Grid

The grid in this example is obtained with the onedgrid.m m-file which can be downloaded from

http://suntans.stanford.edu/downloads_stanford .

In this case, the one-dimensional grid contains 100 cells in the horizontal and 100 in the vertical, and the domain is 100 km long with a maximum depth of 3000 m. All edges are of type 1 except for the western boundary edge, which is of type 2. The shelf slope geometry is given by

$$d(x) = \left\{\begin{array}{ll} D_0 & x\le x_{mid}-L_s/2\\ ... ..._s+\frac{1}{2}\right] & \mbox{otherwise} . \end{array}\right.$$

where

$L_s=20$ km: Horizontal extent of slope.

$x_{mid}=65$ km: Center of slope.

$D_0=3000$ m: Maximum depth.

$D_s=500$ m: Shelf depth.

This depth profile is specified in boundaries.c in the function ReturnDepth with

Ls = 20000;
xmid = 65000;
D0 = 3000;
Ds = 500;
if(x<=xmid-Ls/2)
  return D0;
else if(x>xmid+Ls/2)
  return Ds;
else
  return D0-(D0-Ds)*((x-xmid)/Ls+0.5);

As with all the present examples, in order for this depth to be specified, the IntDepth parameter must be set to 0 in the suntans.dat parameter file, otherwise, depth data must be supplied in the file specified by depth in suntans.dat. As shown in Figure 14, this grid is stretched in the vertical in order to provide extra resolution at the top boundary. This is done by specifying a positive stretching factor (as opposed to a negative stretching factor for the bottom boundary layer, as in Section 6.4) of $r=1.025$ (suntans.dat: rstretch = 1.025), which causes each grid layer to be 1.025 times thicker than the layer above it.

Figure 14: Depiction of the bathymetry and vertically stretched grid for the internal waves problem. Minimum grid spacing: 6.94 m, maximum: 79.94 m.

0.8