Colliding Modons: A Nonlinear Test for the Evaluation of Global Dynamical Cores

Abstract

The modon, a pair of counter-rotating vortices propelling one another along a straight line, is an idealization of some observed large-scale and small-scale atmospheric and oceanic processes (e.g., twin cyclones), providing a challenging nonlinear test for fluid-dynamics solvers (known as “dynamical cores”). We present an easy-to-setup test of colliding modons suitable for both shallow-water and three-dimensional dynamical cores on the sphere. Two pairs of idealized modons are configured to collide, exchange vortices, and depart in opposite directions, repeating indefinitely in the absence of ambient rotation. This test is applicable to both hydrostatic and nonhydrostatic dynamical cores and is particularly challenging for refined grids on the sphere, regardless of solution methodology, or vertical coordinate. We applied this test to three popular dynamical cores, used by three different general circulation models: the Spectral-Element (SE) core of the Community Atmosphere Model, the Geophysical Fluid Dynamics Laboratory (GFDL) spectral core, and the GFDL Finite-Volume Cubed-Sphere dynamical core (FV3). Tests with a locally refined grid and nonhydrostatic dynamics were also performed with FV3. All cores tested were able to capture the propagation, collision, and exchange of the modons, albeit the rate at which the modon was diffused varied between the three cores and showed a strong dependence on the strength of hyperdiffusion.