From Interactive System for Ice sheet Simulation


Line 1: 
Line 1: 
−  ===Stokes Equations===
 
   
−  In Cartesian coordinates, the Stokes equations are given by,
 
− 
 
− 
 
−  <math>\begin{align}
 
−  & x:\quad \frac{\partial \tau _{xx}}{\partial x}\frac{\partial P}{\partial x}+\frac{\partial \tau _{xy}}{\partial y}+\frac{\partial \tau _{xz}}{\partial z}=0 \\
 
−  & y:\quad \frac{\partial \tau _{yy}}{\partial y}\frac{\partial P}{\partial y}+\frac{\partial \tau _{xy}}{\partial x}+\frac{\partial \tau _{yz}}{\partial z}=0 \\
 
−  & z:\quad \frac{\partial \tau _{zz}}{\partial z}\frac{\partial P}{\partial z}+\frac{\partial \tau _{zy}}{\partial y}+\frac{\partial \tau _{xz}}{\partial x}=\rho g \\
 
−  \end{align}</math>,
 
− 
 
− 
 
−  where ''P'' is the pressure and <big>τ</big> is the deviatoric stress tensor. The latter is given by
 
− 
 
− 
 
−  <big><math>\tau _{ij}=\sigma _{ij}+P\delta _{ij}</math></big>,
 
− 
 
− 
 
−  where <big>σ</big> is the full stress tensor.
 
− 
 
− 
 
−  ===Constitutive Relation===
 
Latest revision as of 21:00, 30 July 2009