AIAA 2010-4300
40th Fluid Dynamics Conference and Exhibit
28 June - 1 July 2010, Chicago, Illinois
Influence of Persistent Companion Clouds on Geophysical
Vortex Dynamics
Raymond P. LeBeau, Jr.*
University of Kentucky, Lexington, KY 40506
Xiaolong Deng†
University of California-Santa Barbara, Santa Barbara, CA
Csaba Palotai1
University of Central Florida, Orlando, FL
Large geophysical vortices provide some of the most dramatic features in the known
atmospheres, from hurricanes on Earth to the Great Red Spot on Jupiter. A notable
difference between the Great Red Spot and terrestrial hurricanes is that hurricanes are more
dynamic, changing shape and location in response to internal and external conditions. In
contrast, large vortices on the outer two gas giant planets, Uranus and Neptune, have
exhibited a greater tendency toward dynamics more akin to hurricanes. The most notable of
these dynamic vortices was the original Great Dark Spot observed by Voyager II in 1989,
which through eight months of observation drifted towards the equator by ten degrees in
latitude and oscillated in shape over an eight-day period during the month of closest
observation. Also like hurricanes, it now appears that clouds also play a critical role in
governing the dynamics of these features, most importantly in terms of persistent orographic
companion clouds that form in the vicinity of some of these vortices. However, to better
understand the vertical as well as horizontal motions requires highest resolution simulations
of these features. This paper will discuss the evidence of cloud effects on the vortex dynamics
and progress on achieving the higher resolution vortex simulations that more accurately
simulate the cloud physics. A deeper exploration of the cloud-vortex interaction will give us a
better understanding of the physics of the ice giant atmospheres. In turn, this may help
elucidate the motions of hurricanes on Earth through the application of comparative
planetology.
Nomenclature
g
h
K
M
p
Q
T

u
z

= gravitational acceleration
= hybrid layer thickness
= specific kinetic energy
= Montgomery potential
= pressure
= heat flux
= temperature
= velocity
= altitude coordinate
= Exner function
*
Research Assistant Professor, 177 Chem-Phys Building, Associate Fellow AIAA
Postdoctoral Researcher, Center for Risk Studies and Safety, Member AIAA
1
Postdoctoral Researcher, Dept. of Physics, Building 12 Room 310
†
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American Institute of Aeronautics and Astronautics
Copyright © 2010 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.




= pressure-based vertical coordinate
= potential temperature
= kinematic viscosity
= hybrid vertical coordinate
I. Introduction
L
ARGE, solitary vortices on the ice giant planets of Uranus and Neptune appear periodically in the atmospheres,
generally as elliptical regions of a darker blue than the surrounding atmosphere. The first observed of these
vortices was the Great Dark Spot, now known as GDS-89, imaged during the Voyager II encounter with Neptune.
After Hubble Space Telescope (HST) observations of the early 1990s indicated that GDS-89 was no longer
observable, two new Dark Spots were observed on Neptune, the Northern Great Dark Spot 32 (NGDS-32) and 15
(NGDS-15), first observed in 1994 and 1996 respectively. Both these vortices appeared to be unobservable in 1997,
and the current state of Neptune not well known due to limited observations with sufficient resolution. Still, while no
further Great Dark Spots have been spotted, the series of observations suggest that large vortex features are a regular
feature of the atmosphere of Neptune. More recently, the first ever observed probable vortex feature has been seen on
Uranus through the HST. This feature is known as the Uranian Dark Spot (UDS), appeared at 28 degrees north and
existed for at least three months.
Three of these features (GDS-89, NGDS-32, and UDS) were observed in conjunction with a persistent companion
cloud that appears to be generated orographically as the atmosphere moves over the vortex. These clouds are made of
methane ice and move with the feature, even in the case of GDS-89 as it moved more than 10 degrees in latitude (Fig.
1). There is also some evidence that these companion clouds even persist in cases where the vortex is no longer
observable—the cloud associated with NGDS-32 appeared to exist a year after the vortex had faded from view.
Another candidate for a companion cloud-unobservable vortex pairing is S34, now known referred to colloquially as
“The Berg”, as it has now drifted towards the equator over the past several years from its previous location near 34
degrees south latitude. This type of coherent behavior is unique among large cloud features on the gas giants, and it
seems improbable unless some other atmospheric phenomenon like an unobserved vortex is keeping the cloud
compact despite large changes in background atmospheric conditions.
Initial simulations of these orographic clouds indicate that their magnitude and extent influence the dynamics of
the associated vortices. Comparisons of vortex simulations with and without clouds result in changes in the motions—
drift rate, oscillation rate, oscillation magnitude. These appear to be related to changes in the local vertical conditions
and mass loading generated by the clouds, but simulations that achieve higher resolutions comparable to gas giant
trace gas studies are needed to fully understand the cloud-vortex interaction, with the most obvious target the wellobserved GDS-89.
II. Critical Observations
Given the variety of motions observed with the original Great Dark Spot, it remains one of the most interesting
subjects for vortex dynamic studies. GDS-89 was a roughly elliptical region that was a darker blue (about a 10%
change in albedo) compared to the surrounding region, the shape partially obscured by a bright methane cloud (the
Bright Companion) as shown in Fig. 1. The morphology of GDS-89 based on the Voyager II observations is
characterized by its drift rate and shape evolution. As summarized in Ingersoll et al.1, GDS-89 drifted northward in
latitude between 27 and 17oS at an average rate of 0.00170 degrees/hour or about 1.2 degrees/month. In longitude, the
motion appeared to correlate well with simple advection by the zonal winds. The observed changes in vortex shape
correspond to a roughly eight day oscillation defined by changes in ellipse orientation (the semimajor axis of the
ellipse oscillated about the horizontal with an amplitude of about 14o) and inverse aspect ratio (which shifted between
0.35 and 0.55). These oscillations corresponded to a longitudinal extent of 30 to 45 degrees and 12 to 17 degrees in
latitude in the time frame best-observed by Voyager II. Unlike the Great Red Spot and White Ovals of Jupiter, there
were no apparent small features within the vortex that allowed for direct measurement of the vorticity within the Great
Dark Spot. The accompanying orographic Bright Companion (BC) tracked along the southern edge of the vortex,
although sometimes strips of clouds would appear to divide the vortex into two sections. The BC was detectable from
Earth, and was seen throughout the Voyager encounter, although its apparent size, shape, and brightness were
variable.
Given the distance to Neptune, after Voyager II the only instrument generally capable of detecting discrete Dark
Spots was the Hubble Space Telescope (HST). Early HST observations suggest that a visible GDS-89 had most likely
vanished from the atmosphere of Neptune by 19922. However, observations in the mid-1990s with the post-repair
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HST revealed new large vortex features on Neptune. The first possible GDS-like vortex in the northern hemisphere
was observed in the fall of 19943, and was later designated Northern Great Dark Spot-32 or NGDS-32 due to its
original location at 32oN latitude. This vortex came with its own bright companion cloud but did not appear to have a
significant equatorward drift in latitude like GDS-89. In 1996, both NGDS-32 and a new vortex, NGDS-15 were seen
on Neptune. NGDS-15 appeared only in the 1996 observations and no bright companion was seen2,4,5. Though NGDS32 as a visible dark spot had disappeared in the direct observations by July 1997, the visible cloud patterns may have
persisted into the year 20006. All these post-Voyager HST observations and ground-based observations are not
surprisingly at much lower resolutions than the Voyager observations, so any detailed motions of NGDS features like
morphology changes cannot be determined.
While Neptune observations proved more dramatic in the 1990s, Uranus has become a more interesting target for
observation about its northern spring equinox, which occurred in December of 2007. The extreme axial tilt of this
planet (its rotational axis is inclined 98o relative to its orbital plane), gives rise to extreme seasonal insolation changes.
The shift from winter solstice at around the Voyager encounter to vernal equinox has been associated with the
appearance of numerous new cloud features7-9, the appearance of the first Uranian Dark Spot (UDS)10, and the
unexpected drift of cloud S34 towards the equator. The UDS was an elongated, elliptical dark spot with semiminor
axis of roughly 1300 km (2o) in latitude and semimajor axis of roughly 2700 km (5o) in longitude, centered at 28oN
latitude. While these observations did not directly reveal a bright companion, earlier observations had shown a bright
cloud at the latitude, which may have been orographic in nature and is therefore potentially associated with this
vortex10. Another bright feature on Uranus, the cloud feature S34, had persisted for more than a decade in
observations, oscillating in position slightly about the latitude of 34oS8. However, around the time of the equinox, this
cloud feature appears to have started moving towards the equator at a rate of a few degrees per year. A possible
explanation for this coherent motion is the existence of a vortex of sufficiently low contrast or depth not to be visibly
observable, but still sufficient to maintain a long-term orographic cloud. This vortex could then start to drift
equatorward like the GDS-89 due to changes in the background zonal wind conditions that are driven by changes in
the seasonal insolation.
Figure 1. Observations of GDS-89 over its eight day cycle, including the Bright Companion cloud (although not
as prominent at this wavelength). The image is courtesy of NASA/JPL-Caltech.
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Figure 2. Image of Uranus in 1998 taken with HST, with the South Pole visible. The image contains about 20
clouds, a previously unheard of number. The image is courtesy of NASA/JPL-Caltech.
III. Numerical Model
The most representative simulations of these ice giant vortices and their companion clouds have been achieved by the
Explicit Planetary Isentropic Coordinate General Circulation Model (EPIC GCM)11. The basic equations solved by the
EPIC GCM are the three-dimensional Navier-Stokes equations in the following form:

h

1 p
   (hu ) 
(h )  0, h  
t

g 
(1)



u
 qkˆ  (uh)  ( M  K )    ( u )
t
(2)
d Q

dt 
(3)
where h is the hybrid density, u is the horizontal velocity in longitude and latitude,  is the hybrid vertical coordinate,
M = cpT + gz is the Montgomery potential, K is the horizontal kinetic energy per unit mass,  is the kinematic
viscosity,  is the potential temperature,  is the Exner function, and Q is the heat source term. The hybrid vertical
coordinate has the form:
  f ( )  g ( ) ,  
log( p / pbot )
log( ptop / pbot )
(4)
where p is pressure, the subscripts indicating the values at the top and bottom boundaries, and f() and g() are
functions defined as appropriate for the problem (g() approaching zero near solid surfaces, f() approaching zero and
g() approaching unity when purely isentropic coordinates are desired). These equations are solved using finite
difference equations on a latitude-longitude grid in vertical layers of constant  on an oblate spheroid geometry
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defined by the measured polar and equatorial radii of the planet. The time integration is explicit, either using the thirdorder Adams-Bashforth or the Asselin-filtered leapfrog timestep. The viscous term has a number of forms, ranging
from numerical hyperviscosity to a variation of Detached Eddy Simulation. The model also accounts for critical
thermodynamic effects such as ortho-para hydrogen conversion and cloud physics (methane abundance and cloud
formation). Because of the large scale of the Uranus and Neptune simulations, laminar and turbulent viscosity effects
are treated as negligible, but a 6th-order hyperviscosity term is added to the momentum equation to suppress the
growth of grid-scale gravity waves which may cause numerical instability.
The zonal wind profile, vertical temperature-pressure structure of the atmosphere, initial structure of the vortex,
and initial average relative humidity are inputs to the model based on observed data and related theory. For Neptune,
HST and ground-based observations in the 1990s generally reinforced the zonal wind structure derived from the
Voyager data2,4,5, although there remain significant latitudes with limited data and a fair bit of variability in frequently
measured latitude bands. Therefore, while the Sromovsky et al.12 fit of cloud drift rate is the baseline profile, other
velocity profiles can be constructed to create regions of uniform absolute vorticity gradient while largely conforming
to the observational data. It is notable that the Sromovsky et al. profile itself corresponds to a large region of uniform
gradient, as seen by the Qy=1 (fit) curve in Fig. 3. Near-uniform gradient regions in potential vorticity have proven
critical for achieving coherent, meridionally drifting vortices while regions of near-zero gradients have been critical to
achieve clear periodic shape oscillations like those seen in GDS-8913,14,15. For Uranus, there are ongoing discussions
about whether the zonal wind profile is changing significantly with the seasonal changes or if the observed differences
are simply within the range of observational error. The Uranus profiles used therefore vary between the original
Voyager fit of Smith et al.16 from 1986, the revised fit of Karkoschka7 from 1998, and the Sromovsky and Fry fit from
20058. These zonal wind profiles, along with recent observations in the vicinity of the UDS, are shown in Fig. 4.
The vertical temperature-pressure profile is assumed to be initially uniform over the entire planet and is based on
observed conditions down to the opaque clouds tops (roughly 1-2 bars of pressure for Uranus and Neptune). This
height is well into the planetary troposphere, so the common assumption is the atmospheric temperature varies in an
approximately adiabatic fashion below this height, usually with a fixed buoyancy frequency, N. Table 1 shows the
resulting temperature and pressure distribution for a 10-layer model of Neptune, corresponding to a roughly fixed
buoyancy frequency of 0.008 s-l below 2 bar.
Currently, the physical source of the vortices on the ice giants is not known. Therefore, for these studies they are
induced into the model by introducing vortex like winds on top of the zonal background along with altering the
background Montgomery potential in a consistent fashion. However, the quasi-geostrophic balance assumed to
generate these vortices is approximate, so the resulting features generally undergo a several simulated day period of
adjustment before achieving a more stable state. Examples of the wind fields associated with the vortices used in this
study are shown in Fig. 5. The Gaussian ellipsoid is used for the UDS, while the LeBeau and Dowling version is used
for GDS-89 simulations since the relatively flatter potential vorticity profile appears critical for achieving oscillatory
shape changes.
The cloud microphysics model being incorporated into EPIC for Uranus and Neptune will ultimately include five
phases of methane from vapor to ice, and eleven phase change mechanisms. The parameterization of these phase
change processes is described in Palotai et al.17 and this approach has been successfully applied to Jupiter. The five
phases are vapor, cloud ice, cloud liquid, rain, and snow, although the liquid phases are uncommon to non-existent for
methane on Uranus and Neptune. The phase-change processes include condensation of vapor to cloud liquid and the
reverse evaporation process, the equivalent process for vapor and cloud ice (deposition and sublimation), the initiation
of ice crystals, the melting of cloud ice to cloud liquid and its reverse, the collection and autoconversion of cloud
liquid into rain and the equivalent processes for cloud ice and snow, and the melting and freezing exchange between
rain and snow. The current results use only the dominant methane vapor and methane ice phases. The assumption is
that the initial methane distribution is at a uniform relative humidity, but this will then change as the model evolves.
Regions of persistent humidity 100% or greater will become clouds of methane ice following the cloud microphysics
model.
EPIC is designed to run in parallel using MPI protocols. The computational platforms used in this research to date
are primarily the commodity Kentucky Fluid Cluster (KFC) 5 and KFC6I. KFC5 has 47 nodes each with one AMD
Athlon 2500+ Barton processor and 512 MB RAM linked by a single Gigabit switch network. KFC6I has 24 nodes
each with one 2.13GHz Intel e6400 Core Duo 64 bit processor and 1GB RAM linked by a single 48 port Gigabit
switch network. For the Neptune simulations presented here, typically a full globe is used with an atmospheric depth
from a few millibars to 6-10 bars in pressure. The initial standard grid is 512 longitudinal points, 256 latitudinal
points, and 10 vertical layers, a total of around 13 million points and a horizontal grid spacing of about 0.7 degrees.
The time step used on this grid is 60 seconds. With these parameters and 8 nodes/16 cores of KFC6I, the simulation
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rate is about 10 simulated days for each actual day when including the two-phase cloud model; purely dynamical
simulations run considerably faster. For Uranus, finer grids with twice the horizontal grid spacing are generally used
to better represent the smaller vortex, reducing the grid spacing to 0.35 degrees and the timestep to 30 seconds.
Figure 3. Sample zonal wind profiles for Neptune, with the traditional Sromovsky et al fit corresponding the
Qy=1 (exact) profile. Also shown are the corresponding relative vorticity and the absolute vorticity (relative
vorticity plus the coriolis parameter representing the effect of planetary rotation). The absolute vorticity closely
matched the variations in the background potential vorticity in these simulations.
Figure 4. Sample zonal wind profiles for Uranus, along with recent cloud-tracking measurements in the vicinity
of the UDS. Absolute vorticity is also shown as it closely matched the variations in the background potential
vorticity in these simulations.
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Table 1. Sample atmosphere layer set up for a ten-layer model of Neptune.
Figure 5. Wind profiles of the initial generated vortices. The L&D (LeBeau and Dowling) version creates a
vortex with a region of relatively uniform potential vorticity in the center, similar to what is observed within
the Great Red Spot and typically useful for GDS-89 simulations as well. The stream function case corresponds
to an ellipsoid distribution of potential vorticity and creates a more elongated vortex with constantly changing
potential vorticity across the vortex.
IV. Current Results
After defining the planet, zonal wind profile, vertical temperature-pressure structure, initial methane distribution,
and initial vortex, a given simulation is allowed to evolve in a time-accurate fashion and the subsequent motions of the
vortex formation and patterns of cloud formation are compared to other simulations and known observations.
Comparisons between ten-layer cases without the cloud model (and therefore no companion clouds) and those with
the cloud model, revealed the effects of the clouds on the vortex dynamics15,18.
Examples of the cloud model in conjunction with a GDS-89 simulation are shown in Fig. 6. These contour plots
illustrate that the existence of a small, poleward cloud that qualitatively mimics the Bright Companion is a relatively
straightforward result from these simulations assuming a sufficiently high initial relative methane humidity (in these
cases 60%). The cloud forms orographically as flow moves over the vortex, appears a couple of layers above the main
layer of the vortex, consistent with observations that place the clouds at higher altitudes than the dark spots. The less
straightforward results are the changes in the vortex shape and motion that are generated. GDS-89 simulations can
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naturally yield shape changes similar to those seen in observations. These changes are typified by looking at the
inverse aspect ratio and orientation of the semi-major axis relative to a parallel of constant latitude of an ellipse fit to
the observed or simulated vortex. Figure 7 presents the resulting variations in these measurements for four
simulations, one without the cloud model, the other three with the cloud model. The three cloud model cases are
typified by smaller magnitude oscillations as well as a greater degree of stability—in this case, the no cloud model
effectively loses coherence due to shearing by day 100 of the simulation. The effect on the drift rate is considerable
smaller, although the cloud appears to reduce the likelihood of large, rapid, and highly variable changes in the drift
rate. The clouds may help explain how an oscillating GDS could remain stable for several months or more; however,
it also makes it more challenging for simulations to achieve the observed magnitude of the shape oscillations. For the
UDS, similar clouds poleward clouds can be generated (Fig. 8) and in this the critical effect is on longevity. Induced
vortices on Uranus have a strong tendency to shear and dissipate, which is not inconsistent with the lack of observed
vortices on Uranus. However, the inclusion of a cloud allows the vortices to better maintain their shape for longer
simulations (Fig. 9). Thus, the existence of a cloud may be critical for the existence of long-lived, compact vortices on
Uranus.
These ten layer results, while illustrative of the basic structure and effects of the bright companion-vortex
interaction, have proven less illuminating in terms of understanding the mechanisms that drive the change in vortex
behavior. It is apparent (Fig. 10) that the vertical deflections generated by the vortex remain more defined in the bright
companion cases, but there is not sufficient vertical resolution to draw strong conclusions. The cloud formation also
has a considerable vertical component that is not fully captured in ten-layer models designed to focus on horizontal
motions. For the gas giant, typical cloud formation studies have 30-50 layers of resolution, but are only twodimensional assuming axisymmetric conditions. As a compromise, current models use 20 layers of vertical resolution
with the standard horizontal resolution from the dynamics models. An example of this layer distribution,
superimposed on the temperature-pressure profile, is shown in Fig. 11.
The addition of more layers has proven destabilizing for the current vortex formation process and as such the
typical no-cloud model results in a vortex that either drifts rapidly northward and dissipates or that shears out.
However, as more evidence of the stabilization of the cloud model on the vortex motions, long-lived vortices are more
common with reasonable initial relative humidity (although still with more difficulty than in the ten-layer case).
Examples of the drift rate and oscillation behavior of several runs are presented in Figs. 12-14. All these simulations
use the same background conditions and initial methane humidity (60%), with the only changes being the strength,
size, and layer center of the vortex. In most of these selected cases the vortices drift at rates comparable to GDS-89 for
multiple months Most notable is that the longest-lived vortices tend to occur when the vortex is centered higher in the
atmosphere (layer 12 being the highest case; layer 14 the lowest). These longer-lived cases also tend to have most
regular, but low amplitude, oscillations.
V. Summary
The ten layer simulations reveal significant dynamical effects on the motions of GDS and UDS vortices due to the
introduction of bright companion cloud features. Shifting to twenty layer models has proven more challenging than
anticipated, with few simulations with no clouds producing stable vortices. Adding significant initial methane
humidity does appear to stabilize the vortex in the twenty-layer simulations, in that initial conditions which yield
rapidly destabilizing vortices with no cloud can yield long-lived vortices when bright companions form. However, like
the ten-layer simulations these vortices exhibit small shape oscillations that do not match the observed motions of
GDS-89. Vortices also appears to become more stable at higher layers in the atmospheres, which is not consistent with
observations which suggest that dark spots are located at around one bar or below. More research is needed to address
these issues surrounding these simulations of the dark spots and their bright companions.
Acknowledgments
This work is supported by NASA Planetary Atmospheres Grant No. NNX09AB66G.
References
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Ingersoll, A.P., C.D. Barnet, R.F. Beebe, F.M. Flasar, D.P. Hinson, S.S. Limaye, L.A. Sromovsky, and V.E. Suomi. Dynamic
Meteorology of Neptune. In Neptune and Triton, ed. D.P. Cruikshank, University of Arizona Press, pp. 613-684, 1995.
2
Sromovsky, L.A., S.S. Limaye, and P.M. Frye. Clouds and circulation on Neptune: Implications of 1991 HST observations. Icarus
118, pp. 25-38, 1995.
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Hammel, H.B., G.W. Lockwood, J.R. Mills, and C.D. Barnet. Hubble Space Telescope Imaging of Neptune’s Cloud Structure in
1994. Science 268, pp. 1740-1742, 1995.
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Sromovsky, L.A., P. M. Fry, T.E. Dowling, K.H. Baines, and S.S. Limaye. Coordinated 1996 HST and IRTF Imaging of Neptune
and Triton: III. Neptune’s Atmospheric Circulation and Cloud Structure. Icarus 149, pp. 459-488, 2001.
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Hammel, H.B. and G.W. Lockwood. Atmospheric Structure of Neptune in 1994, 1995, and 1996. Icarus 129, pp. 466-481, 1997.
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Sromovsky, L.A., P.M. Fry, and K.H. Baines. The Unusual Dynamics of Northern Dark Spots on Neptune. Icarus 156, pp. 16-36,
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Karkoschka, E. Clouds of High Contrast on Uranus. Science, 280, p. 570, 1998.
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Sromovsky, L.A., P. M. Fry. Dynamics of cloud features on Uranus. Icarus 179, pp.459-484, 2005
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Hammel, H.B. Uranus nears Equinox: A report from the 2006 Pasadena Workshop. 5 September 2006
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Hammel, H. B. , L. A. Sromovsky, P. M. Fry, K. Ragesc, M. Showalter, I. de Pater, M. A. van Dam, R. P. LeBeau, and X. Deng,
The Dark Spot in the Atmosphere of Uranus in 2006: Discovery, Description, and Dynamical Simulations, accepted by Icarus,
2009.
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Dowling, T.E., M.E. Bradley, E. Colon, J. Kramer, R.P. LeBeau, G.C.H. Lee, T.I. Mattox, R. Morales-Juberias, C.J. Palotai, V.K.
Parimi, and A.P. Showman. The EPIC Atmospheric Model with an Isentropic/Terrain-Following Hybrid Vertical Coordinate.
Icarus 182, pp. 259-273, 2006.
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Sromovsky, L.A., S.S. Limaye, and P.M. Frye. Dynamics of Neptune’s major cloud features. Icarus 105, pp. 110-141, 1993.
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LeBeau, R.P. and T.E. Dowling. EPIC Simulations of Time-Dependent, Three-Dimensional Vortices with Application to
Neptune’s Great Dark Spot. Icarus, 132, pp. 239-265, 1998.
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Deng, X. and R.P. LeBeau. Comparative CFD Simulations of the Dark Spots of Uranus and Neptune. AIAA-2007-3973, 37th
AIAA Fluid Dynamics Conference and Exhibit, Miami, FL, June 25-28, 2007.
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Deng, X., R.P. LeBeau, Jr., and C. Palotai, 2009. Numerical Investigation of Orographic Cloud and Vortex Dynamics on the Ice
Giant Planets. 1st AIAA Atmospheric and Space Environments Conference, AIAA-2009-3643, San Antonio, TX, June 22-25.
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Smith, B.A., L.A. Soderblom, D. Banfield, C. Barnet, A.T. Basilevsky, R.F. Beebe, et. al. Voyager 2 at Neptune: Imaging science
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Palotai, C. and T.E. Dowling. Addition of water and ammonia cloud microphysics to the EPIC model. Icarus 194, pp. 303-326,
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LeBeau, R.P., X. Deng, and C. Palotai, 2009. The Influence of Bright Companion Clouds on Dark Spot Dynamics. 41 st Annual
Meeting of the Division for Planetary Sciences, Fajardo, PR, October 4-9.
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Figure 6. Two simulations of a GDS-like vortex, represented by both the black dashed lines (showing contours
of constant potential vorticity, which acts like a material boundary) and the red elliptical fit, and a BC-like
cloud feature, outlined in the orange dot-dash line. Both simulations have the same initial conditions, with 60%
relative methane humidity, with the exception of the height of the spot—the left one is centered at 866 mbar,
the right at 1640 mbar.
Figure 7. Variations aspect ratio and orientation angle (phi) in GDS-like vortices. The cloud cases are
indentified by the initial methane relative humidity, with the upper notation indicating the vortex is centered at
866 mbar rather than 1640 mbar.
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Figure 8. UDS simulation with the vortex shown in black (at 866 mbar) the cloud in grey (at 266 mbar). Note
that the UDS is in the northern hemisphere, so the dominant cloud is again poleward.
Figure 9 (left). Plot of UDS simulations with and without clouds—the two simulations with clouds (different
initial relative humidity, RH of 60% and 80%) maintain a vortex with a fixed size while the no cloud case is
beginning to stretch and shear out after only 60 days. Figure 10 (right). Vertical structure of the spot in two
layers, showing the difference between the cloud model case (solid line) and the no cloud case (dashed line). The
vertical deflections for the cloud case are notably more pronounced and symmetrical. This data is taken 47
days after simulation start.
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Figure 11. Layer distribution for the twenty-layer model on Neptune superimposed on the background
temperature-pressure profile.
Figure 12. Drift rate for several twenty-layer GDS/BC simulations with differing strength, size, and center
layer. The observed drift rate of the GDS is shown for comparison.
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Figure 13. Aspect ratio variations for the twenty-layer GDS/BC simulations in Fig. 12.
Figure 14. Orientation angle measured between the semi-major axis and a line of constant latitude for the
twenty-layer GDS/BC simulations in Fig. 12.
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