/[MITgcm]/manual/s_overview/text/manual.tex
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revision 1.25 by edhill, Sat Apr 8 01:50:49 2006 UTC revision 1.26 by edhill, Wed Jun 28 15:22:13 2006 UTC
# Line 1077  friction. These coefficients are the sam Line 1077  friction. These coefficients are the sam
1077    
1078  The mixing terms for the temperature and salinity equations have a similar  The mixing terms for the temperature and salinity equations have a similar
1079  form to that of momentum except that the diffusion tensor can be  form to that of momentum except that the diffusion tensor can be
1080  non-diagonal and have varying coefficients. $\qquad $  non-diagonal and have varying coefficients.
1081  \begin{equation}  \begin{equation}
1082  D_{T,S}=\nabla .[\underline{\underline{K}}\nabla (T,S)]+K_{4}\nabla  D_{T,S}=\nabla .[\underline{\underline{K}}\nabla (T,S)]+K_{4}\nabla
1083  _{h}^{4}(T,S)  \label{eq:diffusion}  _{h}^{4}(T,S)  \label{eq:diffusion}
# Line 1489  u=r\cos \varphi \frac{D\lambda }{Dt} Line 1489  u=r\cos \varphi \frac{D\lambda }{Dt}
1489  \end{equation*}  \end{equation*}
1490    
1491  \begin{equation*}  \begin{equation*}
1492  v=r\frac{D\varphi }{Dt}\qquad  v=r\frac{D\varphi }{Dt}
1493  \end{equation*}  \end{equation*}
 $\qquad \qquad \qquad \qquad $  
1494    
1495  \begin{equation*}  \begin{equation*}
1496  \dot{r}=\frac{Dr}{Dt}  \dot{r}=\frac{Dr}{Dt}
# Line 1501  Here $\varphi $ is the latitude, $\lambd Line 1500  Here $\varphi $ is the latitude, $\lambd
1500  distance of the particle from the center of the earth, $\Omega $ is the  distance of the particle from the center of the earth, $\Omega $ is the
1501  angular speed of rotation of the Earth and $D/Dt$ is the total derivative.  angular speed of rotation of the Earth and $D/Dt$ is the total derivative.
1502    
1503  The `grad' ($\nabla $) and `div' ($\nabla $.) operators are defined by, in  The `grad' ($\nabla $) and `div' ($\nabla\cdot$) operators are defined by, in
1504  spherical coordinates:  spherical coordinates:
1505    
1506  \begin{equation*}  \begin{equation*}
# Line 1511  spherical coordinates: Line 1510  spherical coordinates:
1510  \end{equation*}  \end{equation*}
1511    
1512  \begin{equation*}  \begin{equation*}
1513  \nabla .v\equiv \frac{1}{r\cos \varphi }\left\{ \frac{\partial u}{\partial  \nabla\cdot v\equiv \frac{1}{r\cos \varphi }\left\{ \frac{\partial u}{\partial
1514  \lambda }+\frac{\partial }{\partial \varphi }\left( v\cos \varphi \right) \right\}  \lambda }+\frac{\partial }{\partial \varphi }\left( v\cos \varphi \right) \right\}
1515  +\frac{1}{r^{2}}\frac{\partial \left( r^{2}\dot{r}\right) }{\partial r}  +\frac{1}{r^{2}}\frac{\partial \left( r^{2}\dot{r}\right) }{\partial r}
1516  \end{equation*}  \end{equation*}
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