| 12 |
C-grid variants are available; the C-grid code allows for no-slip |
C-grid variants are available; the C-grid code allows for no-slip |
| 13 |
and free-slip lateral boundary conditions; |
and free-slip lateral boundary conditions; |
| 14 |
\item two different solution methods for solving the nonlinear |
\item two different solution methods for solving the nonlinear |
| 15 |
momentum equations have been adopted: LSOR \citep{zha97}, EVP |
momentum equations have been adopted: LSOR \citep{zhang97}, EVP |
| 16 |
\citep{hunke97}; |
\citep{hunke97}; |
| 17 |
\item ice-ocean stress can be formulated as in \citet{hibler87}; |
\item ice-ocean stress can be formulated as in \citet{hibler87}; |
| 18 |
\item ice variables are advected by sophisticated advection schemes; |
\item ice variables are advected by sophisticated advection schemes; |
| 98 |
\left(\dot{\epsilon}_{11}^2+\dot{\epsilon}_{22}^2\right) |
\left(\dot{\epsilon}_{11}^2+\dot{\epsilon}_{22}^2\right) |
| 99 |
(1+e^{-2}) + 4e^{-2}\dot{\epsilon}_{12}^2 + |
(1+e^{-2}) + 4e^{-2}\dot{\epsilon}_{12}^2 + |
| 100 |
2\dot{\epsilon}_{11}\dot{\epsilon}_{22} (1-e^{-2}) |
2\dot{\epsilon}_{11}\dot{\epsilon}_{22} (1-e^{-2}) |
| 101 |
\right]^{-\frac{1}{2}} |
\right]^{\frac{1}{2}} |
| 102 |
\end{align*} |
\end{align*} |
| 103 |
The bulk viscosities are bounded above by imposing both a minimum |
The bulk viscosities are bounded above by imposing both a minimum |
| 104 |
$\Delta_{\min}=10^{-11}\text{\,s}^{-1}$ (for numerical reasons) and a |
$\Delta_{\min}=10^{-11}\text{\,s}^{-1}$ (for numerical reasons) and a |
| 280 |
algorithm following Archimedes' principle) turns snow into ice until |
algorithm following Archimedes' principle) turns snow into ice until |
| 281 |
the ice surface is back at $z=0$ \citep{leppaeranta83}. |
the ice surface is back at $z=0$ \citep{leppaeranta83}. |
| 282 |
|
|
| 283 |
Effective ich thickness (ice volume per unit area, |
Effective ice thickness (ice volume per unit area, |
| 284 |
$c\cdot{h}$), concentration $c$ and effective snow thickness |
$c\cdot{h}$), concentration $c$ and effective snow thickness |
| 285 |
($c\cdot{h}_{s}$) are advected by ice velocities: |
($c\cdot{h}_{s}$) are advected by ice velocities: |
| 286 |
\begin{align} |
\begin{equation} |
| 287 |
\frac{\partial(c\,{h})}{\partial{t}} &= - \nabla\left(\vek{u}\,c\,{h}\right) + |
\label{eq:advection} |
| 288 |
\Gamma_{h} + D_{h} \\ |
\frac{\partial{X}}{\partial{t}} = - \nabla\cdot\left(\vek{u}\,X\right) + |
| 289 |
\frac{\partial{c}}{\partial{t}} &= - \nabla\left(\vek{u}\,c\right) + |
\Gamma_{X} + D_{X} |
| 290 |
\Gamma_{c} + D_{c} \\ |
\end{equation} |
|
\frac{\partial(c\,{h}_{s})}{\partial{t}} &= - \nabla\left(\vek{u}\,c\,{h}_{s}\right) + |
|
|
\Gamma_{h_{s}} + D_{h_{s}} |
|
|
\end{align} |
|
| 291 |
where $\Gamma_X$ are the thermodynamic source terms and $D_{X}$ the |
where $\Gamma_X$ are the thermodynamic source terms and $D_{X}$ the |
| 292 |
diffusive terms for quantity $X=h, c, h_{s}$. |
diffusive terms for quantities $X=(c\cdot{h}), c, (c\cdot{h}_{s})$. |
| 293 |
% |
% |
| 294 |
From the various advection scheme that are available in the MITgcm |
From the various advection scheme that are available in the MITgcm |
| 295 |
\citep{mitgcm02}, we choose flux-limited schemes |
\citep{mitgcm02}, we choose flux-limited schemes |
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