The symmetries of the （2＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq （INHB） equations, which describe the atmospheric gravity waves （GWs）, are researched in this paper. The Lie symmetries...The symmetries of the （2＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq （INHB） equations, which describe the atmospheric gravity waves （GWs）, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. Calculation shows the INHB equations are invariant under some Galilean transformations, scaling transformations, and space-time translations. The symmetry reduction equations and similar solutions of the INHB equations are proposed.展开更多
This paper describes the design of a new kind of miniature abrading sphere, which is magnetically mounted inside a spherical gap and set in rotation pneumatically with air. Large eddy simulation is performed in conjun...This paper describes the design of a new kind of miniature abrading sphere, which is magnetically mounted inside a spherical gap and set in rotation pneumatically with air. Large eddy simulation is performed in conjunction with the compressible Smagorinsky model. Minimal temperature variation allows for the assumption of adiabatic walls. Fluid-solid interaction is modeled using the law of the wall for compressible turbulent flow. A parametric study is done to determine optimal geometric layout while taking physical restrictions into account. The resulting optimal configuration is then examined in detail in order to determine demands to be met by the computerized control of the magnetic bearing as well as to quantify the force available to the abrasion process. Finally, a mathematical relation is given that determines available abrasion force depending on standard volumetric flow rate and rotation frequency. The findings presented here provide a basis for further development of smaller versions of the tool.展开更多
Exact solutions of the atmospheric(2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq(INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, severa...Exact solutions of the atmospheric(2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq(INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space.展开更多
基金Supported by the Scientific Research Foundation for the Doctors of University of Electronic Science and Technology of China Zhongshan Institute under Grant No. 408YKQ09the National Natural Science Foundation of China under Grant No. 10735030
文摘The symmetries of the （2＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq （INHB） equations, which describe the atmospheric gravity waves （GWs）, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. Calculation shows the INHB equations are invariant under some Galilean transformations, scaling transformations, and space-time translations. The symmetry reduction equations and similar solutions of the INHB equations are proposed.
文摘This paper describes the design of a new kind of miniature abrading sphere, which is magnetically mounted inside a spherical gap and set in rotation pneumatically with air. Large eddy simulation is performed in conjunction with the compressible Smagorinsky model. Minimal temperature variation allows for the assumption of adiabatic walls. Fluid-solid interaction is modeled using the law of the wall for compressible turbulent flow. A parametric study is done to determine optimal geometric layout while taking physical restrictions into account. The resulting optimal configuration is then examined in detail in order to determine demands to be met by the computerized control of the magnetic bearing as well as to quantify the force available to the abrasion process. Finally, a mathematical relation is given that determines available abrasion force depending on standard volumetric flow rate and rotation frequency. The findings presented here provide a basis for further development of smaller versions of the tool.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11305031 and 11305106Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No.Yq2013205
文摘Exact solutions of the atmospheric(2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq(INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space.
