/[MITgcm]/manual/s_algorithm/text/nonlin_frsurf.tex
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revision 1.12 by jmc, Tue Apr 4 20:19:00 2006 UTC revision 1.13 by edhill, Tue Jun 27 22:31:23 2006 UTC
# Line 31  For both fluid, using the isomorphic not Line 31  For both fluid, using the isomorphic not
31  $$  $$
32  \phi' = \int^{r_{surf}}_r b~ dr - \int^{R_o}_r b_o dr  \phi' = \int^{r_{surf}}_r b~ dr - \int^{R_o}_r b_o dr
33  $$  $$
34  \begin{eqnarray}  and re-write as:
35  \mathrm{and~re~write:}\hspace{10mm}  \begin{equation}
36  \phi' = \int^{r_{surf}}_{R_o} b~ dr & + & \int^{R_o}_r (b - b_o) dr  \phi' = \int^{r_{surf}}_{R_o} b~ dr + \int^{R_o}_r (b - b_o) dr
37  \label{eq:split-phi-Ro} \\  \label{eq:split-phi-Ro}
38  \mathrm{or:}\hspace{10mm}  \end{equation}
39  \phi' = \int^{r_{surf}}_{R_o} b_o dr & + & \int^{r_{surf}}_r (b - b_o) dr  or:
40    \begin{equation}
41    \phi' = \int^{r_{surf}}_{R_o} b_o dr + \int^{r_{surf}}_r (b - b_o) dr
42  \label{eq:split-phi-bo}  \label{eq:split-phi-bo}
43  \end{eqnarray}  \end{equation}
44    
45  In section \ref{sec:finding_the_pressure_field}, following eq.\ref{eq:split-phi-Ro},  In section \ref{sec:finding_the_pressure_field}, following eq.\ref{eq:split-phi-Ro},
46  the pressure/geo-potential $\phi'$ has been separated into surface ($\phi_s$),  the pressure/geo-potential $\phi'$ has been separated into surface ($\phi_s$),

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