Understanding the Performance of an Unstructured-Mesh Global Shallow Water Model on Kinetic Energy Spectra and Nonlinear Vorticity Dynamics

A strategy for evaluating a global shallow water model based on aspects of kinetic energy spectra and nonlinear vorticity dynamics is proposed in this study. The kinetic energy spectra and nonlinear vorticity dynamics of a recently developed global shallow water model on an unstructured mesh are evaluated in comparison with the benchmark solutions from a global high-resolution spectral model. The results show that the kinetic energy spectra, the rotational and divergent components, the stationary and transient components, and the nonlinear spectral fluxes of the developed shallow water model agree well with those generated by the reference model. In addition, the influence of different flux operators for transporting the potential vorticity (PV) is assessed specifically. It is indicated that the second-order flux operator leads to a spurious increase in the kinetic energy at the tail of the spectrum, whereas the upwind third-order flux operator does not support this behavior owing to implicit numerical diffusion. Moreover, the nonlinear vorticity dynamics is studied by using colliding modons. It is found that the grid-point model maintains the symmetrical pattern of vortices, and generates similar kinetic energy spectra and nonlinear spectral fluxes to the reference model. The evaluation provides a reference for assessing the shallow water model in terms of nonlinear dynamics, and the developed global shallow water model presents a good example.