Saturn's new ribbons: Cassini observations of planetary waves in Saturn's 42N atmospheric jet

The north ribbon was at the northern flank of the jet at 44°N when first imaged by Cassini in October 2005.

“When first imaged by Cassini in October 2005, the north ribbon was at the northern flank of the jet at 44 ∘ N (Figure 1a).”

The ribbon waves appeared and disappeared over a 9-year period from 2005 to 2014.

“We report that three distinct waves at 45 ∘ N, 42 ∘ N, and 39 ∘ N (hereafter referred to as the north, mid, and south ribbons) appeared and disappeared over the course of a 9-year period from 2005 to 2014.”

Three ribbon waves were present in Saturn's 42°N eastward jet at 45°N, 42°N, and 39°N planetocentric latitudes during Cassini observations.

“we analyzed three ribbon waves in Saturn's 42 ∘ N eastward jet at 45 ∘ N, 42 ∘ N, and 39 ∘ N planetocentric latitudes.”

• AssumptionRests on an assumption: The Voyager-era ribbon represented the meandering core of an eastward jet with a wind speed of about 150 m/s.

The ribbons were visible as sharp boundaries between bright and dark areas in CB2 images.

“The ribbons were visible as sharp boundaries between bright and dark areas in CB2 images.”

Cassini discovered waves in the 42°N jet during its 2004-2017 Saturn mission.

“The Cassini spacecraft also discovered waves in the 42N jet during its 2004-2017 Saturn mission.”

• AssumptionRests on an assumption: The Voyager-era ribbon represented the meandering core of an eastward jet with a wind speed of about 150 m/s.

By the end of the Cassini mission in 2017, there were no ribbon waves in the jet.

“By the end of the Cassini mission in 2017, there were no ribbon waves in the jet.”

For the north ribbon (L_x ≈ 3,250 km and L_D = 889 km), the KE/PE ratio is approximately 3.

“For the north ribbon (L x ≈ 3, 250 km and L D = 889 km), ⟨KE⟩∕⟨PE⟩ ≈ 3, which indicates that it is primarily, but not purely, barotropic.”

The mid ribbon remained at the peak of the jet.

“The mid ribbon remained at the peak of the jet.”

The north ribbon propagated meridionally on the time scale of years, with a poleward velocity of about 0.4°/year (0.003 m/s) between 2006 and 2010.

“While it is clear from Figure 2 that the north ribbon propagated meridionally on the time scale of years, between 2006 and 2010 its poleward velocity was about 0.4 ∘ /year or 0.003 m/s.”

The north ribbon's mean latitude increased from 44.2°N to 45.7°N between October 2005 and September 2010.

“From October 2005 to September 2010 its mean latitude increased from 44.2 ∘ N to 45.7 ∘ N.”

The north and mid ribbons disappeared in mid-2014.

“The north and mid ribbons disappeared in mid-2014.”

For the north ribbon, L_D = 889 ± 187 km by dispersion analysis.

“For the north ribbon, we found L D = 889 ± 187 km by dispersion analysis (see section 4.3)”

Both L_D values are shorter than the ribbons' peak wavelengths.

“both of which are shorter than the ribbons' peak wavelengths.”

The mid ribbon was visible in CB2 as a sharp boundary between a bright band to the north and a dark band to the south at the same latitude as the Voyager era ribbon.

“The mid ribbon was visible in CB2 as a sharp boundary between a bright band to the north and a dark band to the south at the same latitude as the Voyager era ribbon.”

The dispersion analysis of the north ribbon in early 2008 shows a clear trend of slower zonal phase speeds (westward propagation relative to the background wind) at lower wavenumbers, despite substantial scatter.

“The result of our dispersion analysis of the north ribbon in early 2008 is shown in Figure 3d.While there is substantial scatter, there is a clear trend to slower zonal phase speeds (westward propagation relative to the background wind) at lower wavenumbers, which is characteristic of Rossby waves.”

The ribbon waves were visible in 5 μm images captured by VIMS.

“The ribbon waves were also visible in 5 μm images captured by VIMS.”

In place of the Voyager-era ribbon was a thin bright line with abrupt southward kinks about every 90-180° in longitude.

“In place of the Voyager-era ribbon was a thin bright line (L in Figure1a) with abrupt southward kinks about every 90-180 ∘ in longitude (e.g., K in Figure1a).”

Cassini found that the 42°N jet's appearance had dramatically changed since the Voyager and Hubble observations.

“Cassini found that the 42 ∘ N jet's appearance had dramatically changed since the Voyager and Hubble observations.”

A good fit to the derived Rossby wave dispersion relation was obtained with reasonable values for β_e and L_D.

“However, we obtained a good fit to our derived Rossby wave dispersion relation with reasonable values for 𝛽 e and L D .”

Cassini's VIMS observed the thin line at 42°N as a band of thick clouds backlit against the 5-μm glow of the planet's interior.

“Cassini's Visual and Infrared Mapping Spectrometer (VIMS) observed this line at 42 ∘ N as a band of thick clouds backlit against the 5-μm glow of the planet's interior (Figure3inChoi et al. (2009); this line is misidentified as the ribbon in earlier literature; e.g., Del Genio et al., 2009).”

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The north ribbon's phase velocities are well fit by a simple Rossby wave dispersion relation with a finite Rossby deformation radius.

“The north ribbon's phase velocities are well fit by a simple Rossby wave dispersion relation with a finite Rossby deformation radius.”

The morphology, wavelength, and propagation of the ribbon waves are consistent with barotropic Rossby waves with a smaller baroclinic component.

“In this report, we demonstrate that the morphology, wavelength, and propagation of the ribbon waves are consistent with barotropic Rossby waves with a smaller baroclinic component.”

• Also stated in: § 1. Introduction · boosted

  “In this report, we demonstrate that the morphology, wavelength, and propagation of Saturn's ribbon waves are consistent with Rossby waves that are primarily barotropic with a smaller baroclinic component.”

• AssumptionThe authors state this as an assumption: The Voyager-era ribbon was located at a sharp meridional potential vorticity gradient.

Voyager spacecraft imaged a dark, sinuous line encircling Saturn at 42°N latitude, dubbed the ribbon wave, embedded in an atmospheric jet stream.

“During their 1980 and1981 flybys of Saturn, the Voyager spacecraft imaged a dark, sinuous line encircling the planet.This feature, dubbed the ribbon wave after its visual appearance, was embedded in an atmospheric jet stream at 42N latitude.”

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The temporal evolution of the ribbon waves is related to the great Saturn storm of 2010-2011.

“We suggest that the temporal evolution of these waves are related to the great Saturn storm of 2010-2011.”

The south ribbon evolved from the storm's wake.

“further suggesting that the south ribbon evolved from the storm's wake.”

Sánchez-Lavega et al. (2012) measured wavelengths of disturbances on the northern boundary of the 2010-2011 storm's wake between 4,500 and 11,000 km, with a peak of 4,800 km.

“Sánchez-Lavega et al. (2012) measured the wavelength of the disturbances on the northern boundary of 2010-2011 storm's wake and obtained wavelengths between 4,500 and 11,000 km, with a peak of 4,800 km”

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Read et al. (2009) obtained L_D ≈ 2,000 km in the 42°N jet using Arno'ld's Second Criterion.

“Read et al. (2009) obtained L D ≈ 2, 000 km in the 42 ∘ N jet using Arno'ld's Second Criterion”

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The mid ribbon's peak wavelength is similar to previously reported Voyager and Hubble observations: Godfrey and Moore (1986) and Sánchez-Lavega (2002) obtained 5,710 and 4,200 km, respectively.

“The mid ribbon's peak wavelength is similar to what has been previously reported for the Voyager and Hubble observations- Godfrey and Moore (1986) and Sánchez-Lavega (2002) obtained 5,710 and 4,200 km, respectively.”

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The ratio of kinetic energy to potential energy of a Rossby wave, averaged over one period, is given by ⟨KE⟩/⟨PE⟩ = 4π^2 L_D^2 / L_x^2.

“The ratio of kinetic energy to potential energy of a Rossby wave, averaged over one period, can be written as ⟨KE⟩ ⟨PE⟩ = 4𝜋 2 L 2 D L 2 x (7 ) (Pedlosky, 2003).”

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The ribbons' wavelengths are consistent with Rossby waves.

“Therefore, we conclude that the ribbons' wavelengths are consistent with Rossby waves.”

• AssumptionThe authors state this as an assumption: The Voyager-era ribbon was located at a sharp meridional potential vorticity gradient.

The level of features sensed by the 5 μm images is between 1 and 4 bar, probably corresponding to the base of the clouds sensed by the CB2 filter.

“The level of features sensed by the 5 μm images is between 1 and 4 bar, probably corresponding to the base of the clouds sensed by the CB2 filter (Choi et al., 2009).”

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A mix of barotropic and baroclinic conditions is likely at play in the 42°N jet.

“As the ribbons' appearance is somewhere in between these two extremes, we conclude that a mix of barotropic and baroclinic conditions is likely at play in the 42 ∘ N jet.”

The ribbons extended from the high tropospheric hazes to the ammonia cloud deck and possibly deeper.

“From these observations we conclude that the ribbons extended from the high tropospheric hazes to the ammonia cloud deck and possibly deeper.”

The background zonal wind u has a standard deviation of 12.2 m/s.

“u has a standard deviation of 12.2 m/s (Blalock et al., 2016).”

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For Rossby waves, the zonal phase speed c is always less than the background zonal wind u (i.e., westward propagation relative to u) because β_e must be positive.

“Because 𝛽 e must be positive, c is always less than u (i.e., westward propagation relative to u).”

Using the assumption N_B ≈ 1.7×10^-3 s^-1 in the ammonia cloud, equation (2) yields a depth D ≈ 125 ± 26 km.

“If we assume that N B ≈ 1.7×10 -3 s -1 in the ammonia cloud (Sánchez-Lavega et al., 2012), using equation (2) yields D ≈ 125 ± 26 km.”

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• AssumptionThe authors state this as an assumption: N_B ≈ 1.7×10^-3 s^-1 in the ammonia cloud.

The north ribbon is primarily, but not purely, barotropic.

“For the north ribbon (L x ≈ 3, 250 km and L D = 889 km), ⟨KE⟩∕⟨PE⟩ ≈ 3, which indicates that it is primarily, but not purely, barotropic.”

The ribbons appeared as meandering paths embedded in vortex streets, similar to barotropic instabilities produced in numerical simulations and laboratory experiments.

“The ribbons appeared as meandering paths embedded in vortex streets, similar to barotropic instabilities produced in numerical simulations (see Figures 13 and 15 in Flierl et al., 1987, andFigures 4 and5 in Poulin &Flierl, 2003) and laboratory experiments (Barbosa Aguiar et al., 2010).”

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The ribbons are primarily barotropic, at least in the altitude range sounded by the MT3 and CB2 filters.

“There was no detectable east-west phase shift or decrease in meridional extent between simultaneous MT3 and CB2 images, which points to the ribbons being primarily barotropic, at least in the altitude range sounded by these filters.”

The 2010-2011 storm had some effect on the north ribbon wave.

“Between September 2010 and February 2011, the north ribbon moved south to 44.5 ∘ and decreased in amplitude, indicating that the storm had some effect on the wave.”

For Rossby waves to propagate, the effective potential vorticity gradient β_e must be positive.

“To provide a restoring force which allows Rossby waves to propagate, 𝛽 e must be positive.”

The fitted β_e for the north ribbon is about 10 times the planetary vorticity gradient (β = 4 × 10^-12 m^-1 s^-1).

“For the north ribbon, we obtained 𝛽 e = (44.5 ± 8.1) × 10 -12 m -1 s -1 , which is about 10 times the planetary vorticity gradient (𝛽 = 4 × 10 -12 m -1 s -1 ).”

The analysis is based on a linear plane wave approximation.

“While the ribbons are discrete and almost certainly nonlinear waves, our analysis is based on a linear plane wave approximation.”

The ribbons' appearance as meandering lines embedded in vortex streets suggests that they are primarily barotropic but with some baroclinic component.

“Their appearance as meandering lines embedded in vortex streets suggests that they are primarily barotropic but with some baroclinic component.”

The potential vorticity gradient in the 42°N jet must have been positive in order for the ribbons to propagate.

“The potential vorticity gradient in the jet must has been positive in order for the ribbons to propagate.”

The ribbon waves in Saturn's 42°N jet are likely Rossby waves.

“We have determined that the ribbon waves in Saturn's 42 ∘ N jet are likely Rossby waves based on the following observations”

Sánchez-Lavega et al. (2012) found that the wave-like northern boundary of the 2010-2011 storm, which would emerge months later as the south-ribbon, also moved westward relative to the zonal wind.

“Sánchez-Lavega et al. (2012) found that the wave-like northern boundary of the 2010-2011 storm, which would emerge months later as the south-ribbon, also moved westward relative to the zonal wind.”

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Sromovsky et al. (1983) and Sánchez-Lavega et al. (2012) give evidence that the mid and south ribbons propagate westward relative to the background wind, which is characteristic of Rossby waves.

“Sromovsky et al. (1983) and Sánchez-Lavega et al. (2012) give evidence that the mid and south ribbons propagate westward relative to the background wind, which is characteristic of Rossby waves.”

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Comparing the peak wavelengths of the ribbons to the deformation radius suggests that they are primarily barotropic Rossby waves with a smaller baroclinic component.

“Comparing the peak wavelengths of the ribbons to this deformation radius suggests that they are primarily barotropic Rossby waves with a smaller baroclinic component.”

Sromovsky et al. (1983) found that the Voyager era ribbon, at the same latitude as the Cassini era mid ribbon, propagated westward relative to the zonal wind.

“Sromovsky et al. (1983) found that the Voyager era ribbon, which was at the same latitude as the Cassini era mid ribbon, propagated westward relative to the zonal wind.”

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