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Jet tutorial with Julia

This is a very simple example that shows the model stability in transitional flows.

Make a bathymetry

Below is a Julia script to make the bathymetry. 

    using GMT

    ny=16*16;
    nx=16*32;

    dx=5.0;

    xmin=0;
    xmax=nx*dx;

    ymin=0;
    ymax=ny*dx;

    Bathy=zeros(nx,ny);

    Bathy.=-5.0;

    Bathy[170:172,:].=5.0;
    Bathy[170:172,127:129].=-5.0;

    Bathy[:,1:2].=5.0;
    Bathy[:,(end-1):end].=5.0;

    G = mat2grid(transpose(Bathy), 1,[xmin xmax ymin ymax -5.0 5.0 1 dx dx])
    cmap = grd2cpt(G);      # Compute a colormap with the grid's data range
    grdimage(G, lw=:thinnest, color=cmap, fmt=:png, show=true)

    gmtwrite("bathy.asc", G; id="ef");

The result is a grid domain looking like this: Bathy file You can also use the bathy.asc file in the example folder.

Make Bnd files

We are going to set the water level to 0.0m on the right and 1.0 on the left and keep it constant. To do that we create 2 files right.txt and left.bnd

right.bnd
# This is the right boundary
0.0 0.0
3600.0 0.0
left.bnd
# This is the left boundary
0.0 1.0
3600.0 1.0

Set up the BG_param.txt file

First it is good practice to document your parameter file:

BG_param.txt
    ##############################
    ## Jet demo
    # CB 04/05/2019
Then specify the bathymetry file to use. We will use the entire domain and resolution of the file so no need for other parameter for specifying the domain. 
    bathy=bathy.asc
Specify the parameter theta to control the numerical diffusion of the model. but first let's leave it to the default. 
    theta=1.3;
This is a relatively small model so we can force the netcdf variable to be saved as floats. 
    smallnc=0
Sepcify the model duration, output timestep and output file name and variables 
    endtime=1800
    outtimestep=10
    outfile=Jet_demo.nc
    outvars=zb,uu,vv,zs,vort;
Specify absorbing boundaries for left and right (There is a wal at the top and bottom so no need to specify any boundary there). 
    right = 3; # Absorbing bnd
    rightbndfile = right.bnd

    left=3; # Absorbing bnd
    leftbndfile = left.txt

Run the model

If you are on windows simply double-click on the executable and on linux launch the binary.

Vorticity output (vort variable) should look like this:

Things to try

  • What happens when using a different value for theta (1-2.0)
  • What happens when specifying a different type of boundary on the right
  • What happens when you bring the boundary close to the jet
  • Why is the jet so unstable/asymmetrical? (what are the initial condition like?)