--- manual/s_algorithm/text/shap.tex 2001/08/09 19:48:39 1.2 +++ manual/s_algorithm/text/shap.tex 2001/10/25 18:36:53 1.3 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/shap.tex,v 1.2 2001/08/09 19:48:39 adcroft Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/shap.tex,v 1.3 2001/10/25 18:36:53 cnh Exp $ % $Name: $ \section{Shapiro Filter} @@ -21,7 +21,7 @@ using pure numerical differences and ignoring grid spacing. This later form is stable whatever the grid is, and therefore -specially useful for highly anisotrope grid such as spherical +specially useful for highly anisotropic grid such as spherical coordinate grid. A damping time-scale parameter $\tau_{shap}$ defines the strength of the filter damping. @@ -46,7 +46,7 @@ [1 - \frac{\Delta t}{\tau_{shap}} (\frac{1}{4}\delta_{jj})^n] $$ -In addition, the S2 operator can easly be extended to +In addition, the S2 operator can easily be extended to a physical space filter: $$ \mathrm{S2g:}\hspace{2cm} @@ -54,7 +54,7 @@ \{ \frac{L_{shap}^2}{8} \overline{\nabla}^2 \}^n] $$ -with the Laplacien operator $\overline{\nabla}^2 $ +with the Laplacian operator $\overline{\nabla}^2 $ and a length scale parameter $L_{shap}$. The stability of this S2g filter requires $L_{shap} < \mathrm{Min}^{(Global)}(\Delta x,\Delta y)$.