mpas_len_disp

Horizontal length scale (in meters) for the diffusion

mpas_len_disp tested at 60000, 120000, 180000; default = 120000 for mpas120

Longer dissipation length scale (larger mpas_len_disp) means stronger dissipation; the length scale is directly proportional to the Smagorinsky viscosity, which is active particularly at high wavenumbers near the grid scale. By increasing this length scale we thus strengthen the diffusion at the grid scale. We tested 60 km, 120 km (default), and 180 km (default) as a way to broadly scale the aggressiveness of the diffusion in the mountain gravity wave test case. 

In the figure below, we plot relative vorticity at 300m altitude in the top row and a vertical slice of horizontal divergence at 45 degN in the bottom row, with mpas_len_disp = 60000 in the first column, 120000 in the second, and 180000 in the third. Notable results: grid imprinting or interpolation artifact at the northern boundary of the vorticity plots; noise in the vorticity plots on the lee side of the second mountain (around 150 deg) which smoothes with stronger diffusion; wave breaking and noise in the stratosphere which weakens with stronger diffusion (gravity waves only weakly penetrate tropopause in strongest diffusion case); generally weaker horizontal divergence with stronger diffusion, particularly around the second moutain. 

We also look at the zonal wind field at 300m altitude in all three cases, and the anomalies relevant to our control case (120000), with the intent to show where the numerical dissipation is acting in space how significant that contribution relative to the total magnitude of the flow. The plot below shows the former on the top row and the latter on the bottom row. In the top row, we see noise on the lee side of both mountains and where shear is the strongest in the center of the wave. These are the regions where the dissipation is the most (in)active (i.e. where we observe anomalies relative to the control). The response to the dissipation is monotonic, in that the weaker diffusion and stronger diffusion cases result in opposite sign responses relative to the control case. 

mpas_smagorinsky

Dimensionless coefficient relating the strain tensor and eddy viscosity for Smagorinsky diffusion

The Smagorinsky coefficient (mpas_smagorinsky_coef), which modulates the strength of diffusion based on local deformation and shear, was varied from 0.05 to 0.4 (default = 0.125). We tested values of 0.05, 0.2, 0.3, and 0.4. Similar to above, the top row shows relative vorticity at 300m altitude and the bottom row shows a vertical cross-section of horizontal divergence at 45 degN. As the diffusion increases, we observe a consistent damping of fine-scale features, indicating stronger smoothing of these structures.