A simple two dimensional model used for simulation of the dynamical instability in tropical cyclones has been adapted to investigate the dynamical instability in the hemispheric vortices centered on each pole of Venus. The investigation was triggered by the VIRTIS observations of the inverted S-shape around the south pole of Venus during the insertion orbit of Venus Express [Piccioni et al., 2007]. Confirming not only the hemispheric symmetry of the atmospheric circulation on Venus in terms of features observed, VIRTIS also presented a day-night view of the planet from a unique polar perspective, by capturing the day side in reflected ultraviolet and by recording the emitted radiation from the night hemisphere in near infrared (e.g., Figure 1b). This instantaneous day-night global view of Venus over the pole confirmed the vortex organization determined from the space time composite view generated by Suomi and Limaye .
|Figure 1a. S-shaped pattern seen near the south pole of Venus in April 2006 in the 5.05 µ VIRTIS observations [from Piccioni et al., 2007]. The bright features show higher radiance values compared to the darker hues and likely reflect warmer temperatures found in the lower atmosphere. However, it is also likely that subsidence, expected from the converging flow is also responsible for the warming of the lower atmosphere somewhat.||Figure 1b. A composite view of the day and night side of Venus from the VIRTIS instrument on Venus Express (ESA Image SEM49273R8F). This global view of Venus is a mosaic of several images taken by the Visible and Infrared Thermal Imaging Spectrometer (VIRTIS) on board ESA's Venus Express on 18 May 2007, at a distance of about 66 000 km from the planet. The images were obtained at 1.7 µ (left) and 3.8 µ (right) wavelength, The wavelength used to obtain the left-hemisphere composite (1.7 µ) provides a dramatic global view of the night-side clouds in the lower atmosphere (approximately 45 km), while the wavelength used to obtain the right-hemisphere composite (3.8 µ) provides a view of the day-side cloud top.|
The presence of the inverted S-shape and its appearance in the early VIRTIS
data prompted us to look at the barotropic instability from the meridional
profiles of the zonal flow which had been extended to higher latitudes [Limaye,
2007]. A profile relative vorticity is needed for the stability analysis
and hence some comments about the determination of the vorticity profile
are necessary. While Venus is completely covered with clouds, the tracking
of (light or dark) ultraviolet features in the global images obtained from
orbit is still challenging due to the peculiar cloud morphology. Discrete,
isolated cloud features at high latitudes are rare. Cloud tracking is therefore
difficult and the resulting flow somewhat uncertain in its precise shape.
Nevertheless, different estimates of the profiles are generally consistent
in the main details, and some temporal variability has been noted on time
scales of weeks to months and perhaps longer. Note that for dynamical studies,
we need measurements and a computation of cyclostrophically balanced flow
is not sufficient (as it would preclude meridional motions).
The relative vorticity profile for Venus is not very well known and does not cover the critical polar region; therefore fits to the calculated relative vorticity profile extrapolated to the center of the vortex based were used. The relative vorticity was estimated from the results of cloud tracking using Pioneer Venus Orbiter images acquired in 1980.
Figure 1c. The latitudinal relative vorticity profile determined from cloud motions derived from Pioneer Venus ultraviolet imagery and two extrapolated profiles (blue and orange lines) that were fit to the data. The error bars on the vorticity profile indicate the error estimated from the longitudinally averaged data [Limaye, 2007].
Vorticity was determined from cloud motions averaged in latitude bins and
error in the vorticity was estimated from the measurements. Beyond 75°,
the analytical profiles in Fig. 1c were arbitrarily extrapolated to either
zero or 2 x 10-5 s-1 at the pole. Since we are interested
in the instability of large scale motions, the idealized, smoothed data
are acceptable. The typical degree of small-scale variability in the meridional
vorticity profile is not yet confidently known from observations.
While recent cloud tracking data from low resolution imagery taken aboard Venus Express [Markiewicz et al., 2007] have revealed a similar atmospheric state, the high latitude vorticity is still not reliably known. Near infrared imagery from Venus Express during April 2006 [Piccioni et al., 2007] revealed an S-shaped feature around the southern pole (Fig. 1) that was nearly a mirror image of feature seen in the northern pole from Pioneer Venus in 1979.
|Figure 2. Animated output from the model, initialized with the profile from Pioneer Venus, shows the development of an S-shape similar to that seen in the Pioneer Venus observations as well as from Venus Express (flipped due to with mirror symmetry). Evolved time is indicated in hours on the top left of the image.||Figure 3. Animation of Hurricane Howard (thermal infrared images) over about a day showing the development of a similar "S" shaped transient feature in the core. Comparison of the model simulation for the Venus vortex (Figure 2) with the evolution of the core region of Hurricane Howard (Figure 3), which also exhibited a similar transient S-shape is shown here.|
Hurricane Howard's S-Shape feature lasts less than two hours, whereas the S shaped feature on Venus is seen to evolve more slowly in the model. Venus Express observations of the S-shape are critical in this respect and show a similar slowly changing appearance.
Figure 4. A view of the model output initialized with the vorticity profile that reaches 2E-05 sec-1 at the pole (blue curve in Figure 1c). The instability takes much longer to grow in this case.
It can be seen from the two different profiles we tried that the growth
rate for the instability depends on the exact shape of the vorticity profile
from the peak value vorticity radius to the center of the vortex. In this
region of Venus however, the cloud motions are very difficult to measure
due to lack of good cloud targets and hence the vorticity profile is more
uncertain, and hence we can gain some insight in the dynamics of the core
region near the pole through the evolution rates of the observed features
through the use of the model simulations.
A vorticity profile that does not decrease to the pole impacts the growth rate of the instability as can be seen in the animation shown to the right. Beyond about 75 deg south, the confidence in the cloud tracked motions is low and the relative vorticity estimates are less reliable. We approximated the profile here between the peak vorticity and the pole as shown here.
Since the initial sighting of the Southern "S" shape, continued VIRTIS observations have shown that the "S" shape feature is not permanent, but quite transient. This is also expected from our simulation results, supporting the dynamical similarity between the tropical cyclone circulation and the Venus vortex, except for a ~ 10 times difference in physical scale.
The VIRTIS observations of the Southern polar region of Venus show other
shapes in the core region of the vortex (Figure 5) which appear similar
to the forms seen in the evolving instability features in the animation
. It is therefore highly suggestive that their origins are also due to barotropic
instability, indicating that the flow at the cloud level has more shear
than the cloud motion measurements might suggest. This is possible due to
lack of reliable tracers and adequate combination of image spatial resolution
and time interval over which the tracer motions need to be measured.
Besides the morphological similarity between a mature tropical cyclone and the Venus hemispheric vortex, another similarity between the observed features in the vortex circulations of Venus and in terrestrial hurricanes is the presence of transverse waves on the spiral bands, away from the vortex centers (Fig. 6). The lack of such transverse waves in Earth’s polar vortices is suggestive that the dynamics of the Venus polar vortices may have more in common with hurricanes than their more direct terrestrial polar counterparts, perhaps due to the large difference in the rotation rates of Earth and Venus.
Figure 5. The geometrical features in the southern polar region observed in multiple orbits of VIRTIS provide an idea of the range of morphologies observed. The data shown above are cloud top brightness temperatures associated with 3.8 µ or 5.1 µ (as available) wavelengths. Here, lighter shades imply higher temperatures. These may be compared with the numerical simulation shown above. Orbit numbers, as well as start and stop times of the observations, are noted in the two rows at the bottom of the table above.
There are still many questions about the vortex circulation on Venus. How deep is it? Does it reach down to the surface in the Polar Regions? Night side near infrared images in the Venus atmospheric spectral windows reveal atmospheric circulation near the base of the cloud, or about 48-53 km above the surface of Venus. A key question is whether the subsidence in the core region reaches all the way down to the surface, and if it leads to "westerly" flow near the surface that might counteract the momentum exchange with the surface by the westward (easterly) flow in low latitudes? This is crucial for the long term balance of the angular momentum budget of the atmosphere and the solid planet. Are there secondary circulations associated with the spiral bands? More precise knowledge of the profiles of average zonal and meridional flow at deeper levels below the ultraviolet cloud top level reaching down to the surface on both the day and night side of the planet is needed. Some of these questions will be answered from the data to be collected from Venus Express, but others must wait until more data are obtained from future missions. Even then, capable global circulation models as are being now developed by many groups will be crucial along with the limited dynamical observations that can be made of the global deep circulation of the Venus atmosphere.
Figure 6. MODIS image of Catarina, a rare Southern Hemisphere Atlantic hurricane (24-28 March 2004) with features in the eye-wall region. Visually, this is a mirror image of the south hemisphere vortex on Venus due to the opposite spin direction of Venus as compared to Earth. The primary spiral bands are most likely associated with vortex Rossby waves in tropical cyclones. We do not yet know for certain the reason for the spiral bans on Venus, although at low and mid latitudes they are consistent with the interpretation of being streak lines.