GEOPHYSICAL RESEARCH LETTERS, VOL. ???, XXXX, DOI:10.1002/, Slantwise Convection on Fluid Planets Morgan E O'Neill1 and Yohai Kaspi1 The second group, focusing on the thin weather layers, Key Points. emphasizes the impact of stratification but uses the `tradi- ◦ Slantwise convection may be important in the rela- tional approximation' of the Coriolis force [Phillips, 1966], tively shallow weather-layer of giant planets wherein only the component normal to the local surface is ◦ At low latitudes, buoyancy perturbations yield net mo- retained: f ≈ f0 sin φ for latitude φ (e.g., Williams [1978]; Dowling [1993]; Lian and Showman [2008]; Liu and Schnei- tion that is more horizontal than vertical der [2010]). The great conceptual advantage of this is that ◦ NASA's Juno microwave measurements of Jupiter these models can be readily modified from the more ad- should be interpreted along angular momentum sur- vanced Earth climate models, which typically use the tradi- faces tional approximation. However, the lower boundary of these models should be much deeper than that on Earth, given previous observational evidence of the stable weather-layer depth (e.g., Seiff et al. [1998],Allison and Atkinson [2001]). Slantwise convection should be ubiquitous in the at- NASA's Juno spacecraft is now in Jupiter's orbit, carry- mospheres of rapidly rotating fluid planets. We argue ing among its instruments a microwave radiometer [Janssen that convectively-adjusted lapse rates should be interpreted et al., 2005] to gather passive soundings of the weather-layer along constant angular momentum surfaces instead of lines and below. In light of this unprecedented data set, these two parallel to the local gravity vector. Using Cassini wind prevailing, distinct sets of assumptions and geometries ap- observations of Jupiter and different lapse rates to con- pear inadequate for data interpretation, particularly in the struct toy atmospheres, we explore parcel paths in sym- equatorial region. The microwave observations, which are expected to retrieve trace element abundances and temper- metrically stable and unstable weather-layers by the nu- ature deeper than 30 bars and into the adiabatic region, merically modeled insertion of negatively buoyant bubbles. will exactly span the common limit of the shallow and deep Low-Richardson number atmospheres are very susceptible to models. Very little work has examined the impact of colum- transient symmetric instability upon local diabatic forcing, nar convection in the presence of a stable stratification that even outside of the tropics. We explore parcel paths in sym- is generally parallel to geopotential surfaces. One recent metrically stable and unstable weather-layer environments, exception is Heimpel et al. [2016], who used a deep model the latter by adding thermal bubbles to the weather-layer. bounded by a parameterized stable weather-layer to induce Parcels that cool in Jupiter's belt regions have particularly coherent surface vortices. Additional theoretical and mod- eling work is in order for a timely interpretation of the Juno horizontal paths, with implications for jetward angular mo- observations. mentum fluxes. These considerations may be relevant to the Here we take a simple approach to explore the impact interpretation of Juno's ongoing observations of Jupiter's of equatorial columnar geometry on parcel motion in the weather-layer. weather-layer, as a function of latitude, wind shear and static stability. In Sections 2 and 3 we review symmetric instability and resulting slantwise convection, and their re- lation to the Richardson number. We then develop a toy 1. Introduction steady-state model of Jupiter's outer atmosphere in Section 4, using thermal wind balance to relate Cassini-observed The fluid planets Jupiter, Saturn, Uranus and Neptune zonal winds to a prescribed static stability profile. This are rapidly rotating and have extensive atmospheres. The provides the basic state for the parcel model developed in field of planetary atmospheric dynamics has generally split Section 5. Sections 6-7 provide results, and Section 8 con- the work of understanding and modeling these atmospheres cludes with a discussion of assumptions and implications for into two groups (see reviews by Vasavada and Showman the Galileo and Juno missions. [2005] and Gerkema et al. [2008]): the deep, well-mixed and adiabatic interiors, and the shallow, stably stratified outer weather-layers. Leading the first group, Busse [1976] pro- 2. Symmetric instability on Earth posed that deep atmospheric motions occur in columns and cylinders parallel with the spin axis. A large body of the- A parcel in a gravitationally and inertially stable atmo- ory and numerical modeling work (e.g., Christensen [2002], sphere, if perturbed slightly from its origin, will oscillate Heimpel and Aurnou [2007], Kaspi et al. [2009]) demon- about the origin. The restoring forces are buoyancy and strates that the spin axis is the preferred direction for con- Coriolis, respectively. Symmetric instability (SI) [Solberg, vective mixing for a dry adiabatic interior, for Jovian rota- 1936] is a generalized framework for inertial and gravita- tion rates. tional stabilities (see Schultz and Schumacher [1999], their Table 1); however, SI even in the presence of both iner- tial and gravitational stability is possible [Ooyama, 1966]. 1Department of Earth and Planetary Sciences, Weizmann The name `symmetric' is due to the phenomenon's two- Institute of Science, Rehovot, Israel. dimensional nature. Much of SI's early terrestrially-focused development was spurred by the desire to understand mesoscale rainbands stretching latitudinally in the neighbor- Copyright 2016 by the American Geophysical Union. hood of midlatitude cyclones [Bennetts and Hoskins, 1979; 0094-8276/16/$5.00 Emanuel, 1979, 1983a, b; Sanders, 1986]. 1 X - 2 O'NEILL AND KASPI: SLANTWISE CONVECTION ON FLUID PLANETS SI can be diagnosed by the sign of potential vorticity Gierasch [1978] and Hathaway et al. [1979] did a linear sta- (PV) [Hoskins, 1974]. In the Northern Hemisphere, quasi- bility analysis with the complete Coriolis force. The latter geostrophic PV is positive everywhere, because of the as- found a latitudinal dependence of SI on Ri due to equato- sumption f >> ζ, where f = 2Ω sin φ is the Coriolis fre- rial solar insolation. Jeffery and Wingate [2009] determined quency at latitude φ and ζ = k^ · r × ~u is the local verti- that the range of Ri that allows SI to dominate baroclinic in- cal relative vorticity (for horizontal wind ~u). However, at stabilities extends to Ri = 2 after considering the horizontal the length and time scales of mesoscale systems and sub- Coriolis component. sequent SI, for which the Rossby number is O(1), quasi- The study of Ri in giant planet atmospheres is still largely geostrophy no longer holds, and PV can be transiently neg- theoretical because there only exists one sounding of any ative. Causes include friction, diabatic heating or cooling, giant planet to date: NASA's Galileo probe. Flasar and and cross-equatorial flow [Dunkerton, 1981]. More generally, Gierasch [1986] and Allison et al. [1995] independently es- SI is present wherever f·PV< 0 [Hoskins, 1974; Stevens, timated that the Jovian Ri should be O(1) even though 1983]. the Rossby number is much less than one, which in the Geometrically, this can be thought of as a condition on Solar System appears unique to giant planet atmospheres the relative orientation of angular momentum contours and (though it can also occur locally on Earth, for example in the potential temperature contours in a dry atmosphere. In Labrador Sea: see Jeffery and Wingate [2009]). This spe- cial Jovian regime is characterized by a near equivalence in a typical stable midlatitude atmosphere, gravitational sta- vertical and horizontal temperature gradients, particularly bility requires that potential temperature (θ) increase with in the equatorial region (Allison et al. [1995], their Fig. 3). height. Inertial stability requires that absolute angular mo- Low Ri indicates low-PV regions throughout the weather- mentum (M) increase toward the equator. This setup is one layer because highly tilted isentropes are more aligned with in which the M gradient is pointed clockwise of the gradient M surfaces, which provides an opportunity for SI to be in- of θ (Orientation A in Fig. 1). Colloquially, if the M sur- duced by deep convection. Several related studies in phys- faces are `steeper' than the potential temperature surfaces ical oceanography examined the problem by using tilted f- then the atmosphere is stable to symmetric perturbations. If planes that include a constant vertical Coriolis component the potential temperature surfaces become steeper than an- [Sun, 1994; Straneo et al., 2002; Itano and Maruyama, 2009; gular momentum surfaces, such that the angular momentum Jeffery and Wingate, 2009] or β-planes [Fruman and Shep- gradient is now counterclockwise of the potential tempera- herd, 2008]. Research into deep flows in stars also includes ture gradient (facing Eastward in the Northern Hemisphere), the full Coriolis force, though it suggests that the balanced the fluid is symmetrically unstable. These two perspectives interior flow structure is perhaps more conical than cylin- on the presence of SI are equivalent because PV can be ex- drical (e.g., Schou et al. [1998]; Brun et al. [2010]). pressed as the cross product between the θ gradient and the M gradient: PV / rθ × rM [Charney, 1973]. 4. A Jovian steady state atmosphere 3. Symmetric instability on fluid planets In order to investigate the slantwise motion of perturbed parcels in Jupiter's weather-layer, we construct a toy Jovian Rapidly rotating fluid planets provide a model laboratory atmosphere model that uses the Cassini-observed latitudinal for slantwise convection studies. In slantwise convection, un- profile of surface winds [Porco et al., 2003] as the steady- stable air parcels adjust to buoyancy perturbations along ab- state zonal winds at 1-bar. The wind profile is assumed to solute angular momentum surfaces instead of through purely be axially symmetric and aligned along cylinders parallel to vertical motions.