Fig. 1
Dependence of the wave frequency ω + (solid lines) and ω − (dashed lines) on the angular velocity parameter α for the azimuthal wavenumbers 1, 2, 3, 4, 5 as given by eq. (46), assuming the Coriolis parameter f=10−4 s −1, the maximum 10 m wind of 70 ms −1, the RMW of 30 km (i.e. α s =2.3×10−3 s −1). Shaded areas denote the regions where the linearisation and related wave approximations cannot be applied. Note that α=0 corresponds roughly to the tropopause at which , while α=α s corresponds to the Earth's surface z=0. Both ω ± and α are normalised by α s .
Fig. 2
(a) Time series of the maximum surface wind (blue) and the minimum surface pressure at the vortex centre (red) from the 120-h simulation of an idealised vortex using the HWRF model; and (b) radial profiles of the geopotential height wave amplitudes (m) valid at 72 h into integration for wavenumber 1 (black), wavenumber 2 (red), wavenumber 3 (blue), wavenumber 4 (cyan), and wavenumber 5 (purple). Dash line in the upper panel indicates the reference instant of time from which the wave analyses refer to.
Fig. 3
Evolution of azimuthal wavenumber 1 geopotential height perturbation φ′(r,λ,z,t) (shaded) at 750 hPa from minute 73 to 90 relative to the time origin 72-h into integration (dashed line in Fig. 2a) in a 5-day simulation of an idealised vortex, using the HWRF model. All perturbations are normalised by the wave amplitude Φ(r=R) at each corresponding time. The time stamp denotes the minutes relative to the 72-h reference. Red circle denotes the RMW R at each instant of time, and vectors denote the mean tangential wind.
Fig. 4
Similar to Fig. 3 but for different time window that exhibits the cyclonic propagation of the wavenumber 1.
Fig. 5
Similar to Fig. 3 but for the wavenumber 2 from minute 10 to minute 50.