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3.16.2 Binary input data

Figure 3.17: Horizontal grid spacing, $ \Delta x$ , in the across-slope direction for the gravity plume experiment.
\includegraphics[width=\textwidth,height=.3\textheight]{s_examples/plume_on_slope/dx.eps}

Figure 3.18: Topography, $ h(x)$ , used for the gravity plume experiment.
\includegraphics[width=\textwidth,height=.3\textheight]{s_examples/plume_on_slope/Depth.eps}

Figure 3.19: Upward surface heat flux, $ Q(x)$ , used as forcing in the gravity plume experiment.
\includegraphics[width=\textwidth,height=.3\textheight]{s_examples/plume_on_slope/Qsurf.eps}

The domain is $ 200$  m deep and $ 6.4$  km across. Uniform resolution of $ 60\times3^1/_3$  m is used in the vertical and variable resolution of the form shown in Fig. 3.17 with $ 320$ points is usedin the horizontal. The formula for $ \Delta x$ is:

$\displaystyle \Delta x(i) = \Delta x_1 + ( \Delta x_2 - \Delta x_1 ) ( 1 + \tanh{\left(\frac{i-i_s}{w}\right)} ) /2 $

where
$\displaystyle Nx$ $\displaystyle =$ $\displaystyle 320$  
$\displaystyle Lx$ $\displaystyle =$ $\displaystyle 6400 \;\;$   (m)  
$\displaystyle \Delta x_1$ $\displaystyle =$ $\displaystyle \frac{2}{3} \frac{Lx}{Nx} \;\;$   (m)  
$\displaystyle \Delta x_2$ $\displaystyle =$ $\displaystyle \frac{Lx/2}{Nx-Lx/(2 \Delta x_1)} \;\;$   (m)  
$\displaystyle i_s$ $\displaystyle =$ $\displaystyle Lx/( 2 \Delta x_1 )$  
$\displaystyle w$ $\displaystyle =$ $\displaystyle 40$  

Here, $ \Delta x_1$ is the resolution on the shelf, $ \Delta x_2$ is the resolution in deep water and $ Nx$ is the number of points in the horizontal.

The topography, shown in Fig. 3.18, is given by:

$\displaystyle H(x) = -H_o + (H_o - h_s) ( 1 + \tanh{\left(\frac{x-x_s}{L_s}\right)} ) / 2 $

where
$\displaystyle H_o$ $\displaystyle =$ $\displaystyle 200 \;\;$   (m)  
$\displaystyle h_s$ $\displaystyle =$ $\displaystyle 40 \;\;$   (m)  
$\displaystyle x_s$ $\displaystyle =$ $\displaystyle 1500 + Lx/2 \;\;$   (m)  
$\displaystyle L_s$ $\displaystyle =$ $\displaystyle \frac{(H_o - h_s)}{2 s} \;\;$   (m)  
$\displaystyle s$ $\displaystyle =$ $\displaystyle 0.15$  

Here, $ s$ is the maximum slope, $ H_o$ is the maximum depth, $ h_s$ is the shelf depth, $ x_s$ is the lateral position of the shelf-break and $ L_s$ is the length-scale of the slope.

The forcing is through heat loss over the shelf, shown in Fig. 3.19 and takes the form of a fixed flux with profile:

$\displaystyle Q(x) = Q_o ( 1 + \tanh{\left(\frac{x - x_q}{L_q}\right)} ) / 2 $

where
$\displaystyle Q_o$ $\displaystyle =$ $\displaystyle 200 \;\;$   $\displaystyle \mbox{(W m$^{-2}$)}$  
$\displaystyle x_q$ $\displaystyle =$ $\displaystyle 2500 + Lx/2 \;\;$   (m)  
$\displaystyle L_q$ $\displaystyle =$ $\displaystyle 100 \;\;$   (m)  

Here, $ Q_o$ , is the maximum heat flux, $ x_q$ is the position of the cut-off and $ L_q$ is the width of the cut-off.

The initial tempeture field is unstratified but with random perturbations, to induce convection early on in the run. The random perturbation are calculated in computational space and because of the variable resolution introduce some spatial correlations but this does not matter for this experiment. The perturbations have range $ 0-0.01$   $ ^{\circ}\mathrm{K}$ .

next up previous contents
Next: 3.16.3 Code configuration Up: 3.16 Gravity Plume On Previous: 3.16.1 Configuration   Contents
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