Simulation of equatorial and high-latitude jets on Jupiter in a deep convection model

“…Wicht & Tilgner 2010; Stanley & 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…”

“…we conjecture that if such a cascade were allowed to continue until the latitudinal variation of the Coriolis parameter (i.e. the -effect) were felt, the large-scale dynamics would organize into zonal flows at the Rhines scale as seen in spherical geometry (Heimpel et al. 2005).”

“…Jupiter’s (and Saturn’s) zonal jet structure by a hybrid model of potential vorticity dynamics have succeeded in reproducing the required prograde equatorial jet together with a realistic midlatitudinal and higher-latitudinal structure of zonal jets [Heimpel et al., 2005; Heimpel and Aurnou, 2007].”

“Truncation of the winds in the planet’s convective envelopewould involve breaking the TaylorProudman constraint on cylindrical flow.”

“For those smaller scales, where convergence is steeper than for a n−2 spectrum, the statistical flow assumptions of Hulot et al. (1992) leading to their estimate of the SV signal that results from the interaction between BS and the flow (see section 3.”

“…resolved in state-of-the-art simulations, these spatially anisotropic, and often spectrally non-local, exchanges can lead to novel modes of rotating convective flow (e.g., Heimpel et al., 2005; Käpylä et al., 2011; Chan and Mayr, 2013; Rubio et al., 2014) and dynamo action (Guervilly et al., 2015).”

“This suggests that zonal flows follow a universal behaviour, independent of the density stratification, and may also explain why Boussinesq models were already very successful in reproducing the morphology of the jets observed in gas giants (e.g. Heimpel et al., 2005).”

“…of convection in rotating spherical shells force the system by passing a heat flux through impermeable upper and lower boundaries, either with a constanttemperature or constant heat flux boundary condition (e.g., Christensen 2001, 2002; Aurnou & Olson 2001; Heimpel et al. 2005, and many others).”

“Most previous studies have treated a shallower region than we have done here (e.g. Sun et al., 1993; Heimpel et al., 2005).”

“Evidently, somemechanism not included in the simplest version of the equivalent barotropic equations is required for Jupiter (e.g., Heimpel et al. 2005) and Saturn but not for Uranus and Neptune.”

“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).”

“Following the experience of Heimpel et al. (2005) we increased the radius ratio, from η = 0.”

“In contrast, the deep convection models produce equatorial superrotation in most cases (Aurnou and Olson, 2001; Christensen, 2001; Heimpel et al., 2005; Heimpel and Aurnou, 2007; Glatzmaier et al., 2008), consistent with Jupiter and Saturn but inconsistent with Uranus and Neptune.”

“It is noted the numerical model with χ = 0. 9w as previously presented in Heimpel et al. (2005) .”

“Furthermore, most published computations with such models (e.g., Heimpel et al. 2005; Stanley and Bloxham 2004; Sun et al. 1993) have, to date, used a Boussinesq approximation, implying the density is nearly constant with radius, surely an unrealistic assumption for the massive giant planets.”

“…can be captured in a purely barotropic model although there has been a recent attempt to represent the general atmospheric circulation on Jupiter as a superposition of the barotropic flow at relatively high latitudes and a deep rotating convection in the equatorial region (Heimpel et al., 2005).”

“…with these columns drive prograde equatorial flow with jets that alternate in direction at higher latitudes due to correlation locally between the azimuthal and cylindrically radial flow components (e.g., Aurnou & Olson, 2001; Christensen, 2001; Heimpel et al., 2005; Gastine et al., 2014).”

“…in substantially deeper fluid layers than are estimated on the ice giants (Suomi et al., 1991; Guillot, 1999), the χ = 0.75 spherical shell geometry is still relatively thin and allows us to use a far smaller numerical grid than in the comparable χ = 0.90 simulations of Heimpel et al. (2005).”

“It is however possible that the zonal flow and the enhanced turbulence in the upper layers (Heimpel et al., 2005; Jones and Kuzanyan, 2009, Showman et al., 2011) could influence the dynamics below.”

“To date, most studies of this process involve 3D numerical simulations of convection in a self-gravitating spherical shell excluding the effects of magnetohydrodynamics (e.g., Aurnou and Olson 2001; Christensen 2001, 2002; Heimpel et al. 2005).”

“…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).”

“dynamical models therefore treat the dynamics of these two layers separately, focussing either on the dynamo action [Christensen and Aubert, 2006; Gastine et al., 2012] or on the zonal winds driving [Heimpel et al., 2005; Jones and Kuzanyan , 2009;Kaspi et al. Gastine and Wicht, 2012; Gastine et al., 2014]. However, s…”

“us in Nature. It is found not only in the Earth’s interior and oceans, but also in planetary atmospheres and also inside stars (Marshall & Schott 1999; Miesch 2000; Roberts & Glatzmaier 2000; Heimpel et al. 2005). In all of those ows, the background rotation induces a Coriolis force, which signicantly aects th…”

“The asymptotic theory of the onset of rapidly rotating convection in a Boussinesq sphere was developed by Roberts (1968) and Busse (1970).”

“More recent numerical model studies, such as those by Heimpel et al. (2005) based upon Boussinesq deep convection, and anelastic models by Jones and Kuzanyan (2009) and Gastine and Wicht (2012), put the deep convection hypothesis on a more quantitative basis.”

“…candidates have been identified as barotropic or baroclinic instabilities (e.g., Kaspi and Flierl 2007; Lian and Showman 2008; Schneider and Liu 2009; Liu and Schneider 2010; Young et al. 2019) or the internal convection itself (e.g., Heimpel et al. 2005; Young et al. 2019; Showman et al. 2019).”

“Outside the tangent cylinder, Reynolds stresses drive a retrograde inner and a basically prograde outer flow (Christensen 2002; Heimpel et al. 2005; Aubert 2005).”

“2000, Heimpel et al. 2005, Roberts and King 2013).”

“Based on numerical modelling results ( Heimpel et al. 2005;”

“Furthermore, rotating convection in spherical shells is capable of driving strong zonal flows [e.g., Christensen, 2002; Heimpel et al., 2005].”

“In the rotationally-dominated dynamics ruling planetary atmospheres, interior convection naturally drives zonal winds via Reynolds stresses (i.e. a statistical correlation between the convective flow components; Christensen, 2002; Heimpel et al., 2005).”

“The "zonal flow" phenomenon has been investigated in experiments of geophysical and astrophysical flows [45, 46].”

“…past, both analytically (e.g. Zhang 1992; Busse 1994) and numerically (Gilman 1977; Miesch et al. 2000; Grote et al. 2000; Aurnou and Olson 2001; Christensen 2001, 2002; Heimpel et al. 2005; Ballot et al. 2007; Käpylä et al. 2011; Gastine and Wicht 2012; Guerrero et al. 2013; Hotta et al. 2015).”

“Following our previous parameter studies of compressible convection (Gastine and Wicht, 2012; Gastine et al., 2013), the zonal flow profiles obtained here show many similarities with their Boussinesq counterparts (e.g. Heimpel et al., 2005, HA07).”

“The main caveat to keep in mind regarding the model we used here is the assumed baroclinic structure, which although converted from the standard terrestrial case based on estimates of Ingersoll and Pollard (1982), still is quasigeostrophic, a questionable approximation for deep atmospheres.”

“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;…”

“Typical examples include zonal flow in the atmosphere of Jupiter (Heimpel et al. 2005; Kaspi et al. 2018; Kong et al. 2018) and other three Jovian planets (Ingersoll 1990; Sun et al.”

“Christensen, 2002), multiple jets of alternated directions (Heimpel et al., 2005; Jones and Kuzanyan, 2009; Gastine, Heimpel and Wicht, 2014a), or the formation of large scale vorticies (Heimpel, Gastine and Wicht, 2016).”

“…can lead to equatorial superrotation and multiple jets caused by convective columns (Aurnou and Olson 2001; Christensen 2001; Wicht et al. 2002; Heimpel et al. 2005, 2016; Kaspi et al. 2009; Jones and Kuzanyan 2009; Gastine et al. 2013; Chan and Mayr 2013; Heimpel et al. 2016; Dietrich and…”

“Noting that these jets usually form in the vicinity of the tangent cylinder in such simulations (21, 31, 35), we speculate that Saturn’s atmosphere might extend somewhat deeper than 0.”

“This phenomenon arises from the stable stratification in the bulk (Ravi et al. 1994) and can also be observed in the similarity solutions of the boundary layer equations for natural convection over a vertical hot wall in a stably stratified environment (Henkes & Hoogendoorn 1989).”

“At least the equatorial jet could be a geostrophic structure that reaches through the planets and is maintained by Reynolds stresses, a statistical correlation between smaller-scale convective flow components (Christensen, 2001; Heimpel et al., 2005; Gastine and Wicht, 2012; Gastine et al., 2012).”

“Convectively driven, rotationally constrained flows are the foundation of many geophysical and astrophysical processes, from dynamo action in Earth’s molten iron core [1] to atmospheric patterns in gas giants [2].”

“This has been discussed theoretically since the early papers about Jupiter’s dynamics 18,31 , demonstrated in laboratory experiments 32 and 3D numerical simulations 19,33–35 and used in numerous theoretical studies 36,37 but never confirmed observationally.”

“…state-of-the-art high-resolution numerical simulations, if expressed in dimensional units, typically integrate months to years (e.g., Aurnou et al. 2008; Aurnou and Olson 2001; Christensen 2001, 2002; Heimpel and Aurnou 2007; Heimpel et al. 2005; Jones and Kuzanyan 2009; Kaspi et al. 2009).”

“In the presence of a b effect, this interaction can allow jovian-style jets to emerge from small-scale forcing (e.g., Williams, 1978; Cho and Polvani, 1996; Nozawa and Yoden, 1997; Huang and Robinson, 1998; Showman, 2007; Scott and Polvani, 2007; Sukoriansky et al., 2007; Heimpel et al., 2005; Lian and Showman, 2008,…”

“This is probably due to a combination of anomalous equatorial dynamics (Heimpel et al. 2005) and the manner by which chemical constituents are pumped into the near-equatorial weather layer.”

“In the solar System, several previous studies have investigated processes that could be driving the jet structure at various depths on Jupiter and Saturn (e.g., Galperin et al. 2004; Heimpel et al. 2005; Kaspi and Flierl 2007; Read et al. 2007; ?; Schneider and Liu 2009; Liu and Schneider 2010; Young et al. 2019).”

“ctonics on Earth and possibly also the zonal winds on Jupiter and other giant planets (e.g. Brun et al. 2004; Brandenburg and Subramanian 2005; Trompert and Hansen 1998; Tackley 2000; Bercovici 2003; Heimpel et al. 2005; Verhoeven and Stellmach 2014). The convective regions in stellar and planetary objects typically f…”

“Spherical Couette flow may also be relevant to giant planets: bands of strong zonal winds are visible at their surfaces, and if deep rooted (Heimpel et al. 2005) they can exert a forcing on the outer boundary of the core.”

“These highly resolved 3-d simulations as well as their incompressible counterparts (e.g. Heimpel et al. (2005); Heimpel and Aurnou (2007)) consistently only find two jets on the equatorial plane.”

“It will be also interesting to investigate in future works the dynamics of relatively deep planetary waves close to the tangent equatorial cylinder in Giant planets such as Jupiter [39].”

“Jupiter’s rapid planetary rotation (small Rossby numbers) and negligible viscosity imply that convective motions are predominantly confined to surfaces of constant angular momentum per unit mass (Busse, 1976, 1994; Christensen, 2001; Heimpel et al., 2005; Aurnou et al., 2008; Kaspi et al., 2009; Jones and Kuzanyan, 20…”

“The occurrence of these large-scale structures in experimental and numerical models of turbulent flows [3,4] attracts much interest because they are observed in many geophysical and astrophysical bodies [5,6].”

“…t m 4 u l p m ( i 0 ( w ρ a w N e m l i t d m d a t p f c n s C b a p P 4 n 2 w o n initial trial solution and iterate until convergence is achieved. ubbard (1975) has derived, for the solid-body case, leading order xpansions of J 2 , J 4 , J 6 , A 0 , A 2 , A 4 and k in the small rotation…”

“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.”

“[24] found that zonal flow in the equatorial latitude of Jupiter is prograde with respect to the planet, which is consistent with the actually observed results of Jupiter [25], but the width of equatorial zonal flow does not coincide with the predictions of Rhines scale [26].”

“us in Nature. It is found not only in the Earth’s interior and oceans, but also in planetary atmospheres and also inside stars (Marshall & Schott 1999; Miesch 2000; Roberts & Glatzmaier 2000; Heimpel et al. 2005). In all of those ows, the background rotation induces a Coriolis force, which signicantly aects th…”