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 Rossby waves and two-dimensional turbulence in a large-scale zonal jet

1987 ◽  
Vol 183 ◽  
pp. 467-509 ◽  
Author(s):  
Theodore G. Shepherd
Keyword(s):  
Large Scale ◽  
Zonal Flow ◽  
Order Effect ◽  
Spatial Inhomogeneity ◽  
Mean Flow ◽  
Scale Separation ◽  
Zonal Flows ◽  
Beta Plane ◽  
Zonal Wavenumber ◽  
Scale Shear

The theory of homogeneous barotropic beta-plane turbulence is here extended to include effects arising from spatial inhomogeneity in the form of a zonal shear flow. Attention is restricted to the geophysically important case of zonal flows that are barotropically stable and are of larger scale than the resulting transient eddy field.Because of the presumed scale separation, the disturbance enstrophy is approximately conserved in a fully nonlinear sense, and the (nonlinear) wave-mean-flow interaction may be characterized as a shear-induced spectral transfer of disturbance enstrophy along lines of constant zonal wavenumber k. In this transfer the disturbance energy is generally not conserved. The nonlinear interactions between different disturbance components are turbulent for scales smaller than the inverse of Rhines's cascade-arrest scale κβ≡ (β0/2urms)½ and in this regime their leading-order effect may be characterized as a tendency to spread the enstrophy (and energy) along contours of constant total wavenumber κ ≡ (k2 + l2)½. Insofar as this process of turbulent isotropization involves spectral transfer of disturbance enstrophy across lines of constant zonal wavenumber k, it can be readily distinguished from the shear-induced transfer which proceeds along them. However, an analysis in terms of total wavenumber K alone, which would be justified if the flow were homogeneous, would tend to mask the differences.The foregoing theoretical ideas are tested by performing direct numerical simulation experiments. It is found that the picture of classical beta-plane turbulence is altered, through the effect of the large-scale zonal flow, in the following ways: (i) while the turbulence is still confined to KKβ, the disturbance field penetrates to the largest scales of motion; (ii) the larger disturbance scales K < Kβ exhibit a tendency to meridional rather than zonal anisotropy, namely towards v2 > u2 rather than vice versa; (iii) the initial spectral transfer rate away from an isotropic intermediate-scale source is significantly enhanced by the shear-induced transfer associated with straining by the zonal flow. This last effect occurs even when the large-scale shear appears weak to the energy-containing eddies, in the sense that dU/dy [Lt ] κ for typical eddy length and velocity scales.

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

&lt;p&gt;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 (&lt;em&gt;J&lt;sub&gt;3&lt;/sub&gt;&lt;/em&gt;, &lt;em&gt;J&lt;sub&gt;5&lt;/sub&gt;&lt;/em&gt;, &lt;em&gt;J&lt;sub&gt;7&lt;/sub&gt;&lt;/em&gt;, &lt;em&gt;J&lt;sub&gt;9&lt;/sub&gt;&lt;/em&gt;) 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 &lt;em&gt;J&lt;sub&gt;3&lt;/sub&gt;&lt;/em&gt; values on the same order of magnitude as the Juno measured value, but would not significantly contribute to &lt;em&gt;J&lt;sub&gt;5&lt;/sub&gt;&lt;/em&gt;, &lt;em&gt;J&lt;sub&gt;7&lt;/sub&gt;&lt;/em&gt;, and &lt;em&gt;J&lt;sub&gt;9&lt;/sub&gt;&lt;/em&gt;. 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., &lt;em&gt;z&lt;/em&gt;-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&amp;#176;-26&amp;#176;N) and southern (14&amp;#176;-21&amp;#176;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.&lt;/p&gt;

scholarly journals Triple-Pair Constellation Configurations for Temporal Gravity Field Retrieval

2020 ◽  
Vol 12 (5) ◽  
pp. 831 ◽  
Author(s):  
Anna F. Purkhauser ◽  
Roland Pail
Keyword(s):  
Spherical Harmonic Degree ◽  
The Third ◽  
The Earth ◽  
Average Improvement ◽  
Gravity Fields ◽  
New Generation ◽  
The Impact ◽  
Temporal Gravity ◽  
Harmonic Degree ◽  
Additional Constraints

The goal of next-generation gravity missions (NGGM) is to improve the monitoring of mass transport in the Earth system by an increased space-time sampling capability as well as higher accuracies of a new generation of instrumentation, but also to continue the monitoring time series obtained by past and current missions such as GRACE and GRACE Follow-On. As the likelihood of three satellite pairs being simultaneously in orbit in the mid-term future increased, we have performed a closed-loop simulation to investigate the impact of a third pair in either polar or inclined orbit as an addition to a Bender-type constellation with NGGM instrumentation. For the additional pair, GRACE-like as well as NGGM instrumentation was tested. The analysis showed that the third pair mainly increases the redundancy of the monitoring system but does not significantly improve de-aliasing capabilities. The best-performing triple-pair scenario comprises a third inclined pair with NGGM sensors. Starting with a Bender-type constellation of a polar and an inclined satellite pair, simulation results indicate an average improvement of 11% in case of adding the third pair in a near-polar orbit, and of 21% for the third pair placed in an inclined orbit. The most important advantage of a multi-pair constellation, however, is the possibility to recover daily gravity fields with higher spatial resolution. In the case of the investigated triple-pair scenarios, a meaningful daily resolution with a maximum spherical harmonic degree of 26 can be achieved, while a higher daily parametrization up to degree 40 results in spatial aliasing and thus would need additional constraints or prior information.

scholarly journals The halo model as a versatile tool to predict intrinsic alignments

2020 ◽  
Author(s):  
Maria Cristina Fortuna ◽  
Henk Hoekstra ◽  
Benjamin Joachimi ◽  
Harry Johnston ◽  
Nora Elisa Chisari ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Power Spectra ◽  
Stage Iv ◽  
Stage Iii ◽  
Radial Dependence ◽  
Additional Parameter ◽  
Small Scales ◽  
Cosmic Shear ◽  
Galaxy Populations ◽  
The Impact

Abstract Intrinsic alignments (IAs) of galaxies are an important contaminant for cosmic shear studies, but the modelling is complicated by the dependence of the signal on the source galaxy sample. In this paper, we use the halo model formalism to capture this diversity and examine its implications for Stage-III and Stage-IV cosmic shear surveys. We account for the different IA signatures at large and small scales, as well for the different contributions from central/satellite and red/blue galaxies, and we use realistic mocks to account for the characteristics of the galaxy populations as a function of redshift. We inform our model using the most recent observational findings: we include a luminosity dependence at both large and small scales and a radial dependence of the signal within the halo. We predict the impact of the total IA signal on the lensing angular power spectra, including the current uncertainties from the IA best-fits to illustrate the range of possible impact on the lensing signal: the lack of constraints for fainter galaxies is the main source of uncertainty for our predictions of the IA signal. We investigate how well effective models with limited degrees of freedom can account for the complexity of the IA signal. Although these lead to negligible biases for Stage-III surveys, we find that, for Stage-IV surveys, it is essential to at least include an additional parameter to capture the redshift dependence.

scholarly journals Integral Constraints for Momentum and Energy in Zonal Flows with Parameterized Potential Vorticity Fluxes: Governing Parameters

2014 ◽  
Vol 44 (3) ◽  
pp. 922-943 ◽  
Author(s):  
V. O. Ivchenko ◽  
S. Danilov ◽  
B. Sinha ◽  
J. Schröter
Keyword(s):  
Ocean Circulation ◽  
Potential Vorticity ◽  
Channel Model ◽  
Bottom Topography ◽  
Flat Bottom ◽  
Zonal Flows ◽  
Integral Constraints ◽  
Variable Bottom ◽  
Eddy Fluxes ◽  
The Impact

Abstract Integral constraints for momentum and energy impose restrictions on parameterizations of eddy potential vorticity (PV) fluxes. The impact of these constraints is studied for a wind-forced quasigeostrophic two-layer zonal channel model with variable bottom topography. The presence of a small parameter, given by the ratio of Rossby radius to the width of the channel, makes it possible to find an analytical/asymptotic solution for the zonally and time-averaged flow, given diffusive parameterizations for the eddy PV fluxes. This solution, when substituted in the constraints, leads to nontrivial explicit restrictions on diffusivities. The system is characterized by four dimensionless governing parameters with a clear physical interpretation. The bottom form stress, the major term balancing the external force of wind stress, depends on the governing parameters and fundamentally modifies the restrictions compared to the flat bottom case. While the analytical solution bears an illustrative character, it helps to see certain nontrivial connections in the system that will be useful in the analysis of more complicated models of ocean circulation. A numerical solution supports the analytical study and confirms that the presence of topography strongly modifies the eddy fluxes.

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

&lt;p&gt;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.&lt;/p&gt;

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.

Gravity Measurements of the Juno Spacecraft Matched with Jupiter Models that rely on a Dilute Core and Deep Winds

2021 ◽  
Author(s):  
Burkhard Militzer ◽  
Sean Wahl ◽  
William Hubbard
Keyword(s):  
Phase Separation ◽  
Inner Core ◽  
Interior Layer ◽  
Gravity Fields ◽  
Gravity Measurements ◽  
Theoretical Predictions

&lt;div&gt;&lt;span&gt;Since its arrival at Jupiter in 2016, the Juno spacecraft has measured the planet&amp;#8217;s gravity fields with unprecedented precision. The interpretation of these measurements has been challenging because the magnitudes of the gravity coefficients J&lt;/span&gt;&lt;sub&gt;4&lt;/sub&gt;&lt;span&gt; and J&lt;/span&gt;&lt;sub&gt;6&lt;/sub&gt;&lt;span&gt; were smaller than predicted by traditional interiors models that included a dense inner core composed of rock and ice. Here we instead present models with dilute cores [Geophys. Res. Lett. 44 (2017) 4649] and deep-winds that conform to theoretical predictions of hydrogen-helium phase separation in the interior layer from approximately 0.8 to 0.85 Jupiter radii. Such models match the entire set of zonal gravity measurements by the Juno spacecraft. Our work is based on the accelerated version of the Concentric Maclaurin Spheroid method [Astrophysical J. &lt;/span&gt;&lt;strong&gt;879&lt;/strong&gt;&lt;span&gt;&amp;#160;(2019) 78]. We conclude by comparing with models for Saturn&amp;#8217;s interior.&amp;#160;&lt;/span&gt;&lt;/div&gt;

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.

scholarly journals Regional responses of surface ozone in Europe to the location of high-latitude blocks and subtropical ridges

2016 ◽  
Author(s):  
Carlos Ordóñez ◽  
David Barriopedro ◽  
Ricardo García-Herrera ◽  
Pedro M. Sousa ◽  
Jordan L. Schnell
Keyword(s):  
High Latitude ◽  
Climate Models ◽  
Surface Ozone ◽  
Zonal Flow ◽  
Near Surface ◽  
Air Masses ◽  
Anticyclonic Circulation ◽  
The Uk ◽  
The Impact ◽  
First Time

Abstract. This paper analyses for the first time the impact of high-latitude blocks and subtropical ridges on near-surface ozone in Europe during a 15-year period. For this purpose, a catalogue of blocks and ridges over the Euro-Atlantic region is used together with a gridded dataset of maximum daily 8-hour running average ozone (MDA8 O3) covering the period 1998–2012. The response of ozone to the location of blocks and ridges with centres in three longitudinal sectors (Atlantic, ATL, 30º–0º W; European, EUR, 0º–30º E; Russian, RUS, 30º–60º E) is examined. The impact of blocks on ozone is regionally and seasonally dependent. In particular, blocks within the EUR sector yield positive ozone anomalies of ~ 5–10 ppb over large parts of central Europe in spring and northern Europe in summer. Over 20 % and 30 % of the days with blocks in that sector register exceedances of the 90th percentile of the seasonal ozone distribution at many European locations during spring and summer, respectively. The impacts of ridges during those seasons are subtle and more sensitive to their specific location, although they can trigger ozone anomalies of ~ 5–10 ppb in Italy and the surrounding countries in summer, eventually exceeding European air quality targets. During winter, surface ozone in the northwest of Europe presents completely opposite responses to blocks and ridges. The anticyclonic circulation associated with winter EUR blocking, and to a lesser extent with ATL blocking, yields negative ozone anomalies between −5 ppb and −10 ppb over the UK, Northern France and the Benelux. Conversely, the enhanced zonal flow around 50˚–60˚ N during the occurrence of ATL ridges favours the arrival of background air masses from the Atlantic and the ventilation of the boundary layer, producing positive ozone anomalies above 5 ppb in an area spanning from the British Isles to Germany. This work provides the first quantitative assessments of the remarkable but distinct impacts that the anticyclonic circulation and the diversion of the zonal flow associated with blocks and ridges exert on surface ozone in Europe. The findings reported here can be exploited in the future to evaluate the modelled responses of ozone to circulation changes within chemical transport models (CTMs) and chemistry-climate models (CCMs).

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