Fig. 1
Summary of the simulation set, and key to the scatter plots in this article (Figs. 4a, 4b, 8b, 9, 10, 12–14). The right-most column shows the shade and relative size of symbols used for simulations with parameters given to the left.
Fig. 2
The initial wind field. (a) Relative vorticity and (b) wind speed in the horizontal plane at an arbitrary altitude below z=6 km.
Fig. 3
(a)–(i) Snapshots of the vertically integrated rain mass density (σ) in 9 out of the 12 primary simulations used for this study. The value of σ is normalised to the maximum value in the snapshot. The sea-surface temperature T s and Coriolis parameter f are printed on the upper edge of each panel, whereas the time of the snapshot (in days) is printed on the bottom edge. High-top simulations are labelled with an HT on the bottom-left corner.
Fig. 4
(a) Number of significant vortices (N v) versus the Coriolis parameter f. Downward and upward pointing triangles represent data from LT and HT simulations, respectively. The dotted curves show linear and cubic growth of N v with increasing f, whereas the solid curve shows quadratic growth. (b) Scatter plot of the maximum azimuthal wind speed V max against the radius of maximum wind r max in the TCs considered for statistical analysis. The diamonds and circles respectively represent data points for the strongest and median vortices defined in Section 2.4. A ‘+’ or ‘×’ behind a symbol means that the data point is taken from an HT simulation. The shading and relative size distribution of symbols in (a) and (b) are explained in Fig. 1. Each datum in (b) is a five-snapshot average, as explained in Section 4. (c) Colour contour plot of the azimuthally averaged wind speed () in a typical TC, with markers at V max and r max. Specifically, this TC is from the HT simulation with T s=26°C and f=2.5×10−5 s−1.
Fig. 5
Time series of the maximum wind speed (V max) of TCs selected from HT simulations with (a) T s=32°C and (b) T s=26°C. In both simulations, f=10−4 s−1. The dotted curves show the maximum wind speed given by modern axisymmetric steady-state theory [i.e., V th–l given by eq. (5)]. The time dependence of V th–l is due to changes in local conditions that determine its value. The dotted curves begin when the nominal TC outflow altitude (z 0 defined in Section 3) settles to within one vertical grid point of its final value. The asterisk in each plot marks the time at which sampling begins for obtaining scatter plot data from the depicted simulation.
Fig. 6
Correspondence between the TC outflow region and the altitude z o where the horizontally averaged cloud water mixing ratio q c(z) is peaked. (a) Shaded contour plot of the radial velocity in the r–z plane for the strongest TC in the LT simulation with T s=28°C and f=3.8×10−5 s−1 at t=10 d. The dotted curves are zero-contours of ; dark/bright shades indicate inflow/outflow. A graph of q c (dashed curve) is superposed on the contour plot of . The values of q c are given on the top axis. (b) Same as (a) but for the LT simulation with T s=30°C and f=10−4 s−1at t=5.25 d. (c) Same as (a) but for the HT simulation with T s=32°C and f=10−4 s−1 at t=10.5 d.
Fig. 7
Illustration of the fields used in computing the convective asymmetry variable δσ for an arbitrary TC. Plots (a) and (b) are colour contour plots of the ϕ-averaged and total z-integrated rain-mass densities and σ, respectively, normalised to the maximum of σ. Plot (c) shows the radial profiles of and normalised to max(). The RMW (in the boundary layer) is at r=35.2 km.
Fig. 8
(a) Time series of δσ (solid curve) for a TC found in the HT simulation with T s=26°C and f=10−4 s−1. The dashed curve shows the time series of V th–l/V th–lb, whose difference from unity is a dimensionless measure of imbalance. The statistical relationship between δσ and V th–l/V th–lb is examined in Section 5.1. (b) Scatter plot of δσ against the core vertical kinetic energy asymmetry δKEw. The solid line striking through the data points is a power-law curve-fit. The symbols are the same as in Fig. 4b.
Fig. 9
Maximum wind speed V max divided by one of two theoretical values vs. the inner-core convective asymmetry variable δσ. The theoretical wind speed V th–lb in (a) assumes gradient-wind and hydrostatic balance. The theoretical wind speed V th–l in (b) accounts for imbalance. Data are shown for the median and strongest vortices (after achieving peak intensity) in all simulations. The symbols are the same as in Fig. 4b (cf. Fig. 1). The top dotted line in (a) shows the decay trend for δσ<1 in most simulations. The lower dotted lines in (a) show the decay trends for two simulations that fall below the main curve. The solid horizontal line in both (a) and (b) corresponds to perfect agreement with theory. The dotted lines in (b) correspond to 10% positive and negative deviations from theory. The lightly shaded region in the lower right corner of (b) shows where δσ≥0.8 and only underachieving vortices with V max<V th–l exist.
Fig. 10
The ratio of theoretical wind speeds for unbalanced and balanced TCs (V th–l/V th–lb) vs. δσ. The symbols are generally the same as in Fig. 4b. However, the white plus-marks are from additional simulations with capped surface-exchange coefficients, T s=26°C, and either f=2.5×10−5s−1 (small symbol) or f=10−4s−1 (large symbols).
Fig. 11
Mean structure above the inflow layer for simulated TCs with (a) δσ=0.13 and (b) δσ=1.4. The solid and dashed curves are contours of constant angular momentum (M) and saturation entropy (), sparsely labelled in units of 106 m2s−1 and J kg−1K−1, respectively. The relatively thick contours pass through the location of V max. The shading shows the azimuthally averaged vertical velocity . The TC in (a) is the sole vortex at the end of the HT simulation with T s=26°C and f=2.5×10−5s−1. The TC in (b) is one of the median vortices near the end of the LT simulation with T s=30°C and f=10−4s−1. In both cases, the profiles are averages over five snapshots taken 6 hours apart.
Fig. 12
Comparison of the reliability of different asymmetry variables for predicting V max/V th. (a–d) Scatter plots of V max/V th against (a) δσ, (b) δw, (c) δu and (d) Tilt. The rain-mass asymmetry δσ is the most reliable predictor of those considered here. The symbols are the same as in Fig. 4b.
Fig. 13
(a) Non-dimensional wind speed V max/V th vs. the product of the lower-middle tropospheric moist-entropy deficit and the convective asymmetry variable δσ. The curve-fit (solid line) is given by . (b) Scatter plot of δσ against . The symbols are generally the same as in Fig. 4b, but the small blue dots in (a) show instantaneous measurements as opposed to averages taken over five snapshots (white, black and grey symbols).
Fig. 14
Dimensional wind speed V max versus δσ. The curve-fit (solid line) is given by in units of m s−1. The symbols are the same as in Fig. 4b.
Fig. A.1.
(a) Reference plot of σ showing N v=10 significant vortices at t=8.75 d in the LT RAMS simulation with T s=30°C and f=10−4 s−1. The greyscale is the same as in Fig. 3. (b) Illustration of the areas used to search for the height-dependent vortex centres. A 0,α covers the white region in the vicinity of a particular vortex; A 1,α covers the white and light grey regions; A 2,α covers the white, light grey and dark grey regions. The boundaries of A 2,α are traced with yellow contours to aid the eye. In general, .