--- manual/s_phys_pkgs/text/streamice.tex 2013/11/26 20:35:57 1.1 +++ manual/s_phys_pkgs/text/streamice.tex 2014/08/28 21:42:20 1.2 @@ -38,7 +38,7 @@ \end{equation} From the velocity field, thickness evolves according to the continuity equation: \begin{equation} -\label{eq:cont} +\label{eq:contEq} h_t + \nabla\cdot(h\vec{u}) = -\dot{b}, \end{equation} Where $\dot{b}$ is a basal mass balance (e.g. melting due to contact with the @@ -121,7 +121,7 @@ In the hybrid formulation, $\overline{u}$ and $\overline{v}$, the depth-averaged $x-$ and $y-$ velocities, replace $u$ and $v$ in \eqref{eq:xmom}, -\eqref{eq:ymom}, and \eqref{eq:cont}, and gradients such as $u_x$ are replaced +\eqref{eq:ymom}, and \eqref{eq:contEq}, and gradients such as $u_x$ are replaced by $(\overline{u})_x$. Viscosity becomes \begin{equation} \nu = @@ -353,7 +353,7 @@ \paragraph{Thickness evolution} -\eqref{eq:cont} is solved in the subroutine \texttt{STREAMICE\_ADVECT\_THICKNESS}, similarly to the advection routines in MITgcm. Mass fluxes are evaluated, first in the $x$-direction. This is done in the generic subroutine \texttt{STREAMICE\_ADV\_FLUX\_FL\_X}. Flux velocity in the $x-$direction at face ($i,j$) are generated by averaging $u_{i,j}$ and $u_{i,j+1}$. Assuming the flux velocity is positive, if $hmask_{i-2,j},\ mask{i-1,j}$ and $hmask_{i,j}$ are equal to 1, then flux thickness, i.e. the interpolation of $h$ at face ($i,j$), is through a minmod limiter as in the \texttt{generic\_advdiff} package. If these values are not available, then a zero-order upwind flux is used. The exception is when \texttt{STREAMICE\_ufacemask(i,j)} is equal to 4; then \texttt{u\_flux\_bdry\_SI(i,j)} is used for the flux. Fluxes are then differenced to update $h$ in cells that are active ($hmask=1$); a similar procedure follows for the $y-$direction. +\eqref{eq:contEq} is solved in the subroutine \texttt{STREAMICE\_ADVECT\_THICKNESS}, similarly to the advection routines in MITgcm. Mass fluxes are evaluated, first in the $x$-direction. This is done in the generic subroutine \texttt{STREAMICE\_ADV\_FLUX\_FL\_X}. Flux velocity in the $x-$direction at face ($i,j$) are generated by averaging $u_{i,j}$ and $u_{i,j+1}$. Assuming the flux velocity is positive, if $hmask_{i-2,j},\ mask{i-1,j}$ and $hmask_{i,j}$ are equal to 1, then flux thickness, i.e. the interpolation of $h$ at face ($i,j$), is through a minmod limiter as in the \texttt{generic\_advdiff} package. If these values are not available, then a zero-order upwind flux is used. The exception is when \texttt{STREAMICE\_ufacemask(i,j)} is equal to 4; then \texttt{u\_flux\_bdry\_SI(i,j)} is used for the flux. Fluxes are then differenced to update $h$ in cells that are active ($hmask=1$); a similar procedure follows for the $y-$direction. \paragraph{Ice front advance}