/[MITgcm]/manual/s_examples/deep_convection/convection.tex
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revision 1.1 by helen, Wed Dec 19 14:34:39 2001 UTC revision 1.2 by cnh, Thu Feb 28 19:32:19 2002 UTC
# Line 1  Line 1 
1  \section{Example: Surface driven convection}  \section{Surface Driven Convection}
2  \label{sect:eg-bconv}  \label{sect:eg-bconv}
3    
4  \bodytext{bgcolor="#FFFFFFFF"}  \bodytext{bgcolor="#FFFFFFFF"}
# Line 22  Line 22 
22  for the surface driven convection experiment. The domain is doubly periodic  for the surface driven convection experiment. The domain is doubly periodic
23  with an initially uniform temperature of 20 $^oC$.  with an initially uniform temperature of 20 $^oC$.
24  }  }
25  \label{FIG:simulation_config}  \label{FIG:eg-bconv-simulation_config}
26  \end{figure}  \end{figure}
27    
28  This experiment, figure \ref{FIG:simulation_config}, showcasing MITgcm's non-hydrostatic capability, was designed to explore  This experiment, figure \ref{FIG:eg-bconv-simulation_config}, showcasing MITgcm's non-hydrostatic capability, was designed to explore
29  the temporal and spatial characteristics of convection plumes as they might exist during a  the temporal and spatial characteristics of convection plumes as they might exist during a
30  period of oceanic deep convection. It is  period of oceanic deep convection. It is
31    
# Line 50  uniform reference potential temperature Line 50  uniform reference potential temperature
50  used in this experiment is linear  used in this experiment is linear
51    
52  \begin{equation}  \begin{equation}
53  \label{EQ:linear1_eos}  \label{EQ:eg-bconv-linear1_eos}
54  \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )  \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )
55  \end{equation}  \end{equation}
56    
57  \noindent which is implemented in the model as a density anomaly equation  \noindent which is implemented in the model as a density anomaly equation
58    
59  \begin{equation}  \begin{equation}
60  \label{EQ:linear1_eos_pert}  \label{EQ:eg-bconv-linear1_eos_pert}
61  \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}  \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}
62  \end{equation}  \end{equation}
63    
# Line 72  the quantity that is carried in the mode Line 72  the quantity that is carried in the mode
72  As the fluid in the surface layer is cooled (at a mean rate of 800 Wm$^2$), it becomes  As the fluid in the surface layer is cooled (at a mean rate of 800 Wm$^2$), it becomes
73  convectively unstable and  convectively unstable and
74  overturns, at first close to the grid-scale, but, as the flow matures, on larger scales  overturns, at first close to the grid-scale, but, as the flow matures, on larger scales
75  (figures \ref{FIG:vertsection} and \ref{FIG:horizsection}), under the influence of  (figures \ref{FIG:eg-bconv-vertsection} and \ref{FIG:eg-bconv-horizsection}), under the influence of
76  rotation ($f_o = 10^{-4}$ s$^{-1}$) .  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
77    
78    \begin{rawhtml}MITGCM_INSERT_FIGURE_BEGIN surf-convection-vertsection\end{rawhtml}
79  \begin{figure}  \begin{figure}
80  \begin{center}  \begin{center}
81   \resizebox{15cm}{10cm}{   \resizebox{15cm}{10cm}{
# Line 83  rotation ($f_o = 10^{-4}$ s$^{-1}$) . Line 84  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
84  \end{center}  \end{center}
85  \caption{  \caption{
86  }  }
87  \label{FIG:vertsection}  \label{FIG:eg-bconv-vertsection}
88    \label{fig:surf-convection-vertsection}
89  \end{figure}  \end{figure}
90    \begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml}
91    
92    \begin{rawhtml}MITGCM_INSERT_FIGURE_BEGIN surf-convection-horizsection\end{rawhtml}
93  \begin{figure}  \begin{figure}
94  \begin{center}  \begin{center}
95   \resizebox{10cm}{10cm}{   \resizebox{10cm}{10cm}{
# Line 94  rotation ($f_o = 10^{-4}$ s$^{-1}$) . Line 98  rotation ($f_o = 10^{-4}$ s$^{-1}$) .
98  \end{center}  \end{center}
99  \caption{  \caption{
100  }  }
101  \label{FIG:horizsection}  \label{FIG:eg-bconv-horizsection}
102    \label{fig:surf-convection-horizsection}
103  \end{figure}  \end{figure}
104    \begin{rawhtml}MITGCM_INSERT_FIGURE_END\end{rawhtml}
105    
106  Model parameters are specified in file {\it input/data}. The grid dimensions are  Model parameters are specified in file {\it input/data}. The grid dimensions are
107  prescribed in {\it code/SIZE.h}. The forcing (file {\it input/Qsurf.bin}) is specified  prescribed in {\it code/SIZE.h}. The forcing (file {\it input/Qsurf.bin}) is specified
# Line 111  The implicit free surface form of the Line 117  The implicit free surface form of the
117  pressure equation described in Marshall et. al \cite{marshall:97a} is  pressure equation described in Marshall et. al \cite{marshall:97a} is
118  employed. A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous  employed. A horizontal Laplacian operator $\nabla_{h}^2$ provides viscous
119  dissipation. The thermodynamic forcing appears as a sink in the potential temperature,  dissipation. The thermodynamic forcing appears as a sink in the potential temperature,
120  $\theta$, equation (\ref{EQ:global_forcing_ft}). This produces a set of equations  $\theta$, equation (\ref{EQ:eg-bconv-global_forcing_ft}). This produces a set of equations
121  solved in this configuration as follows:  solved in this configuration as follows:
122    
123  \begin{eqnarray}  \begin{eqnarray}
124  \label{EQ:model_equations}  \label{EQ:eg-bconv-model_equations}
125  \frac{Du}{Dt} - fv +  \frac{Du}{Dt} - fv +
126    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -    \frac{1}{\rho}\frac{\partial p^{'}}{\partial x} -
127    \nabla_{h}\cdot A_{h}\nabla_{h}u -    \nabla_{h}\cdot A_{h}\nabla_{h}u -
# Line 190  For an extreme maximum flow speed of $ | Line 196  For an extreme maximum flow speed of $ |
196  50 m, the implied maximum timestep for stability, $\delta t_u$ is  50 m, the implied maximum timestep for stability, $\delta t_u$ is
197    
198  \begin{eqnarray}  \begin{eqnarray}
199  \label{EQ:advectiveCFLcondition}  \label{EQ:eg-bconv-advectiveCFLcondition}
200  %\delta t_u = \frac{\Delta x}{| \vec{u} \} = 50 s  %\delta t_u = \frac{\Delta x}{| \vec{u} \} = 50 s
201  \end{eqnarray}  \end{eqnarray}
202    
# Line 669  cg3dTargetResidual=1.E-9, Line 675  cg3dTargetResidual=1.E-9,
675  \end{verbatim}  \end{verbatim}
676  Sets the tolerance which the three-dimensional, conjugate  Sets the tolerance which the three-dimensional, conjugate
677  gradient solver will use to test for convergence in equation  gradient solver will use to test for convergence in equation
678  \ref{EQ:congrad_3d_resid} to $1 \times 10^{-9}$.  \ref{EQ:eg-bconv-congrad_3d_resid} to $1 \times 10^{-9}$.
679  The solver will iterate until the  The solver will iterate until the
680  tolerance falls below this value or until the maximum number of  tolerance falls below this value or until the maximum number of
681  solver iterations is reached. Used in routine  solver iterations is reached. Used in routine
# Line 801  directed upwards, according to the model Line 807  directed upwards, according to the model
807  \end{center}  \end{center}
808  \caption{  \caption{
809  }  }
810  \label{FIG:Qsurf}  \label{FIG:eg-bconv-Qsurf}
811  \end{figure}  \end{figure}
812    
813  \subsection{Running the example}  \subsection{Running the example}
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