--- manual/s_phys_pkgs/text/seaice.tex 2010/08/30 23:09:21 1.12 +++ manual/s_phys_pkgs/text/seaice.tex 2011/02/28 16:05:07 1.14 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_phys_pkgs/text/seaice.tex,v 1.12 2010/08/30 23:09:21 jmc Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_phys_pkgs/text/seaice.tex,v 1.14 2011/02/28 16:05:07 mlosch Exp $ % $Name: $ %%EH3 Copied from "MITgcm/pkg/seaice/seaice_description.tex" @@ -531,7 +531,9 @@ \phantom{=}& \phantom{\frac{1}{A_{i,j}^w} \biggl\{} + (\Delta{x}_1\sigma_{21})_{i,j+1}^Z - (\Delta{x}_1\sigma_{21})_{i,j}^Z \biggr\} - \intertext{with} +\end{align} +with +\begin{align} (\Delta{x}_2\sigma_{11})_{i,j}^C =& \phantom{+} \Delta{y}_{i,j}^{F}(\zeta + \eta)^{C}_{i,j} \frac{u_{i+1,j}-u_{i,j}}{\Delta{x}_{i,j}^{F}} \\ \notag @@ -573,7 +575,9 @@ \phantom{=}& \phantom{\frac{1}{A_{i,j}^s} \biggl\{} + (\Delta{x}_1\sigma_{22})_{i,j}^C - (\Delta{x}_1\sigma_{22})_{i,j-1}^C \biggr\} - \intertext{with} +\end{align} +with +\begin{align} (\Delta{x}_1\sigma_{12})_{i,j}^Z =& \phantom{+} \Delta{y}_{i,j}^{U}\overline{\eta}^{Z}_{i,j} \frac{u_{i,j}-u_{i,j-1}}{\Delta{y}_{i,j}^{U}} @@ -670,14 +674,15 @@ diffusive terms for quantities $X=(c\cdot{h}), c, (c\cdot{h}_{s})$. % From the various advection scheme that are available in the MITgcm, we -choose flux-limited schemes \citep[multidimensional 2nd and 3rd-order -advection scheme with flux limiter][]{roe:85, hundsdorfer94} to -preserve sharp gradients and edges that are typical of sea ice +recommend flux-limited schemes \citep[multidimensional 2nd and +3rd-order advection scheme with flux limiter][]{roe:85, hundsdorfer94} +to preserve sharp gradients and edges that are typical of sea ice distributions and to rule out unphysical over- and undershoots -(negative thickness or concentration). These scheme conserve volume +(negative thickness or concentration). These schemes conserve volume and horizontal area and are unconditionally stable, so that we can set -$D_{X}=0$. Run-timeflags: \code{SEAICEadvScheme} (default=2), -\code{DIFF1} (default=0.004). +$D_{X}=0$. Run-timeflags: \code{SEAICEadvScheme} (default=2, is the +historic 2nd-order, centered difference scheme), \code{DIFF1} +(default=0.004). There is considerable doubt about the reliability of a ``zero-layer'' thermodynamic model --- \citet{semtner84} found significant errors in @@ -834,5 +839,5 @@ %%% Local Variables: %%% mode: latex -%%% TeX-master: "../manual" +%%% TeX-master: "../../manual" %%% End: