Contributions to Jupiter's gravity field from dynamics in the dynamo region and deep atmosphere

2020 ◽  
Author(s):  
Laura Kulowski ◽  
Hao Cao ◽  
Jeremy Bloxham
Keyword(s):  
Zonal Flow ◽  
Stable Stratification ◽  
Dynamical Process ◽  
Mean Square ◽  
Antisymmetric Part ◽  
Zonal Flows ◽  
Order Of Magnitude ◽  
Density Perturbations ◽  
Gravity Signal ◽  
Gravitational Contribution

<p>The antisymmetric part of Jupiter's zonal flows is responsible for the large odd gravity harmonics measured by the Juno spacecraft. Here, we investigate the contributions to Jupiter's odd gravity harmonics (<em>J<sub>3</sub></em>, <em>J<sub>5</sub></em>, <em>J<sub>7</sub></em>, <em>J<sub>9</sub></em>) from dynamics in the dynamo region and the deep atmosphere. First, we estimate the odd gravity harmonics produced by zonal flows in the dynamo region. Using Ferraro's law of isorotation, we construct physically motivated profiles for dynamo region zonal flow. We use the vorticity equation to determine the density perturbations associated with the flows and then calculate the odd gravity harmonics. We find that dynamo zonal flows with root mean square (RMS) velocities of 10 cm/s would produce <em>J<sub>3</sub></em> values on the same order of magnitude as the Juno measured value, but would not significantly contribute to <em>J<sub>5</sub></em>, <em>J<sub>7</sub></em>, and <em>J<sub>9</sub></em>. Next, we examine the gravitational contribution from zonal flows above the dynamo region. We consider a simple model where the observed surface winds are barotropic (i.e., <em>z</em>-invariant) until they are truncated at some depth by some dynamical process, such as stable stratification and/or MHD processes. We find that barotropic zonal flow in the strongly antisymmetric northern (13°-26°N) and southern (14°-21°S) jets extending to the likely depth of a rock cloud layer or deep radiative zone can account for a significant fraction of the observed gravity signal.</p>

scholarly journals Linking zonal winds and gravity: the relative importance of dynamic self-gravity

2020 ◽  
Vol 492 (3) ◽  
pp. 3364-3374 ◽  
Author(s):  
Johannes Wicht ◽  
Wieland Dietrich ◽  
Paula Wulff ◽  
Ulrich R Christensen
Keyword(s):  
Zonal Flow ◽  
Order Effect ◽  
Radial Dependence ◽  
Spherical Harmonic Degree ◽  
Zonal Flows ◽  
Gravity Fields ◽  
Gravity Measurements ◽  
Density Perturbations ◽  
Self Gravity ◽  
The Impact

ABSTRACT Recent precise measurements of Jupiter’s and Saturn’s gravity fields help constraining the properties of the zonal flows in the outer envelopes of these planets. The link is provided by a simplified dynamic equation, which connects zonal flows to related buoyancy perturbations. These can result from density perturbations but also from the gravity perturbations. Whether the latter effect, which we call dynamic self-gravity (DSG), must be included or is negligible has been a matter of intense debate. We show that the second-order differential equation for the gravity perturbations becomes an inhomogeneous Helmholtz equation when assuming a polytrope of index unity for density and pressure. This equation can be solved semi-analytically when using modified spherical Bessel functions for describing the radial dependence. The respective solutions allow us to quantify the impact of the DSG on each gravity harmonic, practically independent of the zonal flow or the details of the planetary interior model. We find that the impact decreases with growing spherical harmonic degree ℓ. For degrees ℓ = 2 to about ℓ = 4, the DSG is a first-order effect and should be taken into account in any attempt of inverting gravity measurements for zonal flow properties. For degrees of about ℓ = 5 to roughly ℓ = 10, the relative impact of DSG is about 10 per cent and thus seems worthwhile to include, in particular since this comes at little extra cost with the method presented here. For yet higher degrees, it seems questionable whether gravity measurements or interior models will ever reach the precision required for disentangling the small DSG effects, which amount to only a few per cent at best.

scholarly journals A full, self-consistent treatment of thermal wind balance on oblate fluid planets

2016 ◽  
Vol 810 ◽  
pp. 175-195 ◽  
Author(s):  
Eli Galanti ◽  
Yohai Kaspi ◽  
Eli Tziperman
Keyword(s):  
Magnitude Estimate ◽  
Zonal Flow ◽  
Perturbation Approach ◽  
Thermal Wind ◽  
Self Consistent ◽  
Order Of Magnitude ◽  
Simplifying Assumptions ◽  
Density Perturbations ◽  
Physical Effects ◽  
Consistent Treatment

The nature of the flow below the cloud level on Jupiter and Saturn is still unknown. Relating the flow on these planets to perturbations in their density field is key to the analysis of the gravity measurements expected from both the Juno (Jupiter) and Cassini (Saturn) spacecrafts during 2016–2018. Both missions will provide latitude-dependent gravity fields, which in principle could be inverted to calculate the vertical structure of the observed cloud-level zonal flow on these planets. Theories to date connecting the gravity field and the flow structure have been limited to potential theories under a barotropic assumption, or estimates based on thermal wind balance that allow baroclinic wind structures to be analysed, but have made simplifying assumptions that neglected several physical effects. These include the effects of the deviations from spherical symmetry, the centrifugal force due to density perturbations and self-gravitational effects of the density perturbations. Recent studies attempted to include some of these neglected terms, but lacked an overall approach that is able to include all effects in a self-consistent manner. The present study introduces such a self-consistent perturbation approach to the thermal wind balance that incorporates all physical effects, and applies it to several example wind structures, both barotropic and baroclinic. The contribution of each term is analysed, and the results are compared in the barotropic limit with those of potential theory. It is found that the dominant balance involves the original simplified thermal wind approach. This balance produces a good order-of-magnitude estimate of the gravitational moments, and is able, therefore, to address the order one question of how deep the flows are given measurements of gravitational moments. The additional terms are significantly smaller yet can affect the gravitational moments to some degree. However, none of these terms is dominant so any approximation attempting to improve over the simplified thermal wind approach needs to include all other terms.

scholarly journals Polar and mid-latitude vortices and zonal flows on Jupiter and Saturn

2020 ◽  
Author(s):  
Moritz Heimpel ◽  
Rakesh Yadav ◽  
Nick Featherstone ◽  
Jonathan Aurnou
Keyword(s):  
Outer Boundary ◽  
Zonal Flow ◽  
Stable Stratification ◽  
Return Flow ◽  
Jet Streams ◽  
Global Pattern ◽  
Zonal Flows ◽  
Zonal Jets ◽  
Divergent Flow ◽  
Cassini Mission

Abstract Zonal flow on Jupiter and Saturn consists of equatorial super–rotation and alternating East-West jet streams at higher latitudes. Interacting with these zonal flows, numerous vortices occur with various sizes and lifetimes. The Juno mission and Cassini’s grand finale have shown that the zonal jets of Jupiter and Saturn extend deeply into their molecular envelopes. On Jupiter, the vast majority of low and mid-latitude jovian vortices are anticyclonic, whereas cyclones appear at polar latitudes. Cassini mission observations revealed a similar pattern on Saturn; its North and South polar vortices are cyclonic, whereas anticyclones occur at mid-latitudes. We use the recently developed code Rayleigh to run high-resolution simulations of rotating convection in 3D spherical shells. Four model runs are presented that result in dynamical flows that are comparable to those on the giant planets. We confirm previous results, finding that deep convective turbulence can explain the structure of jets. However, the strength and depth of stable stratification, and the latitude, can modify jet morphologies and affect the formation and dynamics of vortices. Lower latitudes favour shallow anticyclonic vortices that form due to upward and divergent flow near the outer boundary. These anticyclones are typically shielded by cyclonic filaments associated with downwelling return flow. In contrast, a single polar cyclone, or clusters of cyclones form near the poles. All of our simulations have this global pattern; a strong preference for shallow anticyclones in the first anticyclonic shear zone away from the equatorial jet (corresponding to the region of the great red spot on Jupiter and Storm Alley on Saturn), cyclonic and anticyclonic vortices at higher mid-latitudes, and a deeply seated cyclone or cyclone clusters at each pole. Our results show that Juno and Cassini observations of cloud-level flow can be explained in terms of deep convective dynamics in the molecular envelopes of Jupiter and Saturn.

scholarly journals Comparison of the deep atmospheric dynamics of Jupiter and Saturn in light of the Juno and Cassini gravity measurements

2020 ◽  
Author(s):  
Yohai Kaspi ◽  
Eli Galanti ◽  
Adam Showman ◽  
David Stevenson ◽  
Tristan Guillot ◽  
...  
Keyword(s):  
Planetary Science ◽  
Gravity Inversion ◽  
Zonal Flows ◽  
Zonal Jets ◽  
Cassini Mission ◽  
Gravity Measurements ◽  
Order Of Magnitude ◽  
The Magnetic Field ◽  
Intrinsic Characteristic

<p>The nature and structure of the observed east-west flows on Jupiter and Saturn has been a long-standing mystery in planetary science. This mystery has been recently unraveled by the accurate gravity measurements provided by the Juno mission to Jupiter and the Grand Finale of the Cassini mission to Saturn. These two experiments, which coincidentally happened around the same time, allowed the determination of the overall vertical and meridional profiles of the zonal flows on both planets. In this talk, we discuss what has been learned about the zonal jets on the gas giants in light of the new data from these two experiments. The gravity measurements not only allow the depth of the jets to be constrained, yielding the inference that the jets extend to roughly 3000 and 9000 km below the observed clouds on Jupiter and Saturn, respectively, but also provide insights into the mechanisms controlling these zonal flows. Specifically, for both planets this depth corresponds to the depth where electrical conductivity is within an order of magnitude of 1 S/m, implying that the magnetic field likely plays a key role in damping the zonal flows. An intrinsic characteristic of any gravity inversion, as discussed here, is that the solutions might not be unique. We analyze the robustness of the solutions and present several independent lines of evidence supporting the inference that the jets reach these depths.</p>

scholarly journals Excitation of zonal flow by the modulational instability in electron temperature gradient driven turbulence

2008 ◽  
Vol 74 (3) ◽  
pp. 381-389 ◽  
Author(s):  
Yu. A. ZALIZNYAK ◽  
A. I. YAKIMENKO ◽  
V. M. LASHKIN
Keyword(s):  
Temperature Gradient ◽  
Electron Temperature ◽  
Large Scale ◽  
Modulational Instability ◽  
Zonal Flow ◽  
Finite Amplitude ◽  
Small Scale ◽  
Drift Waves ◽  
Zonal Flows ◽  
Electron Temperature Gradient

AbstractThe generation of large-scale zonal flows by small-scale electrostatic drift waves in electron temperature gradient driven turbulence model is considered. The generation mechanism is based on the modulational instability of a finite amplitude monochromatic drift wave. The threshold and growth rate of the instability as well as the optimal spatial scale of zonal flow are obtained.

scholarly journals Effect of the electron redistribution on the nonlinear saturation of Alfvén eigenmodes and the excitation of zonal flows

2020 ◽  
Vol 86 (3) ◽  
Author(s):  
A. Biancalani ◽  
A. Bottino ◽  
P. Lauber ◽  
A. Mishchenko ◽  
F. Vannini
Keyword(s):  
Magnetic Field ◽  
Zonal Flow ◽  
Large Aspect Ratio ◽  
Nonlinear Saturation ◽  
Energetic Ions ◽  
Electron Population ◽  
Zonal Flows ◽  
Particle In Cell ◽  
Alfven Eigenmodes ◽  
Reversed Shear

Numerical simulations of Alfvén modes driven by energetic particles are performed with the gyrokinetic (GK) global particle-in-cell code ORB5. A reversed shear equilibrium magnetic field is adopted. A simplified configuration with circular flux surfaces and large aspect ratio is considered. The nonlinear saturation of beta-induced Alfvén eigenmodes (BAE) is investigated. The roles of the wave–particle nonlinearity of the different species, i.e. thermal ions, electrons and energetic ions are described, in particular for their role in the saturation of the BAE and the generation of zonal flows. The nonlinear redistribution of the electron population is found to be important in increasing the BAE saturation level and the zonal flow amplitude.

A Series of Zonal Jets Embedded in the Broad Zonal Flows in the Pacific Obtained in Eddy-Permitting Ocean General Circulation Models

2005 ◽  
Vol 35 (4) ◽  
pp. 474-488 ◽  
Author(s):  
Hideyuki Nakano ◽  
Hiroyasu Hasumi
Keyword(s):  
General Circulation ◽  
Bottom Topography ◽  
Zonal Flow ◽  
General Circulation Models ◽  
Wind Forcing ◽  
Zonal Flows ◽  
Zonal Jets ◽  
The Pacific ◽  
Ocean General Circulation Models ◽  
Ocean General Circulation

Abstract A series of zonal currents in the Pacific Ocean is investigated using eddy-permitting ocean general circulation models. The zonal currents in the subsurface are classified into two parts: one is a series of broad zonal flows that has the meridional pattern slanting poleward with increasing depth and the other is finescale zonal jets with the meridional scale of 3°–5° formed in each broad zonal flow. The basic pattern for the broad zonal flows is similar between the coarse-resolution model and the eddy-permitting model and is thought to be the response to the wind forcing. A part of the zonal jets embedded in each zonal flow is explained by the anomalous local wind forcing. Most of them, however, seem to be mainly created by the rectification of turbulent processes on a β plane (the Rhines effect), and zonal jets in this study have common features with the zonally elongated flows obtained in previous modeling studies conducted in idealized basins. The position of zonal jets is not stable when the ocean floor is flat, whereas it oscillates only within a few degrees under realistic bottom topography.

scholarly journals The Dynamics of Baroclinic Zonal Jets*

2015 ◽  
Vol 72 (3) ◽  
pp. 1137-1151 ◽  
Author(s):  
Paul D. Williams ◽  
Christopher W. Kelsall
Keyword(s):  
Root Mean Square ◽  
Power Law ◽  
Zonal Flow ◽  
Small Scale ◽  
Mean Square ◽  
Initial State ◽  
Zonal Jets ◽  
Rotation Periods ◽  
Inverse Energy Cascade ◽  
Geostrophic Turbulence

Abstract Multiple alternating zonal jets are a ubiquitous feature of planetary atmospheres and oceans. However, most studies to date have focused on the special case of barotropic jets. Here, the dynamics of freely evolving baroclinic jets are investigated using a two-layer quasigeostrophic annulus model with sloping topography. In a suite of 15 numerical simulations, the baroclinic Rossby radius and baroclinic Rhines scale are sampled by varying the stratification and root-mean-square eddy velocity, respectively. Small-scale eddies in the initial state evolve through geostrophic turbulence and accelerate zonally as they grow in horizontal scale, first isotropically and then anisotropically. This process leads ultimately to the formation of jets, which take about 2500 rotation periods to equilibrate. The kinetic energy spectrum of the equilibrated baroclinic zonal flow steepens from a −3 power law at small scales to a −5 power law near the jet scale. The conditions most favorable for producing multiple alternating baroclinic jets are large baroclinic Rossby radius (i.e., strong stratification) and small baroclinic Rhines scale (i.e., weak root-mean-square eddy velocity). The baroclinic jet width is diagnosed objectively and found to be 2.2–2.8 times larger than the baroclinic Rhines scale, with a best estimate of 2.5 times larger. This finding suggests that Rossby wave motions must be moving at speeds of approximately 6 times the turbulent eddy velocity in order to be capable of arresting the isotropic inverse energy cascade.

scholarly journals Reduced models of turbulent transport in helical plasmas including effects of zonal flows and trapped electrons

2020 ◽  
Vol 86 (3) ◽  
Author(s):  
S. Toda ◽  
M. Nunami ◽  
H. Sugama
Keyword(s):  
Energy Transport ◽  
Turbulent Transport ◽  
Zonal Flow ◽  
Transport Models ◽  
Nonlinear Simulation ◽  
Ion Energy ◽  
Trapped Electrons ◽  
Zonal Flows ◽  
Reduced Models ◽  
Potential Fluctuation

Using transport models, the impacts of trapped electrons on zonal flows and turbulence in helical field configurations are studied. The effect of the trapped electrons on the characteristic quantities of the linear response for zonal flows is investigated for two different field configurations in the Large Helical Device. The turbulent potential fluctuation, zonal flow potential fluctuation and ion energy transport are quickly predicted by the reduced models for which the linear and nonlinear simulation results are used to determine dimensionless parameters related to turbulent saturation levels and typical zonal flow wavenumbers. The effects of zonal flows on the turbulent transport for the case of the kinetic electron response are much smaller than or comparable to those in an adiabatic electron condition for the two different field configurations. It is clarified that the effect of zonal flows on the turbulent transport due to the trapped electrons changes, depending on the field configurations.

scholarly journals Experimental and numerical study of mean zonal flows generated by librations of a rotating spherical cavity

2010 ◽  
Vol 662 ◽  
pp. 260-268 ◽  
Author(s):  
A. SAURET ◽  
D. CÉBRON ◽  
C. MORIZE ◽  
M. LE BARS
Keyword(s):  
Rate Ratio ◽  
Particle Image ◽  
Numerical Study ◽  
Zonal Flow ◽  
Outer Wall ◽  
Weakly Nonlinear ◽  
Zonal Flows ◽  
Solid Body Rotation ◽  
Weakly Nonlinear Analysis ◽  
Image Velocimetry

We study both experimentally and numerically the steady zonal flow generated by longitudinal librations of a spherical rotating container. This study follows the recent weakly nonlinear analysis of Busse (J. Fluid Mech., vol. 650, 2010, pp. 505–512), developed in the limit of small libration frequency–rotation rate ratio and large libration frequency–spin-up time product. Using particle image velocimetry measurements as well as results from axisymmetric numerical simulations, we confirm quantitatively the main features of Busse's analytical solution: the zonal flow takes the form of a retrograde solid-body rotation in the fluid interior, which does not depend on the libration frequency nor on the Ekman number, and which varies as the square of the amplitude of excitation. We also report the presence of an unpredicted prograde flow at the equator near the outer wall.

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