The deep wind structure of the giant planets: Results from an anelastic general circulation model
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The absence of momentum injection by eddies might be caused by injection of energy at smaller scales not resolvable by the measurements or might reinforce the idea that the jets are deeply rooted structures driven by internal convection, making them insensitive at tropospheric level to the seasonal cycle.
“The absence of momentum injection by eddies might be caused by injection of energy at smaller scales not resolvable by the measurements or might reinforce the idea that the jets are in fact deeply rooted structures driven by the internal convection [ Aurnou and Olson, 2001; Kaspi et al. 2009] making them insensitive at tropospheric level to the seasonal cycle”
From Dynamics of Saturn's polar regions (2015) · cites this paper as Kaspi et al. 2009
Alternating jets on gas giant planets are either shallow, existing above about 10 bars, or deep, extending to tens of thousands of bars.
“on one hand, the alternating jets on gas giant planets are 'shallow', existing above 10 bars or so [15-17]; on the other hand, zonal jets are 'deep', extending to tens of thousands of bars [18-22].”
From Deep rotating convection generates the polar hexagon on Saturn (2020) · cites this paper as [22]
The meridional eddy fluxes of angular momentum per unit volume in deep-flow models have a barotropic structure, extending roughly along cylinders concentric with the planet's spin axis over the entire depth of the fluid, typically to pressures of order 10^6 bar.
“Their meridional eddy fluxes of angular momentum per unit volume (taking density variations into account) have a barotropic structure: they extend roughly along cylinders concentric with the planet's spin axis over the entire depth of the fluid, typically to pressures of order 10 6 bar (e.g., Kaspi et al. 2009, their Fig.10).”
From Mechanisms of Jet Formation on the Giant Planets (2010) · cites this paper as Kaspi et al. 2009
Under conditions of small convective Rossby number and negligible viscous momentum dissipation and thermal diffusion, convective plumes are columns aligned with M_V surfaces because rapid rotation inhibits motion perpendicular to M_V surfaces in the absence of viscous or other stresses.
“Under these circumstances, convective plumes are columns aligned with M V surfaces because, as above, rapid rotation inhibits motion perpendicular to M V surfaces in the absence of viscous or other stresses (e.g., Busse 1976Busse , 1978;;Kaspi et al. 2009;Jones et al. 2009).”
From Mechanisms of Jet Formation on the Giant Planets (2010) · cites this paper as Kaspi et al. 2009
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).”
From Mechanisms of Jet Formation on the Giant Planets (2010) · cites this paper as Kaspi et al. 2009
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Wahl, S., Hubbard, W., Militzer, B., Guillot, T., Miguel, Y., Movshovitz, N., Kaspi, Y., Helled, R., Reese, D., Galanti, E., et al. (2017) · Geophysical Research Letters · doi:10.1002/2017gl073160 · Cited by 207 · see citing works
Self-citationThe Origin of the Moon Within a Terrestrial Synestia
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Jupiter’s atmospheric jet streams extend thousands of kilometres deep
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Self-citationAB INITIO SIMULATIONS FOR MATERIAL PROPERTIES ALONG THE JUPITER ADIABAT
French, M., Becker, A., Lorenzen, W., Nettelmann, N., Bethkenhagen, M., Wicht, J., & Redmer, R. (2012) · The Astrophysical Journal Supplement Series · doi:10.1088/0067-0049/202/1/5 · Cited by 253 · see citing works
“…& Glatzmaier 2010; Schubert & Soderlund 2011), basic properties, such as the observed flow patterns in the atmosphere (Heimpel et al. 2005; Vasavada & Showman 2005; Kaspi et al. 2009; Gastine & Wicht 2012), still await explanations that are consistent with planetary structure and dynamo models.”
MethodResultFrom solar-like to antisolar differential rotation in cool stars
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Anelastic convection-driven dynamo benchmarks
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“…and so allows a much larger timestep, is therefore a popular choice for studies of solar and stellar convection zones and the interior dynamics of giant planets (e.g. Glatzmaier, 1984, 1985; Brun et al., 2004; Jones et al., 2009; Jones and Kuzanyan, 2009; Miesch et al., 2000; Kaspi et al., 2009).”
BackgroundRotating convective turbulence in Earth and planetary cores
Aurnou, J. M., Calkins, M. A., Cheng, J. S., Julien, K. A., King, E. M., Nieves, D., Soderlund, K. M., & Stellmach, S. (2015) · Physics of The Earth and Planetary Interiors · doi:10.1016/j.pepi.2015.07.001 · Cited by 156 · see citing works
“Such effects are likely of relevance in gas planets (e.g., Glatzmaier et al., 2009; Kaspi et al., 2009), and may be relevant in Earth-sized terrestrial cores as well (cf. Anufriev et al., 2005; Verhoeven and Stellmach, 2014).”
BackgroundEffects of compressibility on driving zonal flow in gas giants
Gastine, T., & Wicht, J. (2012) · Icarus · doi:10.1016/j.icarus.2012.03.018 · Cited by 163 · see citing works
“Kaspi et al. (2009) used a modified anelastic approach neglecting viscous heating but including a more realistic equation of state.”
BackgroundMethodInfluentialATMOSPHERIC DYNAMICS OF BROWN DWARFS AND DIRECTLY IMAGED GIANT PLANETS
Showman, A. P., & Kaspi, Y. (2013) · The Astrophysical Journal · doi:10.1088/0004-637x/776/2/85 · Cited by 153 · see citing works
“In contrast, F , g, and cp vary radially by a factor of two or less across the molecular envelope (see Kaspi et al. 2009), and to a first approximation—here seeking simply an order-ofmagnitude expression—we can treat them as constant.”
BackgroundMethodInfluentialSelf-citationLi, C., Ingersoll, A., Janssen, M., Levin, S., Bolton, S., Adumitroaie, V., Allison, M., Arballo, J., Bellotti, A., Brown, S., et al. (2017) · Geophysical Research Letters · doi:10.1002/2017gl073159 · Cited by 116 · see citing works
“…was derived by assuming that there is no lateral temperature gradient on the equipotential surface, because both numerical simulations [e.g., Kaspi et al., 2009; Schneider and Liu, 2009] and infrared observations [e.g., Simon-Miller et al., 2006] suggest that lateral temperature differences…”
BackgroundShowman, A. P., Lewis, N. K., & Fortney, J. J. (2015) · The Astrophysical Journal · doi:10.1088/0004-637x/801/2/95 · Cited by 132 · see citing works
“Models of Jupiter and Saturn have consistently shown that strong convection is a crucial ingredient in causing their equatorial superrotation (e.g. Heimpel et al. 2005; Schneider & Liu 2009; Kaspi et al. 2009; Lian & Showman 2010).”
BackgroundSelf-citationAtmospheric Dynamics of Hot Giant Planets and Brown Dwarfs
Showman, A. P., Tan, X., & Parmentier, V. (2020) · Space Science Reviews · doi:10.1007/s11214-020-00758-8 · Cited by 131 · see citing works
“Scaling analysis and global convection models of planetary interior with uniform surface cooling predict small (∼a few Kelvin) isobaric temperature variation in the convective zone (e.g., Stevenson 1991, Kaspi et al. 2009, Showman et al. 2011, Showman & Kaspi 2013).”
BackgroundSelf-citationZonal flow regimes in rotating anelastic spherical shells: An application to giant planets
Gastine, T., Wicht, J., & Aurnou, J. M. (2013) · Icarus · doi:10.1016/j.icarus.2013.02.031 · Cited by 118 · see citing works
“25◦ latitude and 20% of the maximum zonal wind amplitude just before the transition to regime II (see the inset in Fig. 14). Such a pronounced dimple has also been observed in the anelastic models by Kaspi et al. (2009) who also employed strong density contrasts (see Fig. 13 in their study). Following the sketch displ…”
BackgroundInfluentialMechanisms of Jet Formation on the Giant Planets
Liu, J., & Schneider, T. (2010) · Journal of the Atmospheric Sciences · doi:10.1175/2010jas3492.1 · Cited by 135 · see citing works
Saturn’s zonal wind profile in 2004–2009 from Cassini ISS images and its long-term variability
García-Melendo, E., Pérez-Hoyos, S., Sánchez-Lavega, A., & Hueso, R. (2011) · Icarus · doi:10.1016/j.icarus.2011.07.005 · Cited by 122 · see citing works
Simulation of deep-seated zonal jets and shallow vortices in gas giant atmospheres
Heimpel, M., Gastine, T., & Wicht, J. (2016) · Nature Geoscience · doi:10.1038/ngeo2601 · Cited by 119 · see citing works
A dynamo model of Jupiter’s magnetic field
JONES, C. A. (2014) · Icarus · doi:10.1016/j.icarus.2014.06.020 · Cited by 104 · see citing works
“We now put this equation into Lantz–Braginsky–Roberts form without assuming a perfect gas: see also (Ingersoll and Pollard, 1982; Braginsky and Roberts, 1995; Kaspi et al., 2009).”
MethodAtmospheric confinement of jet streams on Uranus and Neptune
Kaspi, Y., Showman, A. P., Hubbard, W. B., Aharonson, O., & Helled, R. (2013) · Nature · doi:10.1038/nature12131 · Cited by 98 · see citing works
Self-citationThe transition to superrotation in terrestrial atmospheres
Mitchell, J. L., & Vallis, G. K. (2010) · Journal of Geophysical Research Atmospheres · doi:10.1029/2010je003587 · Cited by 97 · see citing works
“that do not involve a global mode but that may involve convection at the equator [Yamazaki et al., 2005; Lian and Showman, 2009; Schneider and Liu, 2009] or deep convection [Heimpel and Aurnou, 2007; Kaspi et al., 2009]. 7. Conclusions We have described the mechanism of transition of a terrestrial atmosphere to superr…”
BackgroundInfluentialGravitational signature of Jupiter's internal dynamics
Kaspi, Y., Hubbard, W. B., Showman, A. P., & Flierl, G. R. (2010) · Geophysical Research Letters · doi:10.1029/2009gl041385 · Cited by 94 · see citing works
Self-citationSaturn's Deep Atmospheric Flows Revealed by the Cassini Grand Finale Gravity Measurements
Galanti, E., Kaspi, Y., Miguel, Y., Guillot, T., Durante, D., Racioppa, P., & Iess, L. (2019) · Geophysical Research Letters · doi:10.1029/2018gl078087 · Cited by 90 · see citing works
Self-citationAtmospheric Circulation of ExoplanetsPreprint
Showman, A. P., Cho, J. Y. K., & Kristen Menou, A. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0911.3170 · Cited by 103 · see citing works
“To attack the problem more rigorously, Kaspi et al. (2009) performed full 3D numerical simulations of convection in giant-planet interiors, suggesting that the compressibility may play an important role in allowing the generation of thermal-wind shear within giant planets, especially in the…”
BackgroundInfluentialSelf-citationShowman, A. P., Tan, X., & Zhang, X. (2019) · The Astrophysical Journal · doi:10.3847/1538-4357/ab384a · Cited by 86 · see citing works
“…spherical convection models show how interior convection can induce the formation of zonal jets in the deep interior, although such models usually do not include a representation of the overlying atmosphere (e.g. Christensen 2002; Heimpel et al. 2005; Kaspi et al. 2009; Duarte et al. 2013).”
BackgroundSelf-citationExplaining Jupiter's magnetic field and equatorial jet dynamics
Gastine, T., Wicht, J., Duarte, L., Heimpel, M. H., & Becker, A. (2014) · Geophysical Research Letters · doi:10.1002/2014gl060814 · Cited by 85 · see citing works
“t equatorial jet which remains conned to the weakly conducting outer envelope. Some authors predict that the secondary jets remain restricted to Jupiter’s weather layer not represented in our model [Kaspi et al., 2009]. The gravity signal measured by the Juno mission will provide additional constraints on the depth of…”
BackgroundInferring the depth of the zonal jets on Jupiter and Saturn from odd gravity harmonics
Kaspi, Y. (2012) · Geophysical Research Letters · doi:10.1029/2012gl053873 · Cited by 84 · see citing works
“…Rossby numbers, the flow to leading order is in geostrophic balance, and therefore, the thermal wind balance must hold so that 2Ω rð Þ eru½ ¼ rr0 g0; (3) where Ω is the planetary rotation rate, u(r) is the full 3D velocity, and g0(r) is the mean gravity vector [Pedlosky, 1987; Kaspi et al., 2009].”
BackgroundInfluentialSelf-citationTHEORY AND SIMULATIONS OF ROTATING CONVECTION
Barker, A. J., Dempsey, A. M., & Lithwick, Y. (2014) · The Astrophysical Journal · doi:10.1088/0004-637x/791/1/13 · Cited by 79 · see citing works
Kaspi, Y., Galanti, E., Showman, A. P., Stevenson, D. J., Guillot, T., IESS, L., & Bolton, S. J. (2020) · Space Science Reviews · doi:10.1007/s11214-020-00705-7 · Cited by 77 · see citing works
Self-citationConvectively driven shear and decreased heat flux
Goluskin, D., Johnston, H., Flierl, G. R., & Spiegel, E. A. (2014) · Journal of Fluid Mechanics · doi:10.1017/jfm.2014.577 · Cited by 75 · see citing works
Self-citationUsing the UM dynamical cores to reproduce idealised 3-D flows
Mayne, N. J., Baraffe, I., Acreman, D. M., Smith, C., Wood, N., Amundsen, D. S., Thuburn, J., & Jackson, D. R. (2014) · Geoscientific model development · doi:10.5194/gmd-7-3059-2014 · Cited by 75 · see citing works
“However, the models of Kaspi et al. (2009) are based on the anelastic approximation which assumes the flow is incompressible and filters out sound waves (as well as breaking down for flows with Mach numbers of close to175 one).”
BackgroundMethodConvective heat transfer in planetary dynamo models
King, E. M., Soderlund, K. M., Christensen, U. R., Wicht, J., & Aurnou, J. M. (2010) · Geochemistry Geophysics Geosystems · doi:10.1029/2010gc003053 · Cited by 68 · see citing works
Anelastic dynamo models with variable electrical conductivity: An application to gas giants
Duarte, L., Gastine, T., & Wicht, J. (2013) · Physics of The Earth and Planetary Interiors · doi:10.1016/j.pepi.2013.06.010 · Cited by 67 · see citing works
“Kaspi et al. (2009), on the other hand, present an anelastic deep convection model where the equatorial zonal flow is geostrophic and the higher latitude jets are confined to the outer few percent in radius.”
BackgroundPolar vortex formation in giant-planet atmospheres due to moist convection
O’Neill, M. E., Emanuel, K., & Flierl, G. R. (2015) · Nature Geoscience · doi:10.1038/ngeo2459 · Cited by 66 · see citing works
Self-citationIntercomparison of general circulation models for hot extrasolar planets
Polichtchouk, I., Cho, J. Y., Watkins, C. N., Thrastarson, H. T., Umurhan, O. M., & Juárez, M. D. L. T. (2013) · Icarus · doi:10.1016/j.icarus.2013.11.027 · Cited by 62 · see citing works
Zonal flow scaling in rapidly-rotating compressible convection
Gastine, T., Heimpel, M. H., & Wicht, J. (2014) · Physics of The Earth and Planetary Interiors · doi:10.1016/j.pepi.2014.03.011 · Cited by 62 · see citing works
“While, following Jones and Kuzanyan (2009), we adopt here a fixed entropy contrast, Kaspi et al. (2009) used flux-boundary conditions and internal heating.”
BackgroundMethodInfluentialTheory and Simulations of Rotating Convection
Barker, A., Dempsey, A., & Lithwick, Y. (2014) · White Rose Research Online (University of Leeds, The University of Sheffield, University of York) · Cited by 63 · see citing works
The transition to superrotation in terrestrial atmospheresPreprint
Mitchell, J. L., & Vallis, G. K. (2010) · Cited by 62 · see citing works
Spiga, A., Guerlet, S., Millour, E., Indurain, M., Meurdesoif, Y., Cabanes, S., Dubos, T., Leconte, J., Boissinot, A., Lebonnois, S., et al. (2019) · Icarus · doi:10.1016/j.icarus.2019.07.011 · Cited by 55 · see citing works
“Two distinct modeling approaches have been adopted to account for Saturn's tropospheric jets: “shallow-forcing” climate models [see next paragraph for references] account for processes in the weather layer (baroclinic instability, moist convective storms), while “deep-forcing” dynamo-like models (Heimpel et al., 2005;…”
Exploring Ocean Circulation on Icy Moons Heated From Below
Bire, S., Kang, W., Ramadhan, A., Campin, J., & Marshall, J. C. (2022) · Journal of Geophysical Research Planets · doi:10.1029/2021je007025 · Cited by 57 · see citing works
CONSISTENT SCALING LAWS IN ANELASTIC SPHERICAL SHELL DYNAMOS
Yadav, R. K., Gastine, T., Christensen, U. R., & Duarte, L. (2013) · The Astrophysical Journal · doi:10.1088/0004-637x/774/1/6 · Cited by 54 · see citing works
“Following Kaspi et al. (2009), Gastine & Wicht (2012) expressed the velocity scaling in their anelastic convection simulations using a mass averaged 〈Ra∗Q〉ρ, where 〈·〉ρ stands for ∫ (·) ρ̃ r2 dr/ ∫ ρ̃ r2 dr, to better collapse simulations with different density stratifications.”
Simulating Jupiter’s weather layer. Part I: Jet spin-up in a dry atmosphere
Young, R. M. B., Read, P. L., & Wang, Y. (2018) · Icarus · doi:10.1016/j.icarus.2018.12.005 · Cited by 49 · see citing works
Ingersoll, A. P., Adumitroaie, V., Allison, M., Atreya, S., Bellotti, A., Bolton, S. J., Brown, S., Gulkis, S., Janssen, M., Levin, S. M., et al. (2017) · Geophysical Research Letters · doi:10.1002/2017gl074277 · Cited by 32 · see citing works
Superrotation in Planetary Atmospheres
Imamura, T., Mitchell, J. L., Lebonnois, S., Kaspi, Y., Showman, A. P., & Korablev, O. (2020) · Space Science Reviews · doi:10.1007/s11214-020-00703-9 · Cited by 52 · see citing works
“Therefore, the convectively driven flow is not only driven by buoyancy (in which case it would be mainly in the radial direction), but also by the limitation that the flow must be aligned with the direction of the axis of rotation (Kaspi et al. 2009; O’Neill and Kaspi 2016).”
BackgroundInfluentialSelf-citationDynamics of Saturn's polar regions
Antuñano, A., del Río‐Gaztelurrutia, T., Sánchez‐Lavega, A., & Hueso, R. (2015) · Journal of Geophysical Research: Planets · doi:10.1002/2014je004709 · Cited by 50 · see citing works
Mechanisms for Limiting the Depth of Zonal Winds in the Gas Giant Planets
Christensen, U. R., Wicht, J., & Dietrich, W. (2020) · The Astrophysical Journal · doi:10.3847/1538-4357/ab698c · Cited by 50 · see citing works
Deep rotating convection generates the polar hexagon on Saturn
Yadav, R. K., & Bloxham, J. (2020) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2000317117 · Cited by 45 · see citing works
Physical conditions for Jupiter-like dynamo models
Duarte, L., Wicht, J., & Gastine, T. (2017) · Icarus · doi:10.1016/j.icarus.2017.07.016 · Cited by 48 · see citing works
“The interior dynamics of Jupiter has been the topic of an increasing number of studies over the last ten years (Heimpel et al., 2005; Lian and Showman, 2008; Stanley and Glatzmaier, 2010; Kaspi et al., 2009; Heimpel and Gómez-Pérez, 2011; Gastine and Wicht, 2012; Duarte et al., 2013; Gastine et al., 2014b; Jones, 2014…”
BackgroundCombined magnetic and gravity measurements probe the deep zonal flows of the gas giants
Galanti, E., & Kaspi, Y. (2020) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staa3722 · Cited by 48 · see citing works
“This also implies that the entropy expansion coefficient does not change considerably with depth, as the decay rate of the flow is a product of the entropy gradients and the entropy expansion coefficient (Kaspi et al. 2009).”
BackgroundInfluentialSelf-citationObservational evidence for cylindrically oriented zonal flows on Jupiter
Kaspi, Y., Galanti, E., Park, R. S., Duer, K., Gavriel, N., Durante, D., IESS, L., Parisi, M., Buccino, D., Guillot, T., et al. (2023) · Nature Astronomy · doi:10.1038/s41550-023-02077-8 · Cited by 44 · see citing works
“Equatorwards of these jets there is an eastward flow with velocities of ~100 m s −1 , which is super-rotating within 6° of the equator 3 , and polewards of ±65° the jets disappear and the dynamics become dominated by vortices all the way to the poles.”
InfluentialSelf-citationScaling laws for convection and jet speeds in the giant planets
Showman, A. P., Kaspi, Y., & Flierl, G. R. (2010) · Icarus · doi:10.1016/j.icarus.2010.11.004 · Cited by 44 · see citing works
Self-citationWeak Jets and Strong Cyclones: Shallow-Water Modeling of Giant Planet Polar Caps
O’Neill, M. E., Emanuel, K., & Flierl, G. R. (2016) · Journal of the Atmospheric Sciences · doi:10.1175/jas-d-15-0314.1 · Cited by 44 · see citing works
“We still can define a convective Rossby number, Roconv 5Wst/( f0H1) (Kaspi et al. 2009), since its components are all control parameters, but this should not be confused with the global Rossby number that results from horizontal velocity and length scales.”
BackgroundSelf-citationGravity and zonal flows of giant planets: From the Euler equation to the thermal wind equation
Cao, H., & Stevenson, D. J. (2017) · Journal of Geophysical Research Planets · doi:10.1002/2017je005272 · Cited by 43 · see citing works
Ashkenazy, Y., & Tziperman, E. (2021) · Nature Communications · doi:10.1038/s41467-021-26710-0 · Cited by 43 · see citing works
Evidence for Multiple Ferrel‐Like Cells on Jupiter
Duer, K., Gavriel, N., Galanti, E., Kaspi, Y., Fletcher, L. N., Guillot, T., Bolton, S. J., Levin, S., Atreya, S. K., Grassi, D., et al. (2021) · Geophysical Research Letters · doi:10.1029/2021gl095651 · Cited by 43 · see citing works
“For the vertical case, several studies have shown that an equatorial superrotation in giant planets can be driven by eddy momentum fluxes perpendicular to the axis of rotation (Heimpel et al., 2005; Kaspi et al., 2009; Gastine et al., 2014).”
InfluentialSelf-citationSaturn's Deep Atmospheric Flows Revealed by the Cassini Grand Finale Gravity Measurements
Galanti, E., Kaspi, Y., Miguel, Y., Guillot, T., Durante, D., Racioppa, P., & IESS, L. (2019) · Leiden Repository (Leiden University) · Cited by 41 · see citing works
Self-citationJupiter's Temperate Belt/Zone Contrasts Revealed at Depth by Juno Microwave Observations
Fletcher, L. N., Oyafuso, F., Allison, M., Ingersoll, A. P., Li, L., Kaspi, Y., Galanti, E., Wong, M. H., Orton, G. S., Duer, K., et al. (2021) · Journal of Geophysical Research Planets · doi:10.1029/2021je006858 · Cited by 42 · see citing works
“However, as we are dealing here with a relatively shallow layer of atmosphere, with a small aspect ratio between the vertical and horizontal scales, this form of thermal wind is sufficient (Kaspi et al., 2009).”
BackgroundSelf-citationNumerical simulation of convectively generated vortices: Application to the Jovian planets
Chan, K. L., & Mayr, H. G. (2013) · Earth and Planetary Science Letters · doi:10.1016/j.epsl.2013.03.046 · Cited by 37 · see citing works
Constraints on Saturn’s tropospheric general circulation from Cassini ISS images
C, A. D. D. G., & Barbara, J. (2012) · Icarus · doi:10.1016/j.icarus.2012.03.035 · Cited by 36 · see citing works
“Anelastic models of deep cylindrical convection (Kaspi et al., 2009) produce large eddy momentum fluxes at depth when forced with excessive internal heat fluxes; it remains to be seen whether such a model run with realistic forcing can restrict large horizontal eddy flux convergences and energy conversions to a shallo…”
BackgroundInfluentialThe compressional beta effect: A source of zonal winds in planets?
Verhoeven, J., & Stellmach, S. (2014) · Icarus · doi:10.1016/j.icarus.2014.04.019 · Cited by 34 · see citing works
“Among such models, only a few have included the effect of a density increase with depth so far (Kaspi et al., 2009; Jones and Kuzanyan, 2009; Gastine and Wicht, 2012), typically using Ekman numbers between O(10−4) and O(10−6).”
BackgroundGeneration of Large-Scale Winds in Horizontally Anisotropic Convection
von Hardenberg, J., Goluskin, D., Provenzale, A., & Spiegel, E. A. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.134501 · Cited by 33 · see citing works
Predictions of thermal and gravitational signals of Jupiter’s deep zonal winds
Liu, J., Schneider, T., & Kaspi, Y. (2013) · Icarus · doi:10.1016/j.icarus.2013.01.025 · Cited by 32 · see citing works
“Rather, zonal winds generally must be sheared along angular momentum surfaces, as seen in the simulations in Schneider and Liu (2009) and Kaspi et al. (2009).”
BackgroundMethodInfluentialSelf-citationDynamics of Jupiter’s equatorial region at cloud top level from Cassini and HST images
Garcia‐Melendo, E., Arregi, J., Rojas, J. F., Hueso, R., Barrado-Izagirre, N., Gómez-Forrellad, J. M., Pérez-Hoyos, S., Sanz‐Requena, J. F., & Sánchez-Lavega, A. (2010) · Icarus · doi:10.1016/j.icarus.2010.11.020 · Cited by 31 · see citing works
Kaspi, Y., Davighi, J., Galanti, E., & Hubbard, W. B. (2016) · Icarus · doi:10.1016/j.icarus.2016.04.001 · Cited by 30 · see citing works
“For example, if as hyothesized by Liu et al. (2008) , only the outer 4% of the radius ave significant flows in them, that will already involve 1% of the ass of the planet.”
BackgroundSelf-citationThe effect of differential rotation on Jupiter's low‐degree even gravity moments
Kaspi, Y., Guillot, T., Galanti, E., Miguel, Y., Helled, R., Hubbard, W. B., Militzer, B., Wahl, S. M., Levin, S., Connerney, J. E. P., et al. (2017) · Geophysical Research Letters · doi:10.1002/2017gl073629 · Cited by 31 · see citing works
“D hydrodynamical models [e.g., Aurnou and Olson, 2001; Christensen, 2002; Heimpel et al., 2005; Kaspi et al., 2009; Gastine and Wicht, 2012], they may have a nonnegligible effect on the low-degree gravity moments.”
BackgroundSelf-citationLock, S. J., Bermingham, K. R., Parai, R., & Boyet, M. (2020) · Space Science Reviews · doi:10.1007/s11214-020-00729-z · Cited by 30 · see citing works
Galanti, E., & Kaspi, Y. (2016) · The Astrophysical Journal · doi:10.3847/0004-637x/820/2/91 · Cited by 29 · see citing works
“These zonal flows have been shown in numerical models to have a structure which is aligned with the axis of rotation, yet with wind speeds that decay with depth (Kaspi et al. 2009).”
BackgroundInfluentialSelf-citationRapidly rotating Rayleigh-Bénard convection with a tilted axis
Novi, L., von Hardenberg, J., Hughes, D. W., Provenzale, A., & Spiegel, E. A. (2019) · Physical review. E · doi:10.1103/physreve.99.053116 · Cited by 29 · see citing works
Uranus and Neptune are key to understand planets with hydrogen atmospheres
Guillot, T. (2021) · Experimental Astronomy · doi:10.1007/s10686-021-09812-x · Cited by 27 · see citing works
An enduring rapidly moving storm as a guide to Saturn’s Equatorial jet’s complex structure
Sánchez-Lavega, A., Garcia‐Melendo, E., Pérez-Hoyos, S., Hueso, R., Wong, M. H., Simon, A. A., Sanz‐Requena, J. F., Antuñano, A., Barrado-Izagirre, N., Gárate-López, I., et al. (2016) · Nature Communications · doi:10.1038/ncomms13262 · Cited by 27 · see citing works
“For example models of deep extending winds under deep forcing [56-58] reproduce the double jet peak we observe in the Equator of Jupiter [1] and Saturn (figure 7, [32]).”
BackgroundPolar and mid-latitude vortices and zonal flows on Jupiter and Saturn
Heimpel, M. H., Yadav, R. K., Featherstone, N. A., & Aurnou, J. M. (2020) · Icarus · doi:10.1016/j.icarus.2022.114942 · Cited by 26 · see citing works
Internally heated convection beneath a poor conductor
Goluskin, D. (2015) · Journal of Fluid Mechanics · doi:10.1017/jfm.2015.140 · Cited by 26 · see citing works
Probing the depth of Jupiter’s Great Red Spot with the Juno gravity experiment
Parisi, M., Galanti, E., Finocchiaro, S., IESS, L., & Kaspi, Y. (2015) · Icarus · doi:10.1016/j.icarus.2015.12.011 · Cited by 23 · see citing works
Self-citationThe Global Atmospheric Circulation of Saturn
Showman, A. P., Ingersoll, A. P., Achterberg, R. K., & Kaspi, Y. (2018) · Cambridge University Press eBooks · doi:10.1017/9781316227220.011 · Cited by 21 · see citing works
“…tends to be too broad and the higher lati-19 tude jets fewer in number compared to Jupiter and Saturn.20 In the models of Kaspi (2008) and Kaspi et al. (2009), the21 jets exhibit significant shear, becoming weaker with depth;22 in contrast, some other models exhibit weaker shear, with…”
BackgroundSelf-citationDetermining the Depth of Jupiter’s Great Red Spot with Juno: A Slepian Approach
Galanti, E., Kaspi, Y., Simons, F. J., Durante, D., Parisi, M., & Bolton, S. J. (2019) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/ab1086 · Cited by 21 · see citing works
“Due to the strong winds around the vortex the geostrophic gradient creates a density anomaly with respect to its surroundings, that can be calculated via thermal wind balance, namely (2Ω · ∇) [ρ̃u] = ∇ρ′ × g0, (7) where u(r) = [u0, v0] is the 3D velocity, Ω is the planetary rotation rate, ρ̃(r) is the background densi…”
BackgroundSelf-citationConstraining the depth of Saturn’s zonal winds by measuring thermal and gravitational signals
Liu, J., Schneider, T., & Fletcher, L. N. (2014) · Icarus · doi:10.1016/j.icarus.2014.05.036 · Cited by 20 · see citing works
Constraints on the Latitudinal Profile of Jupiter's Deep Jets
Galanti, E., Kaspi, Y., Duer, K., Fletcher, L. N., Ingersoll, A. P., Li, C., Orton, G. S., Guillot, T., Levin, S., & Bolton, S. J. (2021) · Geophysical Research Letters · doi:10.1029/2021gl092912 · Cited by 20 · see citing works
Self-citationAnalysis of Jupiter’s Deep Jets Combining Juno Gravity and Time-varying Magnetic Field Measurements
Duer, K., Galanti, E., & Kaspi, Y. (2019) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/ab288e · Cited by 19 · see citing works
“Consequently, the leading-order vorticity balance is thermal wind balance (Kaspi et al. 2009).”
BackgroundSelf-citationScaling of Off-Equatorial Jets in Giant Planet Atmospheres
Liu, J., & Schneider, T. (2014) · Journal of the Atmospheric Sciences · doi:10.1175/jas-d-13-0391.1 · Cited by 17 · see citing works
“(with Coriolis parameter f 5 2V sinf); it represents the Coriolis torque per unit mass (cf. Kaspi et al. 2009).”
BackgroundThe Range of Jupiter's Flow Structures That Fit the Juno Asymmetric Gravity Measurements
Duer, K., Galanti, E., & Kaspi, Y. (2020) · Journal of Geophysical Research Planets · doi:10.1029/2019je006292 · Cited by 19 · see citing works
“Internal convection models support the scenario that there may be internal shear over the upper few thousand kilometers, but the overall structure of the flow does not change much (Jones & Kuzanyan, 2009; Kaspi et al., 2009).”
BackgroundInfluentialSelf-citationDeitrick, R., Heng, K., Schroffenegger, U., Kitzmann, D., Grimm, S. L., Malik, M., Mendonça, J. M., & Morris, B. M. (2022) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stac680 · Cited by 18 · see citing works
Hierarchical Modeling of Solar System Planets with Isca
Thomson, S. I., & Vallis, G. K. (2019) · Atmosphere · doi:10.3390/atmos10120803 · Cited by 18 · see citing works
“, [56]), to those including varying degrees of three-dimensionality, including the primitive-equation models of Schneider and Liu [62] through to anelastic models [63] and finally to deep-convection models such as those of Heimpel et al.”
BackgroundA Global Simulation of the Dynamo, Zonal Jets, and Vortices on Saturn
Yadav, R. K., Cao, H., & Bloxham, J. (2022) · The Astrophysical Journal · doi:10.3847/1538-4357/ac9d94 · Cited by 15 · see citing works
“This idea was put forth by Busse (1976) and has been extensively explored in many numerical simulation studies (e.g., Aurnou & Olson 2001; Christensen 2001; Heimpel et al. 2005; Jones & Kuzanyan 2009; Kaspi et al. 2009; Gastine et al. 2014a; Yadav & Bloxham 2020).”
BackgroundHay, H. C. F. C., Fenty, I. G., Pappalardo, R. T., & Nakayama, Y. (2023) · Journal of Geophysical Research Planets · doi:10.1029/2022je007648 · Cited by 14 · see citing works
Galanti, E., & Kaspi, Y. (2017) · Icarus · doi:10.1016/j.icarus.2017.01.004 · Cited by 14 · see citing works
“circulation model was forced by an internal heat source (e.g., Heimpel and Gómez Pérez, 2011; Christensen, 2002; Kaspi et al., 2009).”
BackgroundSelf-citationModeling the Interior Dynamics of Gas Planets
Wicht, J., French, M., Stellmach, S., Nettelmann, N., Gastine, T., Duarte, L., & Redmer, R. (2018) · Astrophysics and space science library · doi:10.1007/978-3-319-64292-5_2 · Cited by 13 · see citing works
Galanti, E., Durante, D., Finocchiaro, S., IESS, L., & Kaspi, Y. (2017) · The Astronomical Journal · doi:10.3847/1538-3881/aa72db · Cited by 13 · see citing works
“…using the thermal wind balance W r r = ¢ ´( · )[ ] ( )u g2 , 70 whereW is the planetary rotation rate, r ( )r is the background density field, ( )u r is the 3D velocity, ( )g r0 is the mean gravity vector, and r q f¢( )r, , is the dynamical density anomaly (Pedlosky 1987; Kaspi et al. 2009).”
Self-citationPrediction for the Flow-induced Gravity Field of Saturn: Implications for Cassini ’s Grand Finale
Galanti, E., & Kaspi, Y. (2017) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/aa7aec · Cited by 13 · see citing works
“…to leading order, conservation of angular momentum inhibits, to leading order, the mixing of momentum across lines parallel to the axis of rotation (Kaspi et al. 2009; Schneider & Liu 2009; Liu et al. 2014); therefore, the observed cloud-level zonal winds are projected inward along these lines.”
BackgroundSelf-citationThe turbulent dynamics of Jupiter’s and Saturn’s weather layers: order out of chaos?
Read, P. L., Young, R. M. B., & Kennedy, D. (2020) · Geoscience Letters · doi:10.1186/s40562-020-00159-3 · Cited by 12 · see citing works
A dynamo driven by zonal jets at the upper surface: Applications to giant planets
Guervilly, C., Cardin, P., & Schaeffer, N. (2011) · Icarus · doi:10.1016/j.icarus.2011.11.014 · Cited by 13 · see citing works
“This feature is also present in strongly compressible models provided that the Ekman number is small enough, despite the increase of density with depth yielding ageostrophic convective motions (Jones and Kuzanyan, 2009; Kaspi et al., 2009).”
BackgroundSlantwise convection on fluid planets
O’Neill, M. E., & Kaspi, Y. (2016) · Geophysical Research Letters · doi:10.1002/2016gl071188 · Cited by 13 · see citing works
“A large body of theory and numerical modeling work [e.g., Christensen, 2002; Heimpel and Aurnou, 2007; Kaspi et al., 2009] demonstrates that the spin axis is the preferred direction for convective mixing for a dry adiabatic interior, for Jovian rotation rates.”
BackgroundSelf-citationThe Dynamics of Jupiter's and Saturn's Weather Layers: A Synthesis After Cassini and Juno
Read, P. L. (2023) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-121021-040058 · Cited by 12 · see citing works
THEORY OF SOLAR MERIDIONAL CIRCULATION AT HIGH LATITUDES
Dikpati, M., & Gilman, P. A. (2012) · The Astrophysical Journal · doi:10.1088/0004-637x/746/1/65 · Cited by 12 · see citing works
“Jupiter is a rather fast rotator, and has many axisymmetric meridional cells between equator and pole (see Kaspi et al. 2009 and references therein).”
Dowling, T. E. (2020) · The Planetary Science Journal · doi:10.3847/psj/ab789d · Cited by 12 · see citing works
The Effect of Salinity on Ocean Circulation and Ice–Ocean Interaction on Enceladus
Zeng, Y., & Jansen, M. F. (2024) · The Planetary Science Journal · doi:10.3847/psj/ad0cba · Cited by 11 · see citing works
“The density structure controls the zonal flow via the thermal wind relationship, which can be written as (see e.g. Kaspi et al. 2009; Bire et al. 2022): where ⃗ Ω is the planetary rotation rate, u is the zonal velocity, Z is the axis parallel to rotation, r is radius, ϕ is latitude, and b ≡ − gδρ/ρ…”
BackgroundCONVECTIVE BURSTS AND THE COUPLING OF SATURN'S EQUATORIAL STORMS AND INTERIOR ROTATION
Heimpel, M. H., & Aurnou, J. M. (2012) · The Astrophysical Journal · doi:10.1088/0004-637x/746/1/51 · Cited by 11 · see citing works
“Although it was originally derived for an isothermal, Boussinesq (incompressible) fluid, the Proudman–Taylor theorem holds for the azimuthal velocity component in both incompressible and compressible flows (Jones & Kuzanyan 2009; Rempel 2005; cf. Kaspi et al. 2009).”
BackgroundMethodTHEORY OF SOLAR MERIDIONAL CIRCULATION AT HIGH LATITUDESPreprint
Dikpati, M., & Gilman, P. A. (2016) · Cited by 11 · see citing works
Gas Giant Simulations of Eddy‐Driven Jets Accompanied by Deep Meridional Circulation
Duer, K., Galanti, E., & Kaspi, Y. (2023) · AGU Advances · doi:10.1029/2023av000908 · Cited by 10 · see citing works
“This balance is the zonally averaged geostrophic balance, which is the leading order balance of the zonal momentum equation (Equation 1) for small Rossby and Ekman numbers (Kaspi et al., 2009).”
BackgroundSelf-citationGlobal climate modeling of the Jupiter troposphere and effect of dry and moist convection on jets
Boissinot, A., Spiga, A., Guerlet, S., Cabanes, S., & Bardet, D. (2024) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202245220 · Cited by 10 · see citing works
Nonlinear Atmospheric Flow Patterns Confined to Zonal Cloud Bands
Constantin, A., & Johnson, R. S. (2024) · Journal of the Atmospheric Sciences · doi:10.1175/jas-d-24-0038.1 · Cited by 10 · see citing works
Lian, Y., & Richardson, M. I. (2023) · Planetary and Space Science · doi:10.1016/j.pss.2023.105663 · Cited by 10 · see citing works
Galanti, E., Kaspi, Y., & Guillot, T. (2023) · Geophysical Research Letters · doi:10.1029/2022gl102321 · Cited by 9 · see citing works
Self-citation
- Authors
- Kaspi, Y., Flierl, G. R., & Showman, A. P.
- Affiliations
- Massachusetts Institute of Technology (US)
- University of Arizona (US)
- Corresponding author
- Kaspi, Yohai
- Venue
- Icarus
- Publisher
- Elsevier BV
- Published
- 2009-08
- Volume
- 202
- Issue
- 2
- Pages
- 525-542
- ISSN
- 0019-1035 (ISSN-L)
- OpenAlex
- W2087943296
- Cited by
- 149
- References
- 72
- Citations by year
- 2026: 5 · 2025: 5 · 2024: 9 · 2023: 7 · 2022: 6 · 2021: 8 · 2020: 15 · 2019: 13 · 2018: 9 · 2017: 16 · 2016: 6 · 2015: 11 · 2014: 10 · 2013: 9 · 2012: 8
- FWCI
- 3.36
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Icarus (publishedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Astro and Planetary Science
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Stellar, planetary, and galactic studies
- Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Turbulent Flows
- Keywords
- giant planet atmospheres, baroclinic vorticity, compressibility effects, vertical shear, thermal wind relation, equatorial superrotation, poleward heat transport, Rayleigh number, Jupiter, Saturn
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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