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docs:math:symmetry [2014/12/04 11:46]
gibson
docs:math:symmetry [2014/12/04 11:53] (current)
gibson [Symmetry of flows in channel geometries]
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 \begin{eqnarray*} \begin{eqnarray*}
-  [u,​v,​w](x,​y,​z) &​\rightarrow [-u, v, w](-x,y,z) \\ +  [ u,v,w ](x,y,z) & \rightarrow [-u, v, w](-x,y,z) \\ 
-  [u,​v,​w](x,​y,​z) &​\rightarrow [ u, -v, w](x,-y,z) \\ +  [ u,v,w ](x,y,z) & \rightarrow [ u, -v, w](x,-y,z) \\ 
-  [u,​v,​w](x,​y,​z) &​\rightarrow [ u, v, -w](x, y,-z) \\ +  [ u,v,w ](x,y,z) & \rightarrow [ u, v, -w](x, y,-z) \\ 
-  [u,​v,​w](x,​y,​z) &​\rightarrow [-u,​-v,​-w](x,​y,​z) \\ +  [ u,v,w ](x,y,z) & \rightarrow [-u,​-v,​-w](x,​y,​z) \\ 
-  [u,​v,​w](x,​y,​z) &​\rightarrow [ u, v, w](x+\ell_x,​ y, z+\ell_z) ​+  [ u,v,w ](x,y,z) & \rightarrow [ u, v, w](x+\ell_x,​ y, z+\ell_z) ​
 \end{eqnarray*} \end{eqnarray*}
  
 "​Channel geometry"​ means a domain that is periodic or infinite in //x// and //z// "​Channel geometry"​ means a domain that is periodic or infinite in //x// and //z//
-and bounded in //y//, with //-L_y/​2 ​<= <= L_y/2// and Dirichlet or Neumann ​+and bounded in //y//, with $-L_y/​2 ​\leq \leq L_y/2and Dirichlet or Neumann ​
 boundary conditions at the bounds in //y//. The symmetry groups of velocity ​ boundary conditions at the bounds in //y//. The symmetry groups of velocity ​
 fields for specific flows, with constraints such as incompressibility ​ fields for specific flows, with constraints such as incompressibility ​
docs/math/symmetry.txt · Last modified: 2014/12/04 11:53 by gibson