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.

Assessing Adaptive Mesh Refinement (AMR) in a Forced Shallow-Water Model with Moisture

“…Future work will consist of extending the analysis to AMR in the full 3D nonhydrostatic dynamical core, focusing on similar simplified physics parameterization schemes. This work has already started and initial results for a dry colliding modons test case (Lin et al 2017) and the idealized moist tropical cyclone test case by Reed andJablonowski (2011, 2012) are documented in Ferguson (2018).…”

A Layer‐Averaged Nonhydrostatic Dynamical Framework on an Unstructured Mesh for Global and Regional Atmospheric Modeling: Model Description, Baseline Evaluation, and Sensitivity Exploration

“…We have also examined simulations using NCT non ¯ local ‐PV4 (the neutral fourth‐order flux operator), and the results are similar to those in NCT non ¯ local ‐PV2 (Figure S3a). Compared to the results in Lin et al (), the final position in NCT non ¯ local ‐PV2 is closer to that of FV 3 , while NCT local ‐PV3 is closer to CAM‐SE.…”

“…The colliding modon test was recently proposed to evaluate global dynamical cores in simulating nonlinear vorticity dynamics (Lin et al, 2017). Modons are isolated vortices that can maintain their pattern under relatively weak or random neighboring flow patterns, but they will be destroyed when the neighboring flow gets stronger (McWilliams et al, 1981;McWilliams & Zabusky, 1982).…”

“…These two demands have fostered the creation of global nonhydrostatic models on quasi‐uniform grids (e.g., https://www.earthsystemcog.org/projects/dcmip-2012/; Ullrich et al, ). To this end, most newly developed global nonhydrostatic models have selected the icosahedral or hexagonal grid (e.g., Gassmann, ; Satoh et al, ; Walko & Avissar, ; Wehner et al, ; Zängl et al, ), the cubed sphere grid (e.g., Choi & Hong, ; Giraldo et al, ; Jung et al, ; Lin et al, ; Nair, ; Rancic et al, ; Ullrich & Jablonowski, ), the centroidal Voronoi grid (e.g., Skamarock et al, ), the octagonal grid (e.g., Kühnlein et al, ), and the Yin‐Yang grid (e.g., Qaddouri and Lee, ); see Staniforth and Thuburn () for an earlier review. Meanwhile, because of a trend toward achieving regional modeling at finer scales in the context of a global model (e.g., Weller et al, ), the variable‐resolution (VR) approach has received growing attention in recent years (e.g., Gettelman et al, ; Harris et al, ; Ringler et al, ).…”

Um método robusto de volumes finitos de alta ordem para advecção em malhas esféricas geodésicas

“…No trabalho de Ronchi et al (1996), o pesquisador contribuiu com características adicionais, melhorando o espaçamento e ortogonalidade da malha cubada. Atualmente, essa malha vem sendo usada por grupos de pesquisa na modelagem atmosférica (Chen e Xiao, 2008;Nair et al, 2005; Ullrich e Jablonowski, 2012) e por modelos operacionais, como o FV3 (Finite-Volume Cubed-Sphere) (Lin et al, 2017) e o CAM-SE (Atmosphere Model Spectral Elements) (Lauritzen et al, 2018).…”