http://websrv.cs.umt.edu/isis/index.php?title=Shallow-shelf_approxmation&feed=atom&action=history Shallow-shelf approxmation - Revision history 2020-02-22T07:27:15Z Revision history for this page on the wiki MediaWiki 1.21.1 http://websrv.cs.umt.edu/isis/index.php?title=Shallow-shelf_approxmation&diff=2175&oldid=prev Sprice: New page: The shallow shelf equations are given by [itex]\begin{align} & \frac{\partial }{\partial x}\left( 2\bar{\eta }H\left( 2\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y} \righ... 2009-07-30T21:20:42Z <p>New page: The shallow shelf equations are given by &lt;math&gt;\begin{align} &amp; \frac{\partial }{\partial x}\left( 2\bar{\eta }H\left( 2\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y} \righ...</p> <p><b>New page</b></p><div><br /> The shallow shelf equations are given by<br /> <br /> &lt;math&gt;\begin{align}<br /> &amp; \frac{\partial }{\partial x}\left( 2\bar{\eta }H\left( 2\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y} \right) \right)+\frac{\partial }{\partial y}\left( \bar{\eta }H\left( \frac{\partial u}{\partial y}+\frac{\partial v}{\partial x} \right) \right)=\rho gH\frac{\partial s}{\partial x} \\ <br /> &amp; \frac{\partial }{\partial y}\left( 2\bar{\eta }H\left( 2\frac{\partial v}{\partial y}+\frac{\partial u}{\partial x} \right) \right)+\frac{\partial }{\partial x}\left( \bar{\eta }H\left( \frac{\partial u}{\partial y}+\frac{\partial v}{\partial x} \right) \right)=\rho gH\frac{\partial s}{\partial y} \\ <br /> \end{align}&lt;/math&gt;,<br /> <br /> <br /> where ''u'' and ''v'' are the depth-independent ''x'' and ''y'' components of velocity, &lt;math&gt;\bar{\eta }&lt;/math&gt; is the depth-averaged effective viscosity, ''H'' is the ice thickness, &amp;rho; is the ice density, ''g'' is the acceleration due to gravity, and ''s=s(x,y)'' is the ice surface elevation.<br /> <br /> Notice the symmetry in the equations. This means that, computationally, many of the same subroutines can be used for discretization.</div> Sprice