Fig. 1.
Frequency of gravity wave with g=10 m s−2, C=300 m s−1, Δx=1000 m, Δz=500 m and S 0=1.0−5 m−1: (a) ω δ=1 (with Δt=1.49 s, solid line) and ω δ=1−σ g (dash line); (b) ω δ=4 (with Δt=2.98 s) and ω δ=4−σ g and (c) ω δ=16 (with Δt=5.96 s) and ω δ=16−σ g .
Fig. 2.
ω δ=16 (solid line) with Δt=1.179×10−2 s, Δx=Δz=5 m; and ω δ=16−σ g (dotted line) is from −2.5×10−8 to 2×10−8 s−1 with contour interval of 5×10−9 s−1.
Fig. 3.
(a) ω HE-VI with Δx=1000 m, Δz=500 m, Δt=2.98 s and ω HE-VI−σ g (dash line), contour interval is 5×10−8 s−1; (b) same as (a) except Δx=Δz=5 m, Δt=1.179×10−2 s, contour interval of dotted lines is 1×10−7 s−1.
Fig. 4.
(a) Initial x-component wind for Kelvin–Helmholtz instability for Sections 4.1–4.3; (b) initial background (solid line) and perturbation θ′ (colour) for Section 4.1.
Fig. 5.
(a) Simulated θ at t=320 s with Δtb=0.4 s from θ δ=1 (Δts=0.01 s, black), θ δ=4 (Δts=0.02 s, green), θ δ=16 (Δts=0.04 s, red) and θ HE-VI(Δts=0.02 s, blue), contour interval is 0.5 K; (b) θ δ=1 (Δts=0.01 s)−θ δ=4 (Δts=0.02 s), contours from −0.03 to 0.02 K with interval of 0.005 K; (c) θ δ=1 (Δts=0.01 s)−θ δ=16 (Δts=0.04 s), contours from −0.12 to 0.1 K with interval of 0.02 K; (d) θ δ=1 (Δts=0.01 s)−θ HE-VI (Δts=0.02 s), contours from −0.02 to 0.03 K with interval of 0.005 K.
Table 1. Variation of change of the total mass with respect to its initial value as function of time for MFB (δ=16, Δts=0.04 s) and HE-VI (Δts=0.02 s)
Fig. 6.
(a) Initial background (black) and perturbation θ′ (colour) for Sections 4.2 and 4.3; (b) simulated θ′ at t=240 s from FB with δ=1 (black), δ=4 (green), δ=16 (red) and HE-VI scheme (blue) with Δts=0.0025 s, Δtb=0.1 s and Δx=Δz=5 m. Contour interval is 0.005 K.
Fig. 7.
(a) Simulated θ′ at t=240 s from FB with δ=1, Δts=0.005 s (solid line); δ=4, Δts=0.01 s (long dash) and δ=16 Δts=0.02 s (short dash). Contour interval is 0.005 K; (b) θ′ from HE-VI with Δts=0.005 s (dotted line) and Δts=0.01 s (solid line). Contour interval is 0.005 K.
Fig. 8.
(a) Initial θ for FB with δ=1, Δts=0.008 s, Δx=Δz=5 m and Δtb=0.12 s. Contour interval is 0.05 K; simulated velocity v and θ(with δ=1) (b) at t=6 min; (c) t=12 min; (d) at t=18 min.
Fig. 9.
Simulated v and θ at t=18 min: (a) with δ=16, Δts=0.03 s; (b) with HE-VI, Δts=0.008 s; (c) θ δ=16 (Δts=0.03 s)−θ δ=1 (Δts=0.008 s), contours from −0.03 to 0.06 K with interval of 0.01 K and (d) θ HE-VI (Δts=0.008 s)−θ δ=1 (Δts=0.008 s), contours from −0.3 to 0.2 K with interval of 0.5 K.
Fig. 10.
Simulated w at t=6000 s with Δx=400 m, Δz=125 m and Δtb=10 s: (a) w δ=1 (Δts=0.25 s, black), w δ=4 (Δts=0.5 s, green), w δ=16 (Δts=1.0 s, red) and w HE-VI (Δts=1.0 s, blue); (b) w δ=16−w δ=1 (red) and w HE-VI−w δ=1 (blue), the contour interval is 0.02 ms−1.
