Exact solutions of (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations  

作　　者：刘萍 李子良 

机构地区：[1]College of Electron and Information Engineering,University of Electronic Science and Technology of China Zhongshan Institute [2]Physical Oceanography Laboratory,College of Physical and Environment Oceanography,Ocean University of China

出　　处：《Chinese Physics B》2013年第5期83-90,共8页中国物理B（英文版）

基　　金：Project supported by the Natural Science Foundation of Guangdong Province, China (Grant Nos. 10452840301004616 and S2011040000403);the National Natural Science Foundation of China (Grant No. 41176005);the Science and Technology Project Foundation of Zhongshan, China (Grnat No. 20123A326)

摘　　要：The symmetries and the exact solutions of the （3＋l）-dimensional nonlinear incompressible non-hydrostatic Boussi- nesq （INHB） equations, which describe atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space-time translations. Three types of symmetry reduction equations and similar solutions for the （3＋ 1）-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space-time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the （3＋1）-dimensional INHB system.The symmetries and the exact solutions of the （3＋l）-dimensional nonlinear incompressible non-hydrostatic Boussi- nesq （INHB） equations, which describe atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space-time translations. Three types of symmetry reduction equations and similar solutions for the （3＋ 1）-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space-time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the （3＋1）-dimensional INHB system.

关 键 词：（3＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations atmosphericgravity waves SYMMETRIES exact solutions 

分 类 号：O175.29[理学—数学]