movement theorem of steady flow, and applying the mathematical method of stream function with consideration of the axis symmetry, the three components of velocity quantum of the flow are deduced in detail. Here the overall analysis of the flow is presented in the view of the concept of whole, and the paper gives the necessary corrections of some results of Ref.[1]
文摘A general theorem for the Stokes flow over a plane boundary with mixed stick-slip boundary conditions is established. This is done by using a representation for the velocity and pressure fields in the three-dimensional Stokes flow in terms of a biharmonic function and a harmonic function. The earlier theorem for the Stokes flow due to fundamental singularities before a no-slip plane boundary is shown to be a special case of the present theorem. Furthermore, in terms of the Stokes stream function, a corollary of the theorem is also derived, providing a solution to the problem of the axisymmetric Stokes flow along a rigid plane with stick-slip boundary conditions. The formulae for the drag and torque exerted by the fluid on the boundary are established. An illustrative example is given.
文摘The unsteady axisymmetric incompressible flow between two concentric spheres was discussed in this paper. It is useful to most astrophysical, geophysical and engineering applications. In order to get the existence and uniqueness of weak solution of this flow with the stream_velocity form, firstly, the relations among the nonlinear terms in this equation is found; then, the existence is proved by an auxiliary semi_discrete scheme and a compactness argument.
文摘In this paper, problems of the flow over a fat plate in the large Reynolds numbercase are studied by using the method of multiple scales￣[1,2].We have obtained N-orderuniformly valid asymptotic solutions of the Naver-Stodes equations.
基金the National Natural Science Foundation of China under grant No.51675506.JGK acknowledges support from an EU2020 FET grant(737043 TiSuMR)the Deutsche Forschungsgesellschaft(DFG)(grant KO 1883/20-1 Metacoils)funding within the framework of the German Excellence Initiative under grant EXC 2082“3D Matter Made to Order”,from the VirtMat initiative“Virtual Materials Design”,and from an ERC Synergy Grant(951459,HiSCORE),European Union.
文摘The design methods for gradient coils are mostly based on discrete extrinsic methods(e.g.,the BioteSavart integration calculation),for which the surface normal vector strongly influences any numerical calculation of the discretized surface.Previous studies are mostly based on regular or analytical surfaces,which allow normal vectors to be expressed analytically.For certain applications,design methods for extending currentcarrying surfaces from developable or analytic geometries to arbitrary surfaces generated from a scanned point cloud are required.The key task is to correctly express the discretized normal vectors to ensure geometrical accuracy of the designed coils.Mathematically,it has been proven that applying a Delaunay triangulation to approximate a smooth surface can result in the discrete elemental normal vectors converging to those of the original surface.Accordingly,this article uses Delaunay triangulation to expand upon previous design methods so that they encompass arbitrary piecewise continuous surfaces.Two design methods,the stream function and the so-called solid isotropic material with penalization(SIMP)method,are used to design circumvolute and noncircumvolute gradient coils on general surfaces.
