Rossby Vortex Simulation on a Paraboloidal Coordinate System Using the Lattice Boltzmann Method

In this paper, we apply our compressible lattice Boltzmann model to a rotating parabolic coordinate system to simulate Rossby vortices emerging in a layer of shallow water flowing zonally in a rotating paraboloidal vessel. By introducing a scaling factor, nonuniform curvilinear mesh can be mapped to a flat uniform mesh and then normal lattice Boltzmann method works. Since the mass per unit area on the two-dimensional (2D) surface varies with the thickness of the water layer, the 2D flow seems to be "compressible" and our compressible model is applied. Simulation solutions meet with the experimental observations qualitatively. Based on this research, quantitative solutions and many natural phenomena simulations in planetary atmospheres, oceans, and magnetized plasma, such as the famous Jovian Giant Red Spot, the Galactic Spiral-vortex, the Gulf Stream, and the Kuroshio Current, etc,, can be expected.