Saturn’s North Polar hexagon
A short history of hexagon
Conclusion
On the dynamical nature of Saturn’s North Polar
hexagon.
Masoud Rostami,
1
Vladimir Zeitlin,
Spiga
and Aymeric
Laboratoire de Météorologie Dynamique (LMD),
Université Pierre et Marie Curie (UPMC),
Ecole Normale Supérieure (ENS), Paris, France
27 March, 2017
EGU General Assembly 2017
1
Email: [email protected]
Saturn’s North Polar hexagon
A short history of hexagon
Conclusion
Topic: Dynamical nature of Saturn’s north polar hexagon
Saturn’s North Polar hexagon
Figure: Saturn’s North Polar hexagon (NASA’s Cassini Imaging Team)
Saturn’s North Polar hexagon
A short history of hexagon
Conclusion
A short history of hexagon
• First Visible imagery acquired by Voyager 1 & 2 in 1980-1981.
• Hexagon has been observed again after ≈35 years by Cassini.
• Morales (2015) proposed an alternative “meandering jet”
model which matches the morphology of Saturn’s hexagon,
provided that an ad hoc vertical shear of the jet is introduced.
• There is not enough convincing dynamical explanation of the
existence and origin of Saturn’s North pole hexagon, as well as
the absence of its counterpart at Saturn’s South pole.
Saturn’s North Polar hexagon
A short history of hexagon
Conclusion
Initial velocity profiles
0.16
0.16
0.14
0.14
0.12
0.12
0.1
Velocity
Velocity
0.1
0.08
0.06
0.08
0.06
0.04
0.04
0.02
0.02
0
0
0
1
2
3
4
r
Figure:
Dashed lines
Solid lines
Left panel
Right panel
5
6
0
1
2
3
4
r
Observed zonal velocity profiles + margins
Analytical velocity profiles
Northern hemisphere
Southern hemisphere
5
6
Saturn’s North Polar hexagon
A short history of hexagon
Conclusion
3
3
2.5
2.5
2
2
PV
PV
Initial potential vorticity (PV) profiles
1.5
1.5
1
0
1
1
2
3
4
r
Figure:
Dashed lines
Solid lines
Left panel
Right panel
5
6
0
1
2
3
4
5
r
PV distributions of observed profiles + margins
PV distributions of Analytical fit
Northern hemisphere
Southern hemisphere
6
Saturn’s North Polar hexagon
A short history of hexagon
Conclusion
Results of linear stability analysis
8
0.025
R = 2400 km
d
12
R = 2800 km
d
7
R = 3200 km
0.02
10
d
6
5
0.01
6
4
4
2
2
σ
m
0.015
8
3
Figure:
Left panel
r0 [Rd ]
m
Black square
White square
Right panel
4
r0 [Rd]
5
3
0.005
2
0
2
4
6
8
10
12
14
16
l
Distribution of azimuthal wavenumbers
Distance of jet from the pole
A parameter related to the curvature of the jet’s velocity
Jet’s situation (Northern hemisphere)
Jet’s situation (Southern hemisphere)
Linear stability growth rate (jet-only)
Saturn’s North Polar hexagon
A short history of hexagon
Conclusion
Nonlinear saturation of "jet-only " case (pressure and PVA)
Figure:
Left panel
Right panel
Pressure (time = 150 f0 −1 )
PVA (time = 150 f0 −1 )
Saturn’s North Polar hexagon
A short history of hexagon
Conclusion
Nonlinear saturation of "jet-only " case (pressure)
Figure:
Left panel
Right panel
Pressure (time = 350 f0 −1 )
Pressure (time = 450 f0 −1 )
Saturn’s North Polar hexagon
A short history of hexagon
Conclusion
Nonlinear saturation of "jet+vortex" case (pressure)
Figure:
Left panel
Right panel
Pressure (time = 150 f0 −1 )
Pressure (time = 1000 f0 −1 )
Saturn’s North Polar hexagon
A short history of hexagon
Conclusion
Nonlinear saturation of "jet+vortex" case (PVA)
Figure:
Left panel
Right panel
PVA (time = 150 f0 −1 )
PVA (time = 1000 f0 −1 )
Saturn’s North Polar hexagon
A short history of hexagon
Conclusion
Radial distribution of zonally averaged PVA
0.7
0.6
Time = 0
[f−1
]
0
Time = 150
[f−1
]
0
[f−1
]
0
[f−1
]
0
Time = 450
−1
[f0 ]
−1
Time = 150 [f0 ]
0.2
Time = 450 [f−1
]
0
0.15
PVA
PVA
Time = 1000
0.5
Time = 0
0.1
0.4
0.05
0.3
0
0.2
1
2
3
4
r
5
6
−0.05
1
2
3
4
r
Figure:
Left panel
“jet+vortex "
Right panel
“jet-only"
5
6
Saturn’s North Polar hexagon
A short history of hexagon
Conclusion
Emerging l = 6 from white noise (jet+vortex, NH)
2
1.5
FT
1
l=2
l=3
l=4
l=5
l=6
l=7
l=8
0.5
0
−0.5
−1
0
100
200
300
Time [ f−1]
400
500
Figure: Evolution of the logarithms of the normalized amplitudes of the
Fourier modes of the azimuthal velocity.
Saturn’s North Polar hexagon
A short history of hexagon
Conclusion
Angular momentum, M
−1
−1
Time = 100 to 200 [f0 ]
Time = 100 to 450 [f0 ]
0.06
0.06
0.04
0.04
0.02
0.02
0
0
−0.02
−0.02
−0.04
−0.04
Jet
Jet + Vortex
−0.06
−0.08
0
2
Figure:
Left panel
Right panel
Vertical dashed line
4
r [Rd]
6
Jet
Jet + Vortex
−0.06
−0.08
8
0
2
4M(t = 200 f0−1 )
4M(t = 450 f0−1 )
rmax , [V (rmax ) = Vmax ]
4
r [Rd]
6
8
Saturn’s North Polar hexagon
A short history of hexagon
Conclusion
Conclusion
• Result of linear stability analysis:
(a) the most unstable mode depends on the latitude of the
circumpolar jet and curvature of its azimuthal velocity profile.
(b) the difference in morphology between the hexagonal
northern polar jet and the southern polar jet can be explained
by linear stability analysis.
• Result of non-linear stability analysis:
developing barotropic instability of the “jet+vortex” system
produces a long-living structure akin to the observed hexagon,
which is not the case of the “jet-only” system. The north polar
vortex, thus, plays a decisive dynamical role.