Mechanisms of Jet Formation on the Giant Planets

May combine two claims.

Meridional gradients of both absolute vorticity and quasigeostrophic potential vorticity at the levels shown in Fig. 1 are small near zonal velocity minima and are reversed near some of them.

“Indeed, meridional gradients of both absolute vorticity and quasigeostrophic potential vorticity at the levels at which the zonal velocities are shown in Fig. 1 are small near zonal velocity minima and are reversed near some of them (Fig. 2).”

May combine two claims.

The Jupiter and Saturn simulations exhibit equatorial superrotation, and the Uranus and Neptune simulations exhibit equatorial subrotation.

“The Jupiter and Saturn simulations exhibit equatorial superrotation, the Uranus and Neptune simulations equatorial subrotation.”

May combine two claims.

The equatorial jet in the Saturn simulation is stronger (about 230 m/s) and slightly wider than that in the Jupiter simulation, but it is weaker and narrower than the observed jet at a corresponding level on Saturn.

“The equatorial jet in the Saturn simulation is stronger (;230 m s 21 ) and slightly wider than that in the Jupiter simulation, but it is weaker and narrower than the observed jet at a corresponding level on Saturn.”

May combine two claims.

The overall structure of the jets in the Uranus and Neptune simulations is roughly consistent with observations, but the equatorial jet in the Neptune simulation at the level shown (about 240 m/s) is considerably weaker than that observed.

“The overall structure of the jets in the Uranus and Neptune simulations is roughly consistent with observations, but the equatorial jet in the Neptune simulation at the level shown (;240 m s 21 ) is considerably weaker than that observed.”

May combine two claims.

The equatorial jet in the Jupiter simulation has similar strength (about 150 m/s) and width as the observed jet.

“The equatorial jet in the Jupiter simulation has similar strength (;150 m s 21 ) and width as the observed jet.”

May combine two claims.

In general, the prograde jets (or zonal velocity maxima) are sharper than the retrograde jets (or zonal velocity minima), consistent with the zonal velocity maxima being barotropically more stable.

“In general, the prograde jets (or zonal velocity maxima) are sharper than the retrograde jets (or zonal velocity minima), consistent with the zonal velocity maxima being barotropically more stable (Rhines 1994).”

• cites Rhines 1994 sourceNot checked yet

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May combine two claims.

The Jupiter and Saturn simulations exhibit alternating off-equatorial jets; they are broader than the observed jets but of similar strength.

“The Jupiter and Saturn simulations exhibit alternating offequatorial jets; they are broader than the observed jets but of similar strength.”

May combine two claims.

In the Saturn simulation, the equator-to-pole brightness temperature contrast is 7 K, consistent with observations.

“In the Saturn simulation, the equator-topole brightness temperature contrast is 7 K, consistent with observations (Ingersoll 1990;Fletcher et al. 2007).”

• cites Ingersoll 1990 sourceNot checked yet

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• cites Fletcher et al. 2007 sourceNot checked yet

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May combine two claims.

In the Saturn simulation, the prograde polar jet at 68 degrees N exhibits a wavenumber-8 or -9 undulation, with a zonal phase velocity of -24 m/s.

“In the Saturn simulation, for example, the prograde polar jet at 688N exhibits a wavenumber-8 or -9 undulation (Fig. 4), with a zonal phase velocity of 224 m s 21 .”

May combine two claims.

In the equatorial upper troposphere in the Jupiter and Saturn simulations, where the prograde jets strengthen with depth, temperatures decrease equatorward and have a minimum at the equator.

“Therefore, in the equatorial upper troposphere in the Jupiter and Saturn simulations, where the prograde jets strengthen with depth, temperatures decrease equatorward and have a minimum at the equator (Fig. 5, contours in right column).”

May combine two claims.

In the Uranus and Neptune simulations, the equator-to-pole brightness temperature contrasts are 8 and 2 K, respectively, consistent with observations.

“In the Uranus and Neptune simulations, the equator-to-pole brightness temperature contrasts are 8 and 2 K, respectively, consistent with observations (Ingersoll 1990).”

• cites Ingersoll 1990 sourceNot checked yet

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May combine two claims.

Away from the equator, prograde jets generally weaken with depth and retrograde jets strengthen slightly or do not vary much with depth.

“Away from the equator, prograde jets generally weaken with depth and retrograde jets strengthen slightly or do not vary much with depth.”

May combine two claims.

In the Jupiter simulation with an atmosphere of 3-bar thickness, the radiative time scale is about 10 Earth years; it is about 50 Earth years in the Saturn simulation.

“In the Jupiter simulation with an atmosphere of 3-bar thickness, the radiative time scale is ;10 Earth years; it is ;50 Earth years in the Saturn simulation.”

May combine two claims.

The large coherent vortices extend all the way to the bottom of the domain, with the magnitude of the vorticity decreasing weakly with depth: the peak vorticity at the bottom of the domain is about 80% of its maximum value in the column.

“They extend all the way to the bottom of the domain, with the magnitude of the vorticity decreasing weakly with depth: the peak vorticity at the bottom of the domain is about 80% of its maximum value in the column.”

May combine two claims.

The corresponding vertical shear of the zonal flow, about 1-2 x 10^-3 s^-1, is similar to that measured by the Galileo probe on Jupiter between 0.7 and 4 bar and to that inferred from Cassini data for Saturn between 0.05 and 0.8 bar.

“The corresponding vertical shear of the zonal flow, ;1-2 3 10 23 s 21 , is similar to that measured by the Galileo probe on Jupiter between 0.7 and 4 bar (Atkinson et al. 1998) and to that inferred from Cassini data for Saturn between 0.05 and 0.8 bar (Sanchez-Lavega et al. 2007; see also the zonal-flow observations at different levels in Fig. 1).”

• cites Atkinson et al. 1998 sourceNot checked yet

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• cites Sanchez-Lavega et al. 2007 sourceNot checked yet

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May combine two claims.

The large coherent vortices are cyclonic, with typical vorticities of magnitude about 2 x 10^-5 s^-1.

“The large coherent vortices are cyclonic, with typical vorticities of magnitude ;2 3 10 25 s 21 .”

May combine two claims.

The retrograde equatorial jets in the Uranus and Neptune simulations are strongest in the stratosphere and weaken with depth, consistent with inferences drawn from gravity measurements with the Voyager 2 spacecraft.

“The retrograde equatorial jets in the Uranus and Neptune simulations are strongest in the stratosphere and weaken with depth, consistent with inferences drawn from gravity measurements with the Voyager 2 spacecraft (Hubbard et al. 1991).”

• cites Hubbard et al. 1991 sourceNot checked yet

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May combine two claims.

The jets are evident not only in long-term averages but also in instantaneous flow fields.

“The jets are evident not only in long-term averages but also in instantaneous flow fields.”

May combine two claims.

The large coherent vortices are advected by the flow in their environment and have a local temperature minimum at the center (about 10 K lower temperature than the environment).

“They are advected by the flow in their environment and have a local temperature minimum at the center (;10 K lower temperature than the environment).”

May combine two claims.

In the global mean, the conversion rates are 0.09 and 0.026 W m^-2 in the Jupiter and Saturn simulations, respectively, implying that the conversion rate in either simulation is about 0.6% of the total energy uptake of the atmosphere.

“In the global mean, the conversion rates are 0.09 and 0.026 W m 22 in the Jupiter and Saturn simulations, respectively, implying that the conversion rate in either simulation is about 0.6% of the total energy uptake of the atmosphere.”

May combine two claims.

The off-equatorial jets in the Uranus and Neptune simulations are situated in the stratosphere and are broader than those in the Jupiter and Saturn simulations.

“The off-equatorial jets in the Uranus and Neptune simulations are situated in the stratosphere and are broader than those in the Jupiter and Saturn simulations.”

May combine two claims.

This angular momentum transport has a baroclinic structure and, in the Jupiter and Saturn simulations, is in structure and magnitude consistent with observations.

“It has a baroclinic structure and, in the Jupiter and Saturn simulations, is in structure and magnitude consistent with observations (cf.Ingersoll et al. 1981;Salyk et al. 2006;Del Genio et al. 2007).”

• cites Ingersoll et al. 1981 sourceNot checked yet

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• cites Salyk et al. 2006 sourceNot checked yet

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• cites Del Genio et al. 2007 sourceNot checked yet

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May combine two claims.

The eddy angular momentum flux divergence at the stratospheric jet cores is not even of a consistent sign at all times but exhibits considerable low-frequency variability.

“It is not even of a consistent sign at all times but exhibits considerable low-frequency variability, as indicated by the differences between the statistically identical hemispheres in the long-term (1500-day) averages shown in Fig. 7.”

May combine two claims.

The jets become very weak below the tropopause and, particularly in the Uranus simulation, give way to a tropospheric zonal flow with smaller meridional scales.

“The jets become very weak below the tropopause and, particularly in the Uranus simulation, give way to a tropospheric zonal flow with smaller meridional scales (Fig. 5).”

May combine two claims.

Without intrinsic heat fluxes and the convection that they induce, a Jupiter simulation similar to the one here exhibits equatorial subrotation; the same is true for the Jupiter and Saturn simulations here.

“In SL09, we demonstrated that without intrinsic heat fluxes and the convection that they induce, a Jupiter simulation similar to the one here exhibits equatorial subrotation; the same is true for the Jupiter and Saturn simulations here.”

• cites SL09Not checked yet

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May combine two claims.

The vorticity-mixing estimate is also roughly consistent with our simulations, although a state of homogenized absolute vorticity in the equatorial region of each hemisphere is not attained in the simulations.

“It is also roughly consistent with our simulations, although a state of homogenized absolute vorticity in the equatorial region of each hemisphere is not attained in the simulations.”

May combine two claims.

If the same enhanced drag is used at all latitudes, without an equatorial no-drag region, there is no large-scale prograde jet at the equator, while the off-equatorial flow is not substantially modified.

“However, if the same enhanced drag is used at all latitudes, without an equatorial no-drag region, there is no large-scale prograde jet at the equator, while the off-equatorial flow is not substantially modified (Fig. 9c).”

May combine two claims.

In the Uranus simulation, the intrinsic heat flux is negligible, the atmosphere is stably stratified, and there is no substantial convective Rossby wave source near the equator.

“In the Uranus simulation, the intrinsic heat flux is negligible, the atmosphere is stably stratified, and there is no substantial convective Rossby wave source near the equator.”

May combine two claims.

In the Uranus simulation, the equatorial eddy kinetic energy is weak, and the equatorial flow is retrograde.

“Consequently, the equatorial eddy kinetic energy is weak, and the equatorial flow is retrograde.”

May combine two claims.

In the Neptune simulation, the rms Rossby wave source R' in the upper troposphere near the equator is approximately 10^-12 s^-2, whereas for Jupiter and Saturn it is approximately 10^-10 s^-2.

“the rms Rossby wave source R9 in the upper troposphere near the equator is ;10 212 s 22 for Neptune but ;10 210 s 22 for Jupiter and Saturn.”

May combine two claims.

Because eddy angular momentum fluxes in our simulations generally diverge in retrograde tropospheric jets, or zonal velocity minima, and converge in prograde tropospheric jets, or zonal velocity maxima, the mean meridional mass flux in the off-equatorial upper troposphere is generally poleward in retrograde jets and equatorward in prograde jets.

“Because eddy angular momentum fluxes in our simulations generally diverge in retrograde tropospheric jets, or zonal velocity minima, and converge in prograde tropospheric jets, or zonal velocity maxima, the mean meridional mass flux in the off-equatorial upper troposphere is generally poleward in retrograde jets and equatorward in prograde jets (Fig. 7).”

May combine two claims.

This approach gave statistically steady states in which the angular momentum balance is closed in a manner that is physically plausible and consistent with observations.

“This approach gave statistically steady states in which the angular momentum balance is closed in a manner that is physically plausible and consistent with observations.”

Probably not a substantial claim: may not pass S3 (load-bearing).

In the statistically steady states, the global-mean outgoing thermal radiative flux is within 1% of the sum of the global-mean solar radiative flux and the imposed intrinsic heat flux.

“In the statistically steady states, the global-mean outgoing thermal radiative flux is within 1% of the sum of the global-mean solar radiative flux and the imposed intrinsic heat flux.”

May combine two claims.

In the Jupiter simulation, the stratification at the corresponding level is nearly statically neutral, so potential vorticity is not well defined.

“It is not shown for the Jupiter simulation because the stratification at the corresponding level is nearly statically neutral (cf.Fig.5below), so potential vorticity is not well defined.”

May combine two claims.

The simulations exhibit temperature structures that are broadly consistent with available observations, and they reproduce many details of the observed flows, for example, their vertical structure to the extent it is known and characteristic equatorial waves observed on Jupiter.

“They exhibit temperature structures that are broadly consistent with available observations, and they reproduce many details of the observed flows, for example, their vertical structure to the extent it is known and characteristic equatorial waves observed on Jupiter.”

May combine two claims.

Retrograde equatorial jets result if either convective Rossby wave generation is weak or absent, as on Uranus, or low-latitude angular momentum flux divergence owing to baroclinic eddies is sufficiently strong, as on Neptune.

“Retrograde equatorial jets result if either convective Rossby wave generation is weak or absent (Uranus) or low-latitude angular momentum flux divergence owing to baroclinic eddies is sufficiently strong (Neptune).”

Classified as probably not a substantial claim. May combine two claims.

The equatorial jet is prograde on Jupiter and Saturn and retrograde on Uranus and Neptune.

“with an equatorial jet that is prograde on Jupiter and Saturn and retrograde on Uranus and Neptune.”

May combine two claims.

Prograde equatorial jets result if convective Rossby wave generation is strong and low-latitude angular momentum flux divergence owing to baroclinic eddies generated off the equator is sufficiently weak, as on Jupiter and Saturn.

“Prograde equatorial jets result if convective Rossby wave generation is strong and low-latitude angular momentum flux divergence owing to baroclinic eddies generated off the equator is sufficiently weak (Jupiter and Saturn).”

May combine two claims.

Deep-flow models that posit intrinsic heat fluxes as the sole driver of the flow can generate equatorial superrotation, but they use heat fluxes more than 10^6 times larger than those observed.

“For example, deep-flow models that posit intrinsic heat fluxes as the sole driver of the flow can generate equatorial superrotation, but they use heat fluxes more than 10 6 times larger than those observed (e.g., Heimpel and Aurnou 2007).”

• cites Heimpel and Aurnou 2007 sourceNot checked yet

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Classified as probably not a substantial claim. May combine two claims.

Jupiter and Saturn have multiple off-equatorial jets in each hemisphere, while Uranus and Neptune have only a single off-equatorial jet in each hemisphere.

“Jupiter and Saturn have multiple off-equatorial jets in each hemisphere; Uranus and Neptune have only a single off-equatorial jet in each hemisphere.”

Classified as probably not a substantial claim.

In SL09, the authors postulated that prograde equatorial jets on the giant planets occur when intrinsic heat fluxes are strong enough that Rossby waves generated convectively in the equatorial region transport angular momentum toward the equator.

“In Schneider and Liu (2009, hereafter SL09), we postulated that prograde equatorial jets on the giant planets occur when intrinsic heat fluxes are strong enough that Rossby waves generated convectively in the equatorial region transport angular momentum toward the equator.”

• cites Schneider and Liu (2009)Not checked yet

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May combine two claims.

This total energy conversion rate is already about 4% of the total energy uptake of the atmosphere from intrinsic heat fluxes and absorption of solar radiation for Jupiter, or about 11% for Saturn.

“This is already ;4% of the total energy uptake of the atmosphere from intrinsic heat fluxes and absorption of solar radiation for Jupiter, or ;11% for Saturn.”

May combine two claims.

The observations of Jupiter and Saturn imply that eddy angular momentum fluxes cannot extend unabatedly over great depths and must have a baroclinic structure.

“The observations of Jupiter and Saturn therefore imply that eddy angular momentum fluxes cannot extend unabatedly over great depths and must have a baroclinic structure.”

May combine two claims.

Uranus and Neptune have retrograde equatorial jets that peak at about 100 m/s and about 150-400 m/s.

“Uranus and Neptune have retrograde equatorial jets (subrotation) that peak at ;100 m s 21 and ;150-400 m s 21 .”

May combine two claims.

Deep-flow models generate equatorial subrotation only with intrinsic heat fluxes even stronger than those for which they generate superrotation, although the intrinsic heat fluxes on Uranus and Neptune are weaker than those on Jupiter and Saturn.

“They generate equatorial subrotation only with intrinsic heat fluxes even stronger than those for which they generate superrotation (Aurnou et al. 2007), although the intrinsic heat fluxes on the subrotating planets (Uranus and Neptune) are weaker than those on the superrotating planets (Jupiter and Saturn).”

• cites Aurnou et al. 2007 sourceNot checked yet

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May combine two claims.

The northern and southern hemispheres in the simulations are statistically identical, so differences between the hemispheres in figures showing long-term averages are indicative of the sampling variability of the averages.

“The northern and southern hemispheres in the simulations are statistically identical, so differences between the hemispheres in figures showing long-term averages are indicative of the sampling variability of the averages.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Jupiter and Saturn have prograde equatorial jets that peak at about 100 m/s and about 200-400 m/s, depending on the vertical level considered.

“Jupiter and Saturn have prograde equatorial jets (superrotation) that peak at ;100 m s 21 and ;200-400 m s 21 , depending on the vertical level considered.”

Classified as probably not a substantial claim.

The simulations were run to statistically steady states after long spinup periods.

“We show simulation results from statistically steady states, which were reached after long spinup periods; see the appendix for details.”

Classified as probably not a substantial claim.

It is unclear in shallow-flow models what physical characteristics distinguish the superrotating planets from the subrotating planets.

“It is unclear in those and other shallow-flow models (e.g., Scott and Polvani 2008) what physical characteristics distinguish the superrotating planets from the subrotating planets.”

• cites Scott and Polvani 2008Not checked yet

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Classified as probably not a substantial claim. May combine two claims.

Existing models posit as the driver of the flow either the differential radiative heating of the upper atmosphere or the intrinsic heat fluxes emanating from the deep interior.

“Existing models posit as the driver of the flow either the differential radiative heating of the upper atmosphere (e.g., Williams 1979Williams , 2003b) ) or the intrinsic heat fluxes emanating from the deep interior (e.g., Busse 1976;Heimpel et al. 2005;Aurnou et al. 2007;Chan and Mayr 2008;Kaspi et al. 2009).”

• cites Williams 1979 sourceNot checked yet

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• cites Busse 1976 sourceNot checked yet

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• cites Heimpel et al. 2005 sourceNot checked yet

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Probably not a substantial claim: may not pass S4 (based).

The resolution in each simulation (T85 to T213 spectral resolution in the horizontal and 30 or 40 levels in the vertical) is sufficient to resolve baroclinic instability and the energy-containing eddies in the upper atmosphere.

“The resolution in each simulation (T85 to T213 spectral resolution in the horizontal and 30 or 40 levels in the vertical) is sufficient to resolve baroclinic instability and the energy-containing eddies in the upper atmosphere.”

May combine two claims.

Shallow-flow models that posit differential radiative heating as the driver of the flow can generate equatorial superrotation, but they require artifices such as additional equatorial heat or wave sources that have no clear physical interpretation.

“Similarly, shallow-flow models that posit differential radiative heating as the driver of the flow can generate equatorial superrotation, but they require artifices such as additional equatorial heat or wave sources that have no clear physical interpretation (e.g., Williams 2003a,b;Yamazaki et al. 2005;Lian and Showman 2008).”

• cites Williams 2003a,bNot checked yet

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• cites Yamazaki et al. 2005 sourceNot checked yet

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• cites Lian and Showman 2008Not checked yet

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May combine two claims.

Consistent with thermal wind balance, temperatures increase equatorward along isobars where prograde jets weaken with depth or retrograde jets strengthen with depth, and they decrease equatorward where the opposite is true.

“Consistent with thermal wind balance, temperatures increase equatorward along isobars where prograde jets weaken with depth or retrograde jets strengthen with depth, and they decrease equatorward where the opposite is true.”

May combine two claims.

The vorticity profiles indicate that barotropic instability limits the sharpening of the retrograde jets, though not to the degree that the statistically steady states of the flows would satisfy sufficient conditions for linear barotropic stability for unforced and nondissipative flows.

“The vorticity profiles indicate that barotropic instability limits the sharpening of the retrograde jets, though not to the degree that the statistically steady states of the flows would satisfy sufficient 1.The quasigeostrophic potential vorticity is calculated analogously to Read et al. (2009).”

May combine two claims.

The undulation is retrograde, and retrograde relative to the mean flow, consistent with the undulation being a Rossby wave.

“This is retrograde, and retrograde relative to the mean flow, consistent with the undulation being a Rossby wave.”

May combine two claims.

Coherent vortices preferentially exist in regions where absolute vorticity or potential vorticity gradients vanish, as they can then arise spontaneously in barotropic or quasigeostrophic flows and remain stable.

“Coherent vortices preferentially exist in regions where absolute vorticity or potential vorticity gradients vanish, as they can then arise spontaneously in barotropic or quasigeostrophic flows and remain stable (e.g., McWilliams 1984;Marcus 1988Marcus , 1993)).”

• cites McWilliams 1984 sourceNot checked yet

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• cites Marcus 1988 sourceNot checked yet

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• cites Marcus 1993 sourceNot checked yet

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May combine two claims.

Since the radiative time scale increases with pressure, it is longer for deeper atmospheres, which might explain why the observed coherent vortices such as the Great Red Spot on Jupiter are so long lived.

“Since the radiative time scale increases with pressure, it is longer for deeper atmospheres, which might explain why the observed coherent vortices such as the Great Red Spot on Jupiter are so long lived.”

May combine two claims.

These cyclonic vortices are long lived, with life spans apparently determined by the radiative time scale.

“These cyclonic vortices are long lived, with life spans apparently determined by the radiative time scale (the time scale on which eddies can modify the mean flow).”

May combine two claims.

Away from the equator, the differential radiative heating of the upper atmospheres produces meridional temperature gradients, which are baroclinically unstable and lead to eddy generation.

“Away from the equator, the differential radiative heating of the upper atmospheres produces meridional temperature gradients, which are baroclinically unstable and lead to eddy generation.”

May combine two claims.

More generally, entropy is constant along angular momentum surfaces, to achieve a state of neutrality with respect to slantwise convection.

“[More generally, entropy is constant along angular momentum surfaces, to achieve a state of neutrality with respect to slantwise convection; see Emanuel (1983) and Thorpe and Rotunno (1989).]”

• cites Emanuel (1983) sourceNot checked yet

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• cites Thorpe and Rotunno (1989)Not checked yet

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May combine two claims.

The fundamental reason for the different flow and temperature structures in the giant planet simulations lies in the different strengths of the differential radiative heating and the intrinsic heat flux and in the different ways in which the two can lead to the generation of the eddies that maintain the jets.

“The fundamental reason lies in the different strengths of the differential radiative heating and the intrinsic heat flux and in the different ways in which the two can lead to the generation of the eddies that maintain the jets.”

Probably not a substantial claim: may not pass S4 (based). May combine two claims.

There are no observations of entropy or temperature distributions below the upper troposphere for the giant planets, but the authors expect them to behave similarly as in their simulations.

“There are no observations of entropy or temperature distributions below the upper troposphere for the giant planets, but we expect them to behave similarly as in our simulations, for the reasons discussed in section 5c below.”

May combine two claims.

Although temperature contrasts at the emission level are generally small, equator-to-pole temperature contrasts at higher or lower levels of the simulated atmospheres differ, and the same is likely true for the actual planets.

“However, although temperature contrasts at the emission level are generally small, equator-to-pole temperature contrasts at higher or lower levels of the simulated atmospheres differ, and the same is likely true for the actual planets.”

May combine two claims.

Fluctuations in convective heating are primarily balanced by vertical motion and, at the level of the convective outflows, by horizontal divergence of mass fluxes, as in the tropics of Earth's atmosphere.

“Fluctuations in convective heating are primarily balanced by vertical motion and, at the level of the convective outflows, by horizontal divergence of mass fluxes, as in the tropics of Earth's atmosphere.”

• cites Sobel et al. 2001 sourceNot checked yet

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May combine two claims.

Because the planetary vorticity vanishes at the equator, the Rossby wave source R' typically has largest amplitude just off the equator, but it does not necessarily vanish at the equator or where the absolute vorticity vanishes because absolute vorticity advection by the divergent flow may not vanish.

“Because the planetary vorticity vanishes at the equator, the Rossby wave source R9 typically has largest amplitude just off the equator, but it does not necessarily vanish at the equator or where the absolute vorticity vanishes because absolute vorticity advection by the divergent flow may not vanish.”

May combine two claims.

Fluctuations in the horizontal divergence are a source of equatorial Rossby waves, and the fluctuating vorticity source R' can be taken to be the Rossby wave source.

“As discussed in Sardeshmukh and Hoskins (1988), fluctuations in the horizontal divergence are a source of equatorial Rossby waves, and the fluctuating vorticity source”

• cites Sardeshmukh and Hoskins (1988)Not checked yet

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May combine two claims.

Fluctuations in convective heating lead to horizontal divergence fluctuations, which can generate equatorial Rossby waves through stretching of absolute vorticity or advection of absolute vorticity by the divergent flow.

“Thus, fluctuations in convective heating lead to horizontal divergence fluctuations (1), which can generate equatorial Rossby waves through stretching of absolute vorticity z a or advection of absolute vorticity by the divergent flow v x (2).”

May combine two claims.

The angular momentum transport toward the equatorial region by convectively generated Rossby waves leads to equatorial superrotation if it is sufficiently strong and drag on the zonal flow is sufficiently weak.

“The angular momentum transport toward the equatorial region by convectively generated Rossby waves leads to equatorial superrotation if it is sufficiently strong and drag on the zonal flow is sufficiently weak (SL09).”

• cites SL09Not checked yet

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May combine two claims.

Convectively generated Rossby waves transport angular momentum toward the equatorial region because this is where they are preferentially generated.

“This is generally to be expected for such convectively generated Rossby waves: they transport angular momentum toward the equatorial region because this is where they are preferentially generated.”

May combine two claims.

The structure of the stratospheric jets implies that they interact only weakly with the drag at the lower boundary, so only weak eddy angular momentum flux divergence is necessary to maintain them.

“The structure of the stratospheric jets implies that they interact only weakly with the drag at the lower boundary, so only weak eddy angular momentum flux divergence is necessary to maintain them.”

May combine two claims.

The Rossby wave source R' owing to horizontally divergent flow has largest amplitude in the equatorial region because only there will convective heating fluctuations necessarily lead to horizontal divergence fluctuations on large scales; away from the equator, the WTG approximation does not hold.

“The Rossby wave source R9 owing to horizontally divergent flow has largest amplitude in the equatorial region because only there will convective heating fluctuations necessarily lead to horizontal divergence fluctuations on large scales; away from the equator, the WTG approximation (1) of the thermodynamic equation does not hold.”

• cites SL09Not checked yet

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May combine two claims.

Off-equatorial baroclinic eddy generation implies angular momentum flux convergence in the off-equatorial generation regions and divergence in lower latitudes, and hence a tendency toward retrograde equatorial flow.

“Off-equatorial baroclinic eddy generation implies angular momentum flux convergence in the off-equatorial generation regions and divergence in lower latitudes, and hence a tendency toward retrograde equatorial flow.”

May combine two claims.

Vorticity mixing arguments give an estimate for the maximum strength of the equatorial jet: if the end state of vorticity mixing is a state in which the absolute vorticity is homogenized across the equatorial jet in each hemisphere separately, with a barotropically stable jump at the equator, and if the jet half-width L_s is similar to the equatorial Rossby radius L_b, the jet speed at the equator

“Vorticity mixing arguments give an estimate for the maximum strength of the equatorial jet (Rhines 1994; SL09): If the end state of vorticity mixing is a state in which the absolute vorticity is homogenized across the equatorial jet in each hemisphere separately, with a barotropically stable jump at the equator, and if the jet half-width L s is similar to the equatorial Rossby radius L b , the jet”

• cites Rhines 1994 sourceNot checked yet

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• cites SL09Not checked yet

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May combine two claims.

Neptune's intrinsic heat flux only needs to be larger by an O(1) factor for Neptune's atmosphere to develop equatorial superrotation, implying that Neptune may have been superrotating earlier in its history, when intrinsic heat fluxes were stronger.

“Interestingly, our simulations suggest that Neptune's intrinsic heat flux only needs to be larger by an O(1) factor for Neptune's atmosphere to develop equatorial superrotation, implying that Neptune may have been superrotating earlier in its history, when intrinsic heat fluxes were stronger.”

May combine two claims.

The vorticity-mixing estimate is roughly consistent with observations of Jupiter and Saturn, although the maximum equatorial jet speed on Saturn is not known for lack of observations deeper in the atmosphere.

“This is roughly consistent with observations of Jupiter and Saturn (but the maximum equatorial jet speed on Saturn is not known for lack of observations deeper in the atmosphere).”

May combine two claims.

The same pattern of eddy angular momentum fluxes and mean meridional mass flux is almost certainly true on Jupiter and Saturn, where similar eddy angular momentum fluxes in the upper troposphere have been observed.

“The same is almost certainly true on Jupiter and Saturn, where similar eddy angular momentum fluxes in the upper troposphere have been observed (Salyk et al. 2006;Del Genio et al. 2007).”

• cites Salyk et al. 2006 sourceNot checked yet

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• cites Del Genio et al. 2007 sourceNot checked yet

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May combine two claims.

Neither the precise functional form of the drag, nor the magnitude of the drag coefficient where it is nonzero, nor the width of the no-drag region appears to be essential for our results-as long as there is an equatorial region with no or sufficiently low drag such that a large-scale prograde jet can form.

“However, neither the precise functional form of the drag, nor the magnitude of the drag coefficient where it is nonzero, nor the width of the no-drag region appears to be essential for our results-as long as there is an equatorial region with no or sufficiently low drag such that a large-scale prograde jet can form.”

May combine two claims.

Convection tends to homogenize entropy along columns in the direction of the planet's spin axis (in deep atmospheres) or in the vertical (in thin atmospheres); however, it does not constrain entropy gradients in perpendicular directions.

“Therefore, convection tends to homogenize entropy along columns in the direction of the planet's spin axis (in deep atmospheres) or in the vertical (in thin atmospheres); however, it does not constrain entropy gradients in perpendicular directions.”

May combine two claims.

Convection in general does not homogenize entropy in directions perpendicular to angular momentum surfaces, so an isentropic interior cannot be assumed a priori.

“However, convection in general does not homogenize entropy in directions perpendicular to angular momentum surfaces, so an isentropic interior cannot be assumed a priori.”

May combine two claims.

The WTG approximation holds where the Rossby number satisfies Ro << 1 and the Froude number satisfies Fr << 1.

“The WTG approximation holds where the Rossby number satisfies Ro U/jfLj * 1 and the Froude number satisfies Fr 5 UV/(gH) ( 1, where U is a zonal velocity scale, V a meridional or eddy velocity scale, L a length scale of flow variations, and H the scale height(Charney 1963; SL09).”

• cites Charney 1963 sourceNot checked yet

  Not checked in the free run.

• cites SL09Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

The thermal optical depths t_l0 at pressure p0 are chosen such that the observed thermal emission levels of the giant planets approximately correspond to t_l = 1.

“The thermal optical depths t l0 at pressure p 0 are chosen such that the observed thermal emission levels (e.g., Ingersoll 1990) of the giant planets approximately correspond to t l 5 1.”

• cites Ingersoll 1990 sourceNot checked yet

  Not checked in the free run.

May combine two claims.

The depth of that layer can be expected to affect quantitative aspects such as the vertical shear of the zonal flow, but we do not expect it to affect the qualitative aspects and large-scale flow features on which we have focused.

“The depth of that layer can be expected to affect quantitative aspects such as the vertical shear of the zonal flow, but we do not expect it to affect the qualitative aspects and large-scale flow features on which we have focused.”

May combine two claims.

Equatorial superrotation is generated if convective Rossby wave generation is strong and low-latitude angular momentum flux divergence owing to baroclinic eddies generated off the equator is sufficiently weak (Jupiter and Saturn); equatorial subrotation results if either convective Rossby wave generation is weak or absent (Uranus) or low-latitude angular momentum flux divergence owing to baroclin-

“We have demonstrated that equatorial superrotation is generated if convective Rossby wave generation is strong and low-latitude angular momentum flux divergence owing to baroclinic eddies generated off the equator is sufficiently weak (Jupiter and Saturn); equatorial subrotation results if either convective Rossby wave generation is weak or absent (Uranus) or low-latitude angular momentum flux”

Probably not a substantial claim: may not pass S3 (load-bearing).

To the extent that vertical shear and convective momentum fluxes cannot be neglected, they may amplify the superrotation in the upper troposphere in the Jupiter and Saturn simulations.

“But to the extent that the vertical shear and convective momentum fluxes cannot be neglected, they may amplify the superrotation in the upper troposphere in the Jupiter and Saturn simulations, as the equatorial zonal flow in those simulations is stronger at depth than in the upper troposphere, so that convection can be expected to transport momentum upward.”

• AssumptionThe authors state this as an assumption: The convection scheme assumes a convective Prandtl number of zero (does not transport momentum).

May combine two claims.

In the interiors of Jupiter and Saturn, the conductivity of molecular hydrogen increases with depth and becomes approximately constant where hydrogen becomes metallic at ~1.4 Mbar.

“In the interior of Jupiter and Saturn, the conductivity of molecular hydrogen increases with depth and becomes approximately constant where hydrogen becomes metallic at ;1.4 Mbar (Nellis et al. 1996).”

• cites Nellis et al. 1996 sourceNot checked yet

  Not checked in the free run.

May combine two claims.

In the high-conductivity interior, the interaction of the magnetic field and the fluid flow produces Ohmic dissipation and retards the flow.

“In the high-conductivity interior, the interaction of the magnetic field and the fluid flow produces Ohmic dissipation and retards the flow (Liu et al. 2008).”

• cites Liu et al. 2008 sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Where the convective Rossby number is not necessarily small, convective plumes are aligned with angular momentum (M) surfaces.

“More generally, where the convective Rossby number is not necessarily small, convective plumes are aligned with angular momentum (M) surfaces.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Where latent heat release in phase changes of water is dynamically important, a moist entropy can be expected to be homogenized in the direction of the spin axis.

“Where latent heat release in phase changes of water is dynamically important, a moist entropy rather than a dry entropy should be considered, and such a moist entropy can be expected to be homogenized in the direction of the spin axis.”

Probably not a substantial claim: may not pass S3 (load-bearing).

If entropy deviations from an isentropic reference state are not small so that the anelastic approximation cannot be made, the thermal wind balance becomes more complicated.

“If entropy deviations from an isentropic reference state are not small so that the anelastic approximation cannot be made, the thermal wind balance (13) becomes more complicated(Kaspi et al. 2009).”

• cites Kaspi et al. 2009 sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

All parameter choices are constrained by knowledge of the physical properties of the planets and material properties of their atmospheres, as well as by observations where available.

“All parameter choices are constrained by knowledge of the physical properties of the planets and material properties of their atmospheres, as well as by observations where available.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Latent heat release in phase changes of water does not represent an external heat source, merely a conversion between forms of energy, and hence it does not affect the integrated energy balance.

“Latent heat release in phase changes of water may play a role in that layer, but it does not represent an external heat source, merely a conversion between forms of energy, and hence it does not affect the integrated energy balance.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

This does not affect the qualitative considerations on which the paper's conclusions are based.

“But this does not affect the qualitative considerations on which our conclusions are based.”

May combine two claims.

In the interiors of Uranus and Neptune, the conductivity of the gas envelope increases with depth and is determined by the conductivity of hydrogen and water ice.

“In the interior of Uranus and Neptune, the conductivity of the gas envelope likewise increases with depth and is determined by the conductivity of hydrogen and water ice (Nellis et al. 1997).”

• cites Nellis et al. 1997 sourceNot checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

By choosing drag formulations that differ from planet to planet, better fits to observations could be obtained.

“By choosing drag formulations that differ from planet to planet, better fits to observations could be obtained (cf.section 4d).”