Baroclinic wave

This page shows a simulation result of idealized numerical experiment of baroclinic wave using the discontinuous Galerkin method (DGM). An example of the setting files is given in rootdir/model/atmosphere3d/test/case/baroclinic_wave/.

1. Description of dynamical core

Please see XX.

2. Experimental setup

The experiment setup is based on Ullrich et al. (2015). We consider a three-dimensional channel domain defined as $D = {(x,y,z)| 0 ≤ x ≤ L_x,0 ≤ y ≤ L_y,0 ≤ z ≤ z_T }$, where $L_x = 40000$ km, $L_y = 6000$ km, and $z_T = 30$ km. For the meridional, top, and bottom boundaries, no-flux boundary condition is applied. The zonal boundaries are periodic. As for rotation effect, we assume the beta-plane approximation.

The basic state is a steady-state geostrophically balanced flow, and the analytic expressions are derived by Ullrich et al. (2015). To trigger the baroclinic instability, we add a perturbation into the basic state of zonal flow.

In next section, we show results in the case of using the following model parameters

  • Spatial resolution: NeX=80, NeY=12, NeZ=12, p=7 (LGL nodes)
  • Explicit diffusion with 4th-order differential operator with the decay coefficient 4x10^15[ m4/s]
  • Element-wise 16th-order exponential filter is applied for all modes and the factor of filter strength, $\alpha$, is 1.0; for example, the highest mode is dumped by $\exp{(-\alpha)}$.
  • $\Delta t=30$ [sec] (with HEVI method and temporal scheme of ARK324 )

3. Result

In this animation, upper panel shows the horizontal distributions of surface pressure (tone) and surface temperature (contour). The rectangle region bounded by red line is extended in lower panel.

4. Reference

  • Hesthaven, J. S., and T. Warburton, 2007: Nodal discontinuous Galerkin methods: algorithms, analysis, and applications, Springer Science & Business Media

  • Ullrich, P. A., K. A. Reed, and C. Jablonowski. “Analytical initial conditions and an analysis of baroclinic instability waves in f‐and β‐plane 3D channel models.” Quarterly Journal of the Royal Meteorological Society 141.693 (2015): 2972-2988.