Experiment 2 compared with those in Experiment 1 are the slightly larger maximum at a height of 9 km and the stronger downdraught at a height of 2 km (Table 6.2). The value ofζmax in Experiment 2 is similar also to that in Experiment 1 (Table 6.3). The maximum
at heights of 500 m and 1 km are almost identical in both experiments, which is expected as both have identical wind profiles below a height of 2 km. The maximum at a height of 4 km is larger in Experiment 2, which is due to the additional vertical vorticity generated by the tilting of horizontal vorticity above a height of 2 km.
In Chapter 5 it was shown that a convective cell that develops in an environment where the horizontal vorticity changes sign at some height has a vertical vorticity dipole that reverses in sign with height. Figure 6.10 shows horizontal cross sections of the vertical component of relative vorticity in Experiment 2, at various times and heights. The top panels of Figure 6.10 show the vorticity dipole at early times and at lower levels, where the background vertical wind shear is positive. There is a vertical vorticity dipole that “twists” and changes its orientation with height, similar to the vorticity dipoles shown above. The lower panels of Figure 6.10 show the vorticity dipole at heights where the background vertical shear is negative. The vertical vorticity dipole reverses in sign between heights of 4 km and 6 km, similar to Experiments 2 and 3 in Chapter 5. The dipole at a height of 4 km is the smallest in horizontal extent of all heights shown as it nears the height where it reverses in sign.
In summary, the convective cell that develops in an environment with a clockwise turning hodograph in the boundary layer, and with negative shear above that, develops a vertical vorticity dipole that rotates at lower levels with height and time, and reverses in sign at mid-upper levels. The rotation of the dipole occurs as described in previous sections, and is due to the rotation of the horizontal vorticity vectors associated with the clockwise turning hodograph. Above the boundary layer the horizontal vorticity reverses in sign as the vertical shear becomes negative, and the vertical vorticity dipole reverses also in sign, corroborating results from Chapter 5.
6.5
Stronger and weaker background flow
Experiments 3 and 4 are repeats of Experiment 1 with different magnitudes of background wind speed aloft, Va, which is 5 m s−1 in Experiment 3 and 15 m s−1 in Experiment 4,
compared to 10 m s−1 in Experiment 1 (Table 6.1). Thus Experiment 3 has weaker vertical shear at low levels than in Experiment 1, while Experiment 4 has stronger vertical shear.
The magnitudes of wmax and wmin found in Experiment 3 are the largest of all the
experiments performed, with values of 28.4 and 11.7 m s−1, respectively (Table 6.2). This result is consistent with the findings of Rozoff (2007), Wissmeier and Smith (2011) and Chapter 5 that convective cells rising in a environment with weaker vertical or horizontal shear tend to have the strongest vertical velocities. In Experiment 3 the w2max, w5max
and w9max occur sooner than in any other experiment, while the w2max and w9max are
the largest found in this chapter. In the weakly-sheared environment the initial thermal experiences less deformation and develops more rapidly, a result found also in the previous
104 6. Effects of a vortex boundary-layer wind profile on deep convection
(a) (b) (c)
(d) (e) (f)
Figure 6.10: Horizontal cross section of the vertical vorticity at various heights in Exper- iment 2 at chosen times. Contour interval: 2×10−3 s−1. Solid (red) contours positive, dashed (blue) contours negative. The thin black curve shows the zero contour. The thick black solid contour shows the 2 m s−1 vertical velocity and thick black dashed contour shows the -2 m s−1 vertical velocity.
6.5 Stronger and weaker background flow 105
(a) (b) (c)
(d) (e) (f)
Figure 6.11: Horizontal cross section of the vertical vorticity at heights of 1 km, 2 km and 4 km in Experiment 3 (a, b and c) and Experiment 4 (d, e and f) at chosen times. Contour interval: see Figure 6.10.
chapter. In contrast, the magnitude of wmax and wmin in Experiment 4 are smaller than
those in Experiment 3, and are more comparable to those in Experiment 1. Further,w2max,
w5max and w9max occur later because of the larger deformation of the initial thermal by
the stronger vertical shear.
Despite having the largest wmax, Experiment 3 has the smallest ζmax, ζ0.5max and
ζ4max in this chapter (Table 6.2). The reason may be traced to the smaller vertical wind
shear, and thus smaller magnitude of low-level horizontal vorticity available to be tilted into the vertical. In contrast, the ζmax in Experiment 4 is smaller in magnitude than that
in Experiment 1 for a different reason. The larger magnitude of vertical shear in this experiment leads to a weaker low-level updraught (see Table 6.2), which, in turn, leads to a weaker ζmax in this experiment than in Experiment 1, despite there being a larger
magnitude of horizontal vorticity available to be tilted into the vertical (recall that all of the background horizontal vorticity is located below a height of 2 km).
Horizontal cross sections of the vertical component of relative vorticity at heights of 1, 2 and 4 km in Experiments 3 and 4 are shown in Figure 6.11 at particular times. At 20 min, and at a height of 1 km, the vorticity dipole in Experiment 3 has a slightly north-westerly orientation (panel (a)) while at a height of 4 km (panel (c)), the dipole is orientated in a more north-westerly direction. At 22 min (panel (b)) there is a vorticity tripole, with
106 6. Effects of a vortex boundary-layer wind profile on deep convection
negative patches of vorticity on the east and north of the positive vorticity patch. This structure is similar to that shown in Figure 6.4 (d) and Figure 6.7 (b) where there is a
twisting of the original dipole. A new negative vorticity patch develops north of the original dipole, while the old negative patch in the dipole decays. In Experiment 4 (panels d, e and f) the vorticity dipole at a height of 1 km is larger in horizontal extent when compared to Experiment 3. This is due to the increased deformation of the initial thermal bubble at early times by the larger vertical wind shear. By 30 min, the vorticity dipole is orientated in a north-easterly direction, a difference of about 90 degrees in the clockwise direction when compared to the dipole in Experiment 3.
In summary, the convective cell rising in the experiment with weak vertical shear has the strongest updraught and downdraught in this chapter. In this weakly-sheared environ- ment, the initial thermal experiences less deformation and develops more rapidly, so the updraught reaches a maximum at any height sooner than in the other experiments. In con- trast, the updraught maximum at a particular height occurs later in the strongly-sheared environment because of the larger deformation of the initial thermal by the stronger ver- tical shear. Despite having the largest updraught maximum, the experiment with weak vertical shear has the smallest vertical vorticity maximum because of the smaller vertical wind shear, and thus smaller low-level horizontal vorticity available to be tilted into the vertical.