The mountain-wave test case is actually set up to run on a hexagonal mesh, rather than a quadrilateral mesh; so, you could start with the periodic_hex tool in the MPAS-Tools repository. The mesh that is provided with the mountain-wave test case has just 4 cells in the y-direction, and it is periodic in the y-direction, giving an approximation to an xz-plane.
If you were to try generating your own meshes using the periodic_hex tool, there are a couple of important considerations:
1) Ensure that you have at least 4 cells in the y-direction (assuming you're planning to run the simulation in the xz-plane); and
2) ensure that the orientation of the cells is correct.
The orientation of the cells produced by the periodic_hex tool is as in the attached "incorrect_mesh.png" figure. For the mountain-wave test case, specifically, you'll need to ensure that the orientation of the cells is as in the attached "correct_mesh.png" figure. Although I haven't tried this myself, you may be able to make a yz-plane mesh (with 4 cells in the x-direction) using the periodic_hex tool, then to transpose the x- and y-directions using a python script or something similar.