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revision 1.25 by edhill, Sat Apr 8 01:50:49 2006 UTC revision 1.27 by jmc, Thu Jan 17 21:28:22 2008 UTC
# Line 87  studies. Line 87  studies.
87  computational platforms.  computational platforms.
88  \end{itemize}  \end{itemize}
89    
90    
91  Key publications reporting on and charting the development of the model are  Key publications reporting on and charting the development of the model are
92  \cite{hill:95,marshall:97a,marshall:97b,adcroft:97,marshall:98,adcroft:99,hill:99,maro-eta:99,adcroft:04a,adcroft:04b,marshall:04}:  \cite{hill:95,marshall:97a,marshall:97b,adcroft:97,mars-eta:98,adcroft:99,hill:99,maro-eta:99,adcroft:04a,adcroft:04b,marshall:04}
93    (an overview on the model formulation can also be found in \cite{adcroft:04c}):
94    
95  \begin{verbatim}  \begin{verbatim}
96  Hill, C. and J. Marshall, (1995)  Hill, C. and J. Marshall, (1995)
# Line 1077  friction. These coefficients are the sam Line 1079  friction. These coefficients are the sam
1079    
1080  The mixing terms for the temperature and salinity equations have a similar  The mixing terms for the temperature and salinity equations have a similar
1081  form to that of momentum except that the diffusion tensor can be  form to that of momentum except that the diffusion tensor can be
1082  non-diagonal and have varying coefficients. $\qquad $  non-diagonal and have varying coefficients.
1083  \begin{equation}  \begin{equation}
1084  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
1085  _{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 1491  u=r\cos \varphi \frac{D\lambda }{Dt}
1491  \end{equation*}  \end{equation*}
1492    
1493  \begin{equation*}  \begin{equation*}
1494  v=r\frac{D\varphi }{Dt}\qquad  v=r\frac{D\varphi }{Dt}
1495  \end{equation*}  \end{equation*}
 $\qquad \qquad \qquad \qquad $  
1496    
1497  \begin{equation*}  \begin{equation*}
1498  \dot{r}=\frac{Dr}{Dt}  \dot{r}=\frac{Dr}{Dt}
# Line 1501  Here $\varphi $ is the latitude, $\lambd Line 1502  Here $\varphi $ is the latitude, $\lambd
1502  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
1503  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.
1504    
1505  The `grad' ($\nabla $) and `div' ($\nabla $.) operators are defined by, in  The `grad' ($\nabla $) and `div' ($\nabla\cdot$) operators are defined by, in
1506  spherical coordinates:  spherical coordinates:
1507    
1508  \begin{equation*}  \begin{equation*}
# Line 1511  spherical coordinates: Line 1512  spherical coordinates:
1512  \end{equation*}  \end{equation*}
1513    
1514  \begin{equation*}  \begin{equation*}
1515  \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
1516  \lambda }+\frac{\partial }{\partial \varphi }\left( v\cos \varphi \right) \right\}  \lambda }+\frac{\partial }{\partial \varphi }\left( v\cos \varphi \right) \right\}
1517  +\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}
1518  \end{equation*}  \end{equation*}
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