Fig. 1
Maximum module of the eigenvalues of the amplification matrix for different values of the parameter and wave numbers from 10−2 m−1 to 10−6 m−1, using a time step of 1200 s and 40 regularly spaced vertical levels with the top of the atmosphere at 20 km. Asselin time filter coefficient α=0.07. Decentring factor is ε=0 (thin line) and ε=0.07 (thick line).
Fig. 2
Vertical velocity (contour interval 0.1 ms−1) given by the non-linear model (left) and the linear Boussinesq solution (right) corresponding to the quasi-linear non-hydrostatic flow test. The stability is N=0.02 s−1 and the horizontal initial velocity u =15 ms−1. The mountain parameters are 100 m height and 500 m half width. The results are presented on a domain of 14 km height and 14 km width with the mountain positioned at 3.1 km from the left border of the picture. Horizontal and vertical resolutions are 200 m. Time step is 4 s and the plot corresponds to t=3000 s.
Fig. 3
Vertical velocity at t=1800 s for the Schär test. The time step is Δt=4 s, horizontal resolution Δx=250 m and vertical resolution Δz=150 m. The maximum height of the mountains is 750 m.
Fig. 4
Vertical velocity at t=1800 s for the Baldauf and Brdar test. The time step is Δt=3.125 s, horizontal resolution Δx=156.25 m and vertical resolution Δz=Δx/2.
Table 1
Vertical velocity errors for a test configuration with , U=20 ms−1 and . The tests have different horizontal and vertical resolutions and time steps. Vertical resolutions are
Table 2
Vertical velocity errors. Tests are configured with different values of the reference temperature, background horizontal velocity and decentring factor. Horizontal resolution is Δx=156.25 m and time step Δt=3.125 s in all cases
Fig. 5
Vertical velocity of the analytical linear solution (black line) and three numerical tests at the same horizontal resolution (Δx=625.0 m and Δz=Δx/2) and time steps Δt equal 12.5 s, 2.5 s and 0.5 s (red, green and blue lines, respectively). The tests are performed without background horizontal velocity, ε=0.07 and T¯=300K. (a) vertical velocity at t=1800 s and z=5000 m. (b) vertical velocity at x=200 km and z=5000 m. (c) is the frequency spectrum of (b).
Fig. 6
Rossby–Haurwitz wave test at day 15 simulated at T85 with 26 vertical levels. Fields plotted are zonal wind, meridional wind, vertical velocity and temperature at 850 hPa, and surface pressure and geopotential at 500 hPa.
Fig. 7
Jablonowski steady state test. RMSE of surface pressure for rotated angles of 0° (black), 45° (red) and 90° (blue). Bold lines and thin correspond to T85 and T42, respectively.
Fig. 8
Rossby wave train induced by a 2000-m-high mountain at day 5 and 15: geopotential height, zonal and meridional wind at 700 hPa.
Fig. 9
Rossby wave train induced by a 6000-m-high mountain at day 9. Velocity at level 1 and topography.
Table 3
Relative error of total mass and entropy (factor 10−6) for the different experiments after different integration days