The C^k （k ≥ 3） stability of nonlinear barotropic vorticity equation was proved. The necessary and sufficient conditions for the initial value problem to be well-posed were presented. Under the conditions of well-p...The C^k （k ≥ 3） stability of nonlinear barotropic vorticity equation was proved. The necessary and sufficient conditions for the initial value problem to be well-posed were presented. Under the conditions of well-posedness, the corresponding analytical solution was also gained.展开更多
By the Backlund transformation method, an important （2＋1）-dimensional nonlinear barotropie and quasigeostrophic potential vorticity （BQGPV） equation is investigated. Some simple special Backlund transformation th...By the Backlund transformation method, an important （2＋1）-dimensional nonlinear barotropie and quasigeostrophic potential vorticity （BQGPV） equation is investigated. Some simple special Backlund transformation theorems are proposed and used to get explicit solutions of the BQGPV equation. Furthermore, all solutions of a second order linear ordinary differential equation including an arbitrary function can be used to construct explicit solutions of the （2＋1）-dimensional BQGPV equation. Some figures are also given out to describe these solutions.展开更多
Variable coefficient nonlinear systems, the Korteweg de Vries （KdV）, the modified KdV （mKdV） and the nonlinear Schrǒdinger （NLS） type equations, are derived from the nonlinear inviscid barotropic nondivergent v...Variable coefficient nonlinear systems, the Korteweg de Vries （KdV）, the modified KdV （mKdV） and the nonlinear Schrǒdinger （NLS） type equations, are derived from the nonlinear inviscid barotropic nondivergent vorticity equation in a beta-plane by means of the multi-scale expansion method in two different ways, with and without the so-called y-average trick. The non-auto-Bǎcklund transformations are found to transform the derived variable coefficient equations to the corresponding standard KdV, mKdV and NLS equations. Thus, many possible exact solutions can be obtained by taking advantage of the known solutions of these standard equations. Further, many approximate solutions of the original model are ready to be yielded which might be applied to explain some real atmospheric phenomena, such as atmospheric blocking episodes.展开更多
The linear barotropic vorticity equation describing wind-driven oceancirculation is considered as a convection-diffusion equation that can be numerically solved bylattice Boltzmann method. Numerical experiments are ca...The linear barotropic vorticity equation describing wind-driven oceancirculation is considered as a convection-diffusion equation that can be numerically solved bylattice Boltzmann method. Numerical experiments are carried out to examine the validity of the modelfor the wind-driven circulation. When horizontal viscosity is constant and spatially uniform, allnumerical solutions for different parameters approach analytical solutions well. The spatiallyvarying horizontal viscosity is also included in this model. It is shown that the variant horizontalviscosity increases the meridional transport significantly in west boundary current. By theinvestigation of numerical results, it was concluded that this model is competent for simulatingwestern boundary current.展开更多
基金the Jiangsu Planned Projects for Postdoctral Research Funds (Grant No. 0602024C)the JiangsuKey Laboratory of Meteorological Disaster (Grant No.KLME060201)
文摘The C^k （k ≥ 3） stability of nonlinear barotropic vorticity equation was proved. The necessary and sufficient conditions for the initial value problem to be well-posed were presented. Under the conditions of well-posedness, the corresponding analytical solution was also gained.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10735030, 90718041, and 40975038Shanghai Leading Academic Discipline Project under Grant No. B412Program for Changjiang Scholars and Innovative Research Team in University (IRT0734)
文摘By the Backlund transformation method, an important （2＋1）-dimensional nonlinear barotropie and quasigeostrophic potential vorticity （BQGPV） equation is investigated. Some simple special Backlund transformation theorems are proposed and used to get explicit solutions of the BQGPV equation. Furthermore, all solutions of a second order linear ordinary differential equation including an arbitrary function can be used to construct explicit solutions of the （2＋1）-dimensional BQGPV equation. Some figures are also given out to describe these solutions.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10735030, 10547124, 90503006 and 40305009)the National Basic Research Program of China (Grant Nos 2007CB814800 and 2005CB422301)+3 种基金Specialized Research Fund for the Doctoral Program of Higher Education (Grant No 20070248120)Program for Changjiang Scholars and Innovative Research Team in University (Grant No IRT0734)the Scientific Research Starting Foundation for Returned Overseas Chinese Scholars, Ministry of Education, Chinathe Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No NCET-05-0591)
文摘Variable coefficient nonlinear systems, the Korteweg de Vries （KdV）, the modified KdV （mKdV） and the nonlinear Schrǒdinger （NLS） type equations, are derived from the nonlinear inviscid barotropic nondivergent vorticity equation in a beta-plane by means of the multi-scale expansion method in two different ways, with and without the so-called y-average trick. The non-auto-Bǎcklund transformations are found to transform the derived variable coefficient equations to the corresponding standard KdV, mKdV and NLS equations. Thus, many possible exact solutions can be obtained by taking advantage of the known solutions of these standard equations. Further, many approximate solutions of the original model are ready to be yielded which might be applied to explain some real atmospheric phenomena, such as atmospheric blocking episodes.
文摘The linear barotropic vorticity equation describing wind-driven oceancirculation is considered as a convection-diffusion equation that can be numerically solved bylattice Boltzmann method. Numerical experiments are carried out to examine the validity of the modelfor the wind-driven circulation. When horizontal viscosity is constant and spatially uniform, allnumerical solutions for different parameters approach analytical solutions well. The spatiallyvarying horizontal viscosity is also included in this model. It is shown that the variant horizontalviscosity increases the meridional transport significantly in west boundary current. By theinvestigation of numerical results, it was concluded that this model is competent for simulatingwestern boundary current.
