This tutorial is for less experienced Gimp users.
Open Gimp and create new image. I started with 1024x768 in the example.
Fisrt we want to change the foreground color by clicking on foreground to open the tool.
Use your cursor to choose a color. I chose deep blue as that will contrast nicely against white background. Then click OK.
Select Blend tool.
Select Shape then Bi-linear.
Select Repeat then Triangle.
Now drag a line about a fifth of the way down the image.
You should end up with an image similar to this.
To get the effects we want, open Filters select Distorts and choose IWarp.
In the IWarp window select Swirl CW. Adjust Deform radius to 46 and Deform amount to 0.30. These settings are not carved in stone. Changing them will change the effect on the image. You may want more or less according to what you're working toward.
In the preview window click and drag to see effect applied to the image.
Increase the Deform radius to 125 and stir the image to get the desired swirl effect. When your satisfied with your image click OK and save.