缓变下垫面对浅水方程的动力学订正  

Dynamic modification of the shallow water equation on the slowly changing underlying surface condition

作　　者：达朝究[1,2] 冯爱霞[3] 龚志强[3] 宋健[4] 

机构地区：[1]西北民族大学数学与计算机科学学院,兰州730030 [2]兰州大学大气科学学院,兰州730000 [3]国家气候中心气候研究开放实验室,北京100081 [4]内蒙古工业大学理学院,呼和浩特010062

出　　处：《物理学报》2013年第3期513-518,共6页Acta Physica Sinica

基　　金：全球变化研究国家重大科学研究计划(批准号:2012CB955902);国家自然科学基金(批准号:40930952;41175067);国家科技支撑计划(批准号:2009BAC51B04);公益性行业(气象)科研专项(批准号:GYHY201106016;GYHY201206009);内蒙古自然科学基金(批准号:2011MS0112);中央高校基本科研业务费专项资金(批准号:zyz2011079)资助~~

摘　　要：讨论了当下垫面随时间缓慢变化时浅水方程的形式.从控制大气运动的连续性方程和动量方程出发,将下垫面的缓慢变化作为一个小量叠加到固有下垫面函数上,利用大气的上下边界条件,得到改进的浅水方程.在改进的浅水方程中,由缓变局部水平体积散度,订正了局部水平体积散度和流体局部厚度变化之间的平衡,在此基础上得到包含下垫面缓变的涡度方程.In this paper, the shallow water equation is discussed, when the underlying surface is slowly changing. From the continuity equation and the equation of motion controlling the movement of the atmosphere, the slowly changing of the underlying surface is superimposed on the topography function as a small quantity, using the upper and lower boundary conditions of the atmosphere, the modified shallow water equation is obtained. In the modified shallow water equation, the slowly changing local horizontal divergence modifies the equilibrium between the local horizontal divergence and the local change of the thickness of the atmosphere. On the basis of this, the vorticity equation is obtained, which contains the slowly changing underlying surface.

关 键 词：下垫面 全球变暖 缓变 浅水方程 

分 类 号：P433[天文地球—大气科学及气象学]