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Gaussian Wave

This is a great example to test whether there are bugs in the model and how the boundary work.

Bathymetry

We start with a flat bathymetry with 0.0 everywhere. You still need a file for that!

Here a couple of suggestion on making the file:

  • Using GMT: 
    grdmath -R-5/5/-5/5 -I0.03921 0 MUL = bathy.nc

Using Julia: See section below with the hotstart file.

In any case you can pick up the file in the example folder.

Hortstart

We want to setup a bump in the water level centered in the middle of the bathy. IN the example below this is done using Julia, but it should be easily done in Matlab or Python. Note that the script below also generates a bathymetry file.

    using GMT

    xo=-5;
    yo=-5;

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

    len=10.0;

    dx=len/(nx-1);

    xx=collect(xo:len/(nx-1):(len+xo));
    yy=collect(yo:len/(ny-1):(len+yo));

    # Make a bathy file
    zb=zeros(nx,ny);
    G = mat2grid(transpose(zb), 1,[xx[1] xx[end] yy[1] yy[end] minimum(zb) maximum(zb) 1 dx dx])
    gmtwrite("bathy.asc", G; id="ef");

    #make the hotstart file
    hh=zeros(nx,ny);
    for i=1:nx
        for j=1:ny
            hh[i,j] = 1.0.+ 1.0.*exp.(-1.0*(xx[i].*xx[i] .+ yy[j].*yy[j]));
            #hh[i,j] =
        end
    end

    G = mat2grid(transpose(hh), 1,[xx[1] xx[end] yy[1] yy[end] minimum(hh) maximum(hh) 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("gauss.asc", G; id="ef");
    gmtwrite("gauss.nc", G);
    # GMT netcdf variable is "z" by default but the hotstart file needs "zs" for water surface
    gmt("grdmath gauss.nc 1.0 MUL = gauss_zs.nc?zs");

Make Bnd files

We are going to set the water level to 0.0m on all 4 sides and keep it constant. To do that we create 1 files zero.txt: 

    # This is the a boundary
    0.0 0.0
    3600.0 0.0

Set up the BG_param.txt file

First it is good practice to document your parameter file:

BG_param.txt
    ##############################
    ## Gaussian bump 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
This is a relatively small model so we can force the netcdf variable to be saved as floats. 
    smallnc=0
Specify the hotstart file: 
    hotstartfile=gauss_zs.nc;
Boundary conditions are all the same : 
    right = 3; # Absorbing bnd
    rightbndfile = zeros.txt

    top = 3; # Absorbing bnd
    topbndfile = zeros.txt

    bot = 3; # Absorbing bnd
    botbndfile = zeros.txt

    left=3; # Absorbing bnd
    leftbndfile=zeros.txt
Time keeping: 
    endtime=20;
    outtimestep=1;
Output parameters: 
    # Netcdf file for snapshot of the model domain
    outfile=Gauss_demo.nc
    outvars=zb,uu,vv,zs,vort;

    # Outpout a single txt file with all the model steps at the nearest node to location x=0.0, y=-4.0
    # This file will contain 5 column: time,zs,hh,uu,vv
    TSOfile=Southside.txt;
    TSnode=0.0,-4.0;

Run the model

Plot Southside.txt in your favorite tool.

Things to try

  • What happens with different boundary types
  • Try running with double precision. What is the difference?