Open AccessDynamic modification of the shallow water equation on the slowly changing underlying surface condition
Author(s) -
Chaojiu Da,
Ao Feng,
Zhiqiang Gong,
Jian Song
Publication year - 2013
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.62.039202
Subject(s) - atmosphere (unit) , divergence (linguistics) , surface (topology) , vorticity equation , physics , waves and shallow water , shallow water equations , vorticity , mechanics , boundary value problem , function (biology) , geology , meteorology , mathematics , geometry , vortex , thermodynamics , philosophy , linguistics , quantum mechanics , evolutionary biology , biology
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.