/[MITgcm]/manual/s_phys_pkgs/text/seaice.tex
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revision 1.12 by jmc, Mon Aug 30 23:09:21 2010 UTC revision 1.14 by mlosch, Mon Feb 28 16:05:07 2011 UTC
# Line 531  widths. For the $u$-equation ($\alpha=1$ Line 531  widths. For the $u$-equation ($\alpha=1$
531    \phantom{=}& \phantom{\frac{1}{A_{i,j}^w} \biggl\{}    \phantom{=}& \phantom{\frac{1}{A_{i,j}^w} \biggl\{}
532    + (\Delta{x}_1\sigma_{21})_{i,j+1}^Z - (\Delta{x}_1\sigma_{21})_{i,j}^Z    + (\Delta{x}_1\sigma_{21})_{i,j+1}^Z - (\Delta{x}_1\sigma_{21})_{i,j}^Z
533    \biggr\}    \biggr\}
534    \intertext{with}  \end{align}
535    with
536    \begin{align}
537    (\Delta{x}_2\sigma_{11})_{i,j}^C =& \phantom{+}    (\Delta{x}_2\sigma_{11})_{i,j}^C =& \phantom{+}
538    \Delta{y}_{i,j}^{F}(\zeta + \eta)^{C}_{i,j}    \Delta{y}_{i,j}^{F}(\zeta + \eta)^{C}_{i,j}
539    \frac{u_{i+1,j}-u_{i,j}}{\Delta{x}_{i,j}^{F}} \\ \notag    \frac{u_{i+1,j}-u_{i,j}}{\Delta{x}_{i,j}^{F}} \\ \notag
# Line 573  Similarly, we have for the $v$-equation Line 575  Similarly, we have for the $v$-equation
575    \phantom{=}& \phantom{\frac{1}{A_{i,j}^s} \biggl\{}    \phantom{=}& \phantom{\frac{1}{A_{i,j}^s} \biggl\{}
576    + (\Delta{x}_1\sigma_{22})_{i,j}^C - (\Delta{x}_1\sigma_{22})_{i,j-1}^C    + (\Delta{x}_1\sigma_{22})_{i,j}^C - (\Delta{x}_1\sigma_{22})_{i,j-1}^C
577    \biggr\}    \biggr\}
578    \intertext{with}  \end{align}
579    with
580    \begin{align}
581    (\Delta{x}_1\sigma_{12})_{i,j}^Z =& \phantom{+}    (\Delta{x}_1\sigma_{12})_{i,j}^Z =& \phantom{+}
582    \Delta{y}_{i,j}^{U}\overline{\eta}^{Z}_{i,j}    \Delta{y}_{i,j}^{U}\overline{\eta}^{Z}_{i,j}
583    \frac{u_{i,j}-u_{i,j-1}}{\Delta{y}_{i,j}^{U}}    \frac{u_{i,j}-u_{i,j-1}}{\Delta{y}_{i,j}^{U}}
# Line 670  where $\Gamma_X$ are the thermodynamic s Line 674  where $\Gamma_X$ are the thermodynamic s
674  diffusive terms for quantities $X=(c\cdot{h}), c, (c\cdot{h}_{s})$.  diffusive terms for quantities $X=(c\cdot{h}), c, (c\cdot{h}_{s})$.
675  %  %
676  From the various advection scheme that are available in the MITgcm, we  From the various advection scheme that are available in the MITgcm, we
677  choose flux-limited schemes \citep[multidimensional 2nd and 3rd-order  recommend flux-limited schemes \citep[multidimensional 2nd and
678  advection scheme with flux limiter][]{roe:85, hundsdorfer94} to  3rd-order advection scheme with flux limiter][]{roe:85, hundsdorfer94}
679  preserve sharp gradients and edges that are typical of sea ice  to preserve sharp gradients and edges that are typical of sea ice
680  distributions and to rule out unphysical over- and undershoots  distributions and to rule out unphysical over- and undershoots
681  (negative thickness or concentration). These scheme conserve volume  (negative thickness or concentration). These schemes conserve volume
682  and horizontal area and are unconditionally stable, so that we can set  and horizontal area and are unconditionally stable, so that we can set
683  $D_{X}=0$. Run-timeflags: \code{SEAICEadvScheme} (default=2),  $D_{X}=0$. Run-timeflags: \code{SEAICEadvScheme} (default=2, is the
684  \code{DIFF1} (default=0.004).  historic 2nd-order, centered difference scheme), \code{DIFF1}
685    (default=0.004).
686    
687  There is considerable doubt about the reliability of a ``zero-layer''  There is considerable doubt about the reliability of a ``zero-layer''
688  thermodynamic model --- \citet{semtner84} found significant errors in  thermodynamic model --- \citet{semtner84} found significant errors in
# Line 834  Table \ref{tab:pkg:seaice:diagnostics}. Line 839  Table \ref{tab:pkg:seaice:diagnostics}.
839    
840  %%% Local Variables:  %%% Local Variables:
841  %%% mode: latex  %%% mode: latex
842  %%% TeX-master: "../manual"  %%% TeX-master: "../../manual"
843  %%% End:  %%% End:
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