Rhines Scale Research Articles

Multiple jets in a rotating annulus model with an imposed azimuthal magnetic field

Zonal flows driven by rotation and convection are found commonly within astrophysical and geophysical bodies. Multiple jets are most famously observed on the surface of Jupiter, with prograde and retrograde zonal flows making up part of its banded structure of zones and belts. Non-magnetic studies of convection in a rotating annulus model have previously been shown to produce multiple jet structures, similar to those observed in atmospheres of giant planets such as Jupiter. These giant planets have strong magnetic fields which impact on convection in the electrically conducting regions of their atmospheres. Therefore the effect of a magnetic field on the multiple jet solutions of the annulus model is of astrophysical interest. In this work we impose a uniform azimuthal magnetic field to the annulus model and vary its strength and other control parameters to determine the parameter space where multiple jets exist. Zonal flows and multiple jet solutions are found at weak magnetic field strength and, indeed, the magnetic field can promote the production of these features. Simulations with a weak magnetic field or no magnetic field are also found to match well with the Rhines scaling theory. For cases with multiple jets, a strong inertial force must be present, combined with either a weak Lorentz force, or a Lorentz force entering the main balance with increased contributions from the viscous force. At strong magnetic field strengths two regimes are found. For weak magnetic diffusion zonal flows can be retained, albeit without the multiple jet structure. For larger magnetic diffusion non-axisymmetric solutions without clear bands are found. In these regimes, the Lorentz force appears in the primary balance of forces and zonal flows are only retained at strong driving when inertia is able to also enter the balance at leading order.

Atmospheric Waves Driving Variability and Cloud Modulation on a Planetary-mass Object

Planetary-mass objects and brown dwarfs at the transition (T eff ∼ 1300 K) from relatively red L dwarfs to bluer mid-T dwarfs show enhanced spectrophotometric variability. Multiepoch observations support atmospheric planetary-scale (Kelvin or Rossby) waves as the primary source of this variability; however, large spots associated with the precipitation of silicate and metal clouds have also been theorized and suggested by Doppler imaging. We applied both wave and spotted models to fit near-infrared (NIR), multiband (Y/J/H/K) photometry of SIMP J013656.5+093347 (hereafter SIMP0136) collected at the Canada–France–Hawaii Telescope using the Wide-field InfraRed Camera. SIMP0136 is a planetary-mass object (12.7 ± 1.0 M J) at the L/T transition (T2 ± 0.5) known to exhibit light-curve evolution over multiple rotational periods. We measure the maximum peak-to-peak variability of 6.17% ± 0.46%, 6.45% ± 0.33%, 6.51% ± 0.42%, and 4.33% ± 0.38% in the Y, J, H, and K bands, respectively, and find evidence that wave models are preferred for all four NIR bands. Furthermore, we determine that the spot size necessary to reproduce the observed variations is larger than the Rossby deformation radius and Rhines scale, which is unphysical. Through the correlation between light curves produced by the waves and associated color variability, we find evidence of planetary-scale, wave-induced cloud modulation and breakup, similar to Jupiter’s atmosphere and supported by general circulation models. We also detect a 93.°8 ± 7.°4 (12.7σ) phase shift between the H − K and J − H color time series, providing evidence for complex vertical cloud structure in SIMP0136's atmosphere.

Parameterizing Mesoscale Eddy Buoyancy Transport Over Sloping Topography

AbstractMost of the ocean's kinetic energy is contained within the mesoscale eddy field. Models that do not resolve these eddies tend to parameterize their impacts such that the parameterized transport of buoyancy and tracers reduces the large‐scale available potential energy and spreads tracers. However, the parameterizations used in the ocean components of current generation Earth System Models rely on an assumption of a flat ocean floor even though observations and high‐resolution modeling show that eddy transport is sensitive to the potential vorticity gradients associated with a sloping seafloor. We show that buoyancy transport coefficient diagnosed from idealized eddy‐resolving simulations is indeed reduced over both prograde and retrograde bottom slopes (topographic wave propagation along or against the mean flow, respectively) and that the reduction can be skilfully captured by a mixing length parameterization by introducing the topographic Rhines scale as a length scale. This modified “GM” parameterization enhances the strength of thermal wind currents over the slopes in coarse‐resolution, non‐eddying, simulations. We find that in realistic global coarse‐resolution simulations the impact of topography is most pronounced at high latitudes, enhancing the mean flow strength and reducing temperature and salinity biases. Reducing the buoyancy transport coefficient further with a mean‐flow dependent eddy efficiency factor, has notable effects also at lower latitudes and leads to reduction of global mean biases.

Bathymetry-Aware Mesoscale Eddy Parameterizations across Upwelling Slope Fronts: A Machine Learning–Augmented Approach

Abstract Mesoscale eddy buoyancy fluxes across continental slopes profoundly modulate the boundary current dynamics and shelf–ocean exchanges but have yet to be appropriately parameterized via the Gent–McWilliams (GM) scheme in predictive ocean models. In this work, we test the prognostic performance of multiple GM variants in noneddying simulations of upwelling slope fronts that are commonly found along the subtropical continental margins. The tested GM variants range from a set of constant eddy buoyancy diffusivities to recently developed energetically constrained, bathymetry-aware diffusivities, whose implementation is augmented by an artificial neural network (ANN) serving to predict the mesoscale eddy energy based on the topographic and mean flow quantities online. In addition, an ANN is employed to parameterize the cross-slope eddy momentum flux (EMF) that maintains a barotropic flow field analogous to that in an eddy-resolving model. Our tests reveal that noneddying simulations employing the bathymetry-aware forms of the Rhines scale–based scheme and GEOMETRIC scheme can most accurately reproduce the heat contents and along-slope baroclinic transports as those in the eddy-resolving simulations. Further analyses reveal certain degrees of physical consistency in the ANN-inferred eddy energy, which tends to grow (decay) as isopycnal slopes are steepened (flattened), and in the parameterized EMF, which exhibits the correct strength of shaping the flow baroclinicity if a bathymetry-aware GM variant is jointly used. These findings provide a recipe of GM variants for use in noneddying simulations with continental slopes and highlight the potential of machine learning techniques to augment physics-based mesoscale eddy parameterization schemes. Significance Statement This study evaluates the predictive skill of parameterization schemes of water mass transports induced by ocean mesoscale eddies across continental slopes. Correctly parameterizing these transports in noneddying ocean models (e.g., ocean climate models) is crucial for predicting the ocean circulation and shelf–ocean exchanges. This work highlights the importance of bathymetric effects on eddy transports, as parameterization schemes that account for the influence of a sloping seafloor outperform those developed specifically for a flat-bottomed ocean. This work also highlights the efficacy of machine learning techniques to augment physics-based mesoscale eddy parameterization schemes, for instance, by estimating the mesoscale eddy energy online to realize energy-dependent parameterization schemes in noneddying simulations.

The impact of rough topography on behaviors of mesoscale eddies as revealed by submesoscale resolving simulations

Mesoscale eddies are ubiquitous in the world ocean and are a key factor in maintaining the global oceanic energy balance. Geophysical turbulence theory predicts that the eddy length scale should increase to Rhines scale as it inherits the inverse energy cascade from smaller scales that help to stabilize the ocean circulation system. However, satellite-observed mesoscale eddies are much smaller than predicted, which indicates that unclear forward energy cascades prevail in their life cycles. In this study, we explore the role of finite rough topography in modulating eddy kinetic energy and horizontal length scales by using a series of submesoscale resolving numerical simulations with parameters typical of the Drake Passage. Our results show that, when compared with those generated over a flat bottom, the presence of rough topography can substantially reduce the horizontal length scales of eddies by approximately 60%–70%, even in upper layers 2–3 km above the bottom. Rough topography also consumes significant amounts of eddy kinetic energy, as the volume-mean eddy kinetic energy over a rough bottom decreases by about 70%–80% when compared with that over a flat bottom. By using a dynamics-based decomposition method, we subtracted the submesoscale motions from total flow and found that, in addition to energetic internal lee waves, deep-ocean submesoscale processes (integrated over the bottommost 1 km) contributed roughly 22% of the total viscosity dissipation across the whole research domain over a rough bottom. Therefore, this study indicates that the role of deep-ocean submesoscale motions in the energy cascade and abyssal mixing should be considered in ocean model parameterizations in the future.

Scale-Dependent Eddy Diffusivities at the Kuroshio Extension: A Particle-Based Estimate and Comparison to Theory

Abstract For eddy-permitting climate models, only eddies smaller than the smallest resolvable scale need to be parameterized. Therefore, it is important to study the diffusivities induced by eddies smaller than a specific separation scale L*, that is, the scale-dependent eddy diffusivities. Using a submesoscale-permitting model solution (MITgcm llc4320), we estimate the scale-dependent eddy diffusivity in the Kuroshio Extension. We find that, as the separation scale L* increases, the diffusivity increases, and the spatial structure approaches that of the total eddy diffusivity. We quantify this scale dependence through fitting the diffusivity to L*n. Our derivation shows that n is approximately (a + 1)/2, where a is the eddy kinetic energy spectral slope. For domain-averaged diffusivity, n is 1.33. We then extend four existing mixing theories by including scale dependence. Our results show that both of the theories designed for intense-jet regions, the suppressed mixing length theory and the multiwavenumber theory, closely match the magnitude of the scale-dependent diffusivity but fail to capture well the diffusivity’s spatial structure. However, the other two theories based on eddy size and Rhines scale can reasonably represent the spatial structure. Based on this finding, we propose an empirical formula for scale-dependent eddy diffusivity that well represents both the magnitude and the spatial structure of the eddy diffusivity. Our work demonstrates that climate models should use scale-dependent diffusivity, and designing appropriate empirical formulas may be a reasonable approach to represent these scale-dependent diffusivities. Also, our diagnostic framework and theories for scale-dependent eddy diffusivity may be applicable to the global ocean.

The catalytic effect of near-inertial waves on -plane zonal jets

Zonal jets and inertia–gravity waves are ubiquitous on planets such as Earth, Jupiter and Saturn. Motivated by the modification of energy flux of balanced flow by inertia–gravity waves, this paper studies the impact of near-inertial waves (NIWs) on zonal jets on a $\beta$ -plane. Using a two-dimensional quasi-geostrophic and NIW coupled system on a $\beta$ -plane (Xie & Vanneste, J. Fluid Mech., vol. 774, 2015, pp. 143–169), we find NIWs catalytically impact several features of zonal jets. The NIWs inhibit jet formation due to the waves’ catalytic induction of downscale mean energy flux. As the strength of NIWs increases, a critical point exists beyond which zonal jets are annihilated. The jet spacing is captured by the Rhines scale $L\sim \sqrt {U/\beta }$ with $U$ estimated from the upscale energy flux induced by the mean flow alone, which again shows that the NIWs’ impact is catalytic. Also, the temporal asymmetry of NIWs leads to the spatial asymmetry of jet dynamics. The jet profiles are asymmetric with a stronger shear on the left flank. And similar to the left turning of vortex dipole under the impact of NIWs, the NIW-modified jets migrate poleward. The NIWs also show a catalytic role in jet migration: the net momentum flux directly induced by NIWs is of secondary importance in the zonal mean momentum dynamics and impedes jet migration, while the advective effect of NIW-modified mean flow dominates the jet migration velocity.

Mesoscale Variability, Critical Latitude and Eddy Mean Properties in the Tropical South‐East Atlantic Ocean

AbstractEquatorward decrease of mesoscale eddy abundance, and meridional variations of their mean properties in the tropical South‐East Atlantic Ocean have been investigated on the basis of horizontal length‐scales of geostrophic flows, and theories of two‐dimensional geostrophic turbulence on a β‐plane. Meridional variations of satellite‐derived altimetric eddy kinetic energy density spectra were assessed in bins of 5°, from 5°S to 25°S, zonally averaged between 8°W and 15°E. They revealed two latitudinal bands of minimum eddy energy spectra: one in the northern Angola Basin (5°S–10°S) and the other across the Angola Benguela Front (15°S–20°S). In the latter, both the eddy forcing scale and the Rhines scale were observed at wavelengths of 300 and 350 km respectively, suggesting that only a small spectral range exists for eddies to grow. On the other hand, in the former, the eddy forcing scale and the Rhines scale were observed at wavelengths of 454 and 520 km respectively. The ratio between the Rhines scale and the first baroclinic Rossby radius revealed an onset of a critical latitude at about 11.4°S. Consistently, maps of eddy frequency of occurrence computed from eddies identified in the region has shown a notable decay in signal of the eddy density distribution around that latitude. This could explain the sharp equatorward transition of mesoscale processes observed in this region, which seems to shift from nonlinear eddies to linear Rossby waves, potentially explaining why fewer eddies are observed in the region when compared to other regions of the world oceans.

North Atlantic Tropical Cyclone Outer Size and Structure Remain Unchanged by the Late Twenty-First Century

Abstract There is a lack of consensus on whether North Atlantic tropical cyclone (TC) outer size and structure (i.e., change in outer winds with increasing radius from the TC) will differ by the late twenty-first century. Hence, this work seeks to examine whether North Atlantic TC outer wind field size and structure will change by the late twenty-first century using multiple simulations under CMIP3 SRES A1B and CMIP5 RCP4.5 scenarios. Specifically, our analysis examines data from the GFDL High-Resolution Forecast-Oriented Low Ocean Resolution model (HiFLOR) and two versions of the GFDL hurricane model downscaling climate model output. Our results show that projected North Atlantic TC outer size and structure remain unchanged by the late twenty-first century within nearly all HiFLOR and GFDL hurricane model simulations. Moreover, no significant regional outer size differences exist in the North Atlantic within most HiFLOR and GFDL hurricane model simulations. No changes between the control and late-twenty-first-century simulations exist over the storm life cycle in nearly all simulations. For the simulation that shows significant decreases in TC outer size, the changes are attributed to reductions in storm lifetime and outer size growth rates. The absence of differences in outer size among most simulations is consistent with the process that controls the theoretical upper bound of storm size (i.e., Rhines scaling), which is thermodynamically invariant. However, the lack of complete consensus among simulations for many of these conclusions suggests nontrivial uncertainty in our results.

Planetary Core‐Style Rotating Convective Flows in Paraboloidal Laboratory Experiments

AbstractTurbulent convection in a planet's outer core is simulated here using a thermally‐driven, free surface paraboloidal laboratory annulus. We show that the rapidly rotating convection dynamics in free‐surface paraboloidal annuli are similar those in planetary spherical shell geometries. Three experimental cases are carried out, respectively, at 35 revolutions per minute (rpm), 50 and 60 rpm. Thermal Rossby waves are detected in full disk thermographic images of the fluid's free surface. Ultrasonic flow velocity measurements reveal the presence of multiple azimuthal (zonal) jets, with successively more jets forming in higher rotation rate cases. The jets' cylindrical radial extent is well approximated by the Rhines scale. Over time, the zonal jets migrate to larger radial position with migration rates in good agreement with prior theoretical estimates. Our results suggest that planetary core rotating convection will be comprised of flow structures found in other turbulent geophysical fluid dynamical systems: convective turbulence dominates the small‐scale flow field, and also act to flux energy into larger‐scale, slowly evolving zonal flow structures. How the ambient magnetic fields in planetary core settings affect such turbulent flows remains an open question.

Tropical Cyclone Size Is Strongly Limited by the Rhines Scale: Experiments with a Barotropic Model

Abstract Recent work found evidence using aquaplanet experiments that tropical cyclone (TC) size on Earth is limited by the Rhines scale, which depends on the planetary vorticity gradient β. This study aims to examine how the Rhines scale limits the size of an individual TC. The traditional Rhines scale is first reexpressed as a Rhines speed to characterize how the effect of β varies with radius in a vortex whose wind profile is known. The framework is used to define the vortex Rhines scale, which is the transition radius that divides the vortex into a vortex-dominant region at smaller radii, where the axisymmetric circulation is steady, and a wave-dominant region at larger radii, where the circulation stimulates planetary Rossby waves and dissipates. Experiments are performed using a simple barotropic model on a β plane initialized with a TC-like axisymmetric vortex defined using a recently developed theoretical TC wind profile model. The gradient β and initial vortex size are each systematically varied to investigate the detailed responses of the TC-like vortex to β. Results show that the vortex shrinks toward an equilibrium size that closely follows the vortex Rhines scale. A larger initial vortex relative to its vortex Rhines scale will shrink faster. The shrinking time scale is well described by the vortex Rhines time scale, which is defined as the overturning time scale of the circulation at the vortex Rhines scale and is shown to be directly related to the Rossby wave group velocity. The relationship between our idealized results and the real Earth is discussed. Results may generalize to other eddy circulations, such as the extratropical cyclone. Significance Statement Tropical cyclones vary in size significantly on Earth, but how large a tropical cyclone could potentially be is still not understood. The variation of the Coriolis parameter with latitude is known to limit the size of turbulent circulations, but its effect on tropical cyclones has not been studied. This study derives a new parameter related to this concept called the “vortex Rhines scale” and shows in a simple model how and why storms will tend to shrink toward this size. These results help explain why tropical cyclone size tends to increase slowly with latitude on Earth and can help us understand what sets the size of tropical cyclones on Earth in general.

Role of submesoscale processes in the isopycnal mixing associated with subthermocline eddies in the Philippine Sea

Submesoscale processes are very typical in the ocean interior with a front formed by mesoscale eddies, and contribute to ocean mixing. However, the role of submesoscale processes in the isopycnal mixing associated with ocean eddies has never been explored from observations. Based on hourly velocity and temperature data from the mooring at 8.5°N, 130°E between 26 September 2015 and 22 December 2016, this study provides the horizontal eddy diffusivity using a mixing-length framework and a parameterization related to the Rhines scale, and estimates the contribution of submesoscale processes to isopycnal mixing for the first time. The subthermocline eddies in the Philippine Sea exist between 200 m and 800 m depth, have characteristic speeds of 0.1–0.5 m/s with a typical period of 40–100 days, and can cause the temperature fluctuation of ∼0.5 °C. The horizontal diffusivity due to subthermocline eddies is about 4000–11,000 m2/s, and has a significant maximum near ∼400 m depth but the horizontal diffusivity associated with mixing length gradually increases below ∼700 m. The submesoscale processes can change the current velocity and temperature by ∼5 cm/s and ∼0.1 °C, respectively. The submesoscale processes in the ocean interior can increase the isopycnal mixing associated with subthermocline eddies by about 6–7%. The profile of horizontal eddy diffusivity derived in this study is useful for parameterization of ocean eddies and submesoscale processes in the Philippine Sea in coarse-resolution ocean models.

A Scaling Theory for the Diffusivity of Poleward Eddy Heat Transport Based on Rhines Scaling and the Global Entropy Budget

Abstract Diffusive theories for the meridional atmospheric energy transport can summarize our understanding of this central aspect of the general circulation. They can also be utilized in simple models of Earth’s energy balance to help interpret the response of the system to perturbations. A theory for this diffusivity of eddy heat transport is described based on Rhines scaling and the global entropy budget, each of which provides a constraint between the kinetic energy dissipation and the diffusivity. An expression for the diffusivity is then obtained by eliminating the dissipation from this set of two constraints. The theory can be thought of as a generalization of the theories of Held–Larichev and Barry–Craig–Thuburn. The theory is compared to simulations of the Held–Suarez idealized dry atmospheric model. Limitations of the theory are emphasized. The form of the theory allows it to be readily generalized to a moist atmosphere.

On the spacing of meandering jets in the strong-stair limit

Based on an assumption of strongly inhomogeneous potential vorticity mixing in quasi-geostrophic $\beta$ -plane turbulence, a relation is obtained between the mean spacing of latitudinally meandering zonal jets and the total kinetic energy of the flow. The relation applies to cases where the Rossby deformation length is much smaller than the Rhines scale, in which kinetic energy is concentrated within the jet cores. The relation can be theoretically achieved in the case of perfect mixing between regularly spaced jets with simple meanders, and of negligible kinetic energy in flow structures other than in jets. Incomplete mixing or unevenly spaced jets will result in jets being more widely separated than the estimate, while significant kinetic energy outside the jets will result in jets closer than the estimate. An additional relation, valid under the same assumptions, is obtained between the total kinetic and potential energies. In flows with large-scale dissipation, the two relations provide a means to predict the jet spacing based only on knowledge of the energy input rate of the forcing and dissipation rate, regardless of whether the latter takes the form of frictional or thermal damping. Comparison with direct numerical integrations of the forced system shows broad support for the relations, but differences between the actual and predicted jet spacings arise both from the complex structure of jet meanders and the non-negligible kinetic energy contained in the turbulent background and in coherent vortices lying between the jets.

Eddy Length Scale Response to Static Stability Change in an Idealized Dry Atmosphere: A Linear Response Function Approach*

AbstractThe response of mid-latitude equilibrated eddy length scale to static stability has long been questioned but not investigated in well-controlled experiments with unchanged mean zonal wind and meridional temperature gradient. With iterative use of the linear response function of an idealized dry atmosphere, we obtain a time-invariant and zonally-uniform forcing to decrease the near-surface temperature by over 2 K while keeping the change in zonal wind negligible (within 0.2m s−1). In such experiments of increased static stability, energy-containing zonal scale decreases by 3–4%, which matches with Rhines scale decrease near the jet core. Changes in Rossby radius (+2%), maximum baroclinic growth scale (-1%) and Kuo scale (0%) fail to match this change in zonal scale. These findings and well-controlled experiments help with better understanding of eddy–mean flow interactions and hence the mid-latitude circulation and its response to climate change.

Barotropic and Baroclinic Inverse Kinetic Energy Cascade in the Antarctic Circumpolar Current

AbstractStratified geostrophic turbulence theory predicts an inverse energy cascade for the barotropic (BT) mode. Satellite altimetry has revealed a net inverse cascade in the baroclinic (BC) mode. Here the spatial variabilities of BT and BC kinetic energy fluxes in the Antarctic Circumpolar Current (ACC) were investigated using ECCO2 data, which synthesize satellite data and in situ measurements with an eddy-permitting general circulation model containing realistic bathymetry and wind forcing. The BT and BC inverse kinetic energy cascades both reveal complex spatial variations that could not be explained fully by classical arguments. For example, the BC injection scales match better with most unstable scales than with the first-mode deformation scales, but the opposite is true for the BT mode. In addition, the BT and BC arrest scales do not follow the Rhines scale well in terms of spatial variation, but show better consistency with their own energy-containing scales. The reverse cascade of the BT and BC modes was found related to their EKE, and better correlation was found between the BT inverse cascade and barotropization. Speculations of the findings were proposed; however, further observations and modeling experiments are needed to test these interpretations. Spectral flux anisotropy exhibits a feature associated with oceanic jets that is consistent with classical expectations. Specifically, the spectral flux along the along-stream direction remains negative at scales up to that of the studied domain (~2000 km), while that in the perpendicular direction becomes positive close to the scale of the width of a typical jet.

Global climate modeling of Saturn's atmosphere. Part III: Global statistical picture of zonostrophic turbulence in high-resolution 3D-turbulent simulations

We conduct an in-depth analysis of statistical flow properties calculated from the reference high-resolution Saturn simulation obtained by global climate modelling in Part II. In the steady state of this reference simulation, strongly energetic, zonally dominated, large-scale structures emerge, which scale with the Rhines scale. Spectral analysis reveals a strong anisotropy in the kinetic energy spectra, consistent with the zonostrophic turbulent flow regime. By computing spectral energy and enstrophy fluxes we confirm the existence of a double cascade scenario related to 2D-turbulent theory. To diagnose the relevant 3D dynamical mechanisms in Saturn's turbulent atmosphere, we run a set of four simulations using an idealized version of our Global Climate Model devoid of radiative transfer, with a well-defined Taylor-Green forcing and over several rotation rates (4, 1, 0.5, and 0.25 times Saturn's rotation rate). This allows us to identify dynamics in three distinctive inertial ranges: (1) a “residual-dominated” range, in which non-axisymmetric structures dominate with a −5/3 spectral slope; (2) a “zonostrophic inertial” range, dominated by axisymmetric jets and characterized by the pile-up of strong zonal modes with a steeper, nearly −3, spectral slope; and (3) a “large-scale” range, beyond Rhines' typical length scale, in which the reference Saturn simulation and our idealized simulations differ. In the latter range, the dynamics is dominated by long-lived zonal modes 2 and 3 when a Saturn-like seasonal forcing is considered (reference simulation), and a steep energetic decrease with the idealized Taylor-Green forcing. Finally, instantaneous spectral fluxes show the coexistence of upscale and downscale enstrophy/energy transfers at large scales, specific to the regime of zonostrophic turbulence in a 3D atmosphere.

Global climate modeling of Saturn's atmosphere. Part III: Global statistical picture of zonostrophic turbulence in high-resolution 3D-turbulent simulations

We conduct an in-depth analysis of statistical flow properties calculated from the reference high-resolution Saturn simulation obtained by global climate modelling in Part II. In the steady state of this reference simulation, strongly energetic, zonally dominated, large-scale structures emerge, which scale with the Rhines scale. Spectral analysis reveals a strong anisotropy in the kinetic energy spectra, consistent with the zonostrophic turbulent flow regime. By computing spectral energy and enstrophy fluxes we confirm the existence of a double cascade scenario related to 2D-turbulent theory. To diagnose the relevant 3D dynamical mechanisms in Saturn's turbulent atmosphere, we run a set of four simulations using an idealized version of our Global Climate Model devoid of radiative transfer, with a well-defined Taylor-Green forcing and over several rotation rates (4, 1, 0.5, and 0.25 times Saturn's rotation rate). This allows us to identify dynamics in three distinctive inertial ranges: (1) a ``residual-dominated'' range, in which non-axisymmetric structures dominate with a -5/3 spectral slope; (2) a ``zonostrophic inertial'' range, dominated by axisymmetric jets and characterized by the pile-up of strong zonal modes with a steeper, nearly -3, spectral slope; and (3) a ``large-scale'' range, beyond Rhines' typical length scale, in which the reference Saturn simulation and our idealized simulations differ. In the latter range, the dynamics is dominated by long-lived zonal modes 2 and 3 when a Saturn-like seasonal forcing is considered (reference simulation), and a steep energetic decrease with the idealized Taylor-Green forcing. Finally, instantaneous spectral fluxes show the coexistence of upscale and downscale enstrophy/energy transfers at large scales, specific to the regime of zonostrophic turbulence in a 3D atmosphere.

Dynamical Aquaplanet Experiments with Uniform Thermal Forcing: System Dynamics and Implications for Tropical Cyclone Genesis and Size

Abstract Existing hypotheses for the dynamical dependence of tropical cyclone genesis and size on latitude depend principally on the Coriolis parameter f. These hypotheses are tested via dynamical aquaplanet experiments with uniform thermal forcing in which planetary rotation rate and planetary radius are varied relative to Earth values; the control simulation is also compared to a present-day Earth simulation. Storm genesis rate collapses to a quasi-universal dependence on f that attains its maximum at the critical latitude, where the inverse-f scale and Rhines scale are equal. Minimum genesis distance from the equator is set by the equatorial Rhines (or deformation) scale and not by a minimum value of f. Outer storm size qualitatively follows the smaller of the two length scales, including a slow increase with latitude equatorward of 45° in the control simulation, similar to the Earth simulation. The latitude of peak size scales with the critical latitude for varying planetary radius but not rotation rate, possibly because of the dependence of genesis specifically on f. The latitudes of peak size and peak packing density scale closely together. Results suggest that temporal effects and interstorm interaction may be significant for size dynamics. More generally, the critical latitude separates two regimes: 1) a mixed wave–cyclone equatorial belt, where wave effects are strong and the Rhines scale likely limits storm size, and 2) a cyclone-filled polar cap, where wave effects are weak and cyclones persist. The large-planet limit predicts a world nearly covered with long-lived storms, equivalent to the f plane. Overall, spherical geometry is likely important for understanding tropical cyclone genesis and size on Earthlike planets.

Jupiter's Turbulent Power Spectra From Hubble Space Telescope

AbstractTurbulence in Jupiter's atmosphere was investigated with archival and ongoing observations from the Hubble Space Telescope. Data sets that include one full rotation (360° longitude coverage) were used to produce complete maps of the planet's upper cloud layer. The global maps were analyzed to generate the passive tracer power spectrum of cloud features for single rotation observations, while successive rotations produced pairs of maps such that zonal winds were calculated. An atmosphere's dimensionality and dynamics are reflected in the slopes of such turbulent power spectra. Many of the retrieved passive tracer power spectra have a shallow spectral index over wave numbers k∼1 − 30 and transition to the well‐known Kolmogorov k−5/3 relation at smaller scales between wave numbers k∼30 − 1,000. The transition scale is similar to the number of jets in Jupiter's zonal wind profile and is related to the Rhines scale and the beta effect induced anisotropy scale. We also report on differences found in anticyclonic and cyclonic shear region power spectra and how they correlate to latitudinal changes in the zonal wind profile. We found that properties of Jupiter's power spectra are consistent with quasi‐geostrophic turbulence for shallow fluids.