# Difference between revisions of "Blatter-Pattyn model"

From Interactive System for Ice sheet Simulation

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There are a number of ways to argue that because of the "shallowness" of ice sheets - that is because the ratio of <big>''H''/''L''</big>, where ''H'' is the thickness and ''L'' is a relevant horizontal length scale, is small - the equations above can be reduced to the following "first-order approximation" | There are a number of ways to argue that because of the "shallowness" of ice sheets - that is because the ratio of <big>''H''/''L''</big>, where ''H'' is the thickness and ''L'' is a relevant horizontal length scale, is small - the equations above can be reduced to the following "first-order approximation" | ||

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<math>\begin{align} | <math>\begin{align} | ||

− | & \frac{\partial \tau _{xx}}{\partial x}+\frac{\partial \tau _{xy}}{\partial y}+\frac{\partial \tau _{xz}}{\partial z}= | + | & 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 \\ |

− | & \frac{\partial \tau _{yy}}{\partial y}+\frac{\partial \tau _{xy}}{\partial x}+\frac{\partial \tau _{yz}}{\partial z}= | + | & 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 \\ |

− | & \frac{\partial \tau _{zz}}{\partial z} | + | & z:\quad \frac{\partial \tau _{zz}}{\partial z}-\frac{\partial P}{\partial z}=\rho g \\ |

\end{align}</math> | \end{align}</math> | ||

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## Revision as of 16:47, 30 July 2009

The starting point for the Blatter-Pattyn model is the full Stokes equations

,

where *P* is the pressure and τ is the deviatoric stress tensor. The latter is given by

,

where σ is the full stress tensor.

There are a number of ways to argue that because of the "shallowness" of ice sheets - that is because the ratio of *H*/*L*, where *H* is the thickness and *L* is a relevant horizontal length scale, is small - the equations above can be reduced to the following "first-order approximation"