## Periodic Reporting for period 1 - JUMP (JUpiter Modeling Platform)

Periodo di rendicontazione: 2018-11-01 al 2020-10-31

In planetary atmospheres, it is common that the outer atmospheric envelope contains highly turbulent flows powered by solar energy and by a heat flux from within the planet itself. These thermal energy sources transform into sources of atmospheric motion by driving turbulent eddies whose typical scales do not exceed a typical length scale of ∼ 2,500 km for both Jupiter and Saturn. It ensures the growth of powerful large scale zonal jets, that is east-west directed flow with 10,000–20,000 km latitudinal scale, and a host of waves and vortices, see Figure 1. On planets as Jupiter and Saturn, the jets are profoundly strong, their influence on the distribution of clouds is clearly visible even through relatively simple amateur telescopes, and their appearance is almost unchanging over hundreds of years since early observations. However, how these zonal jets form in planetary flows and how deep they extend within planetary interiors? are long-lived conundrums that aimed to be explored by designing the JUpiter Modelling Platform throughout the project JUMP.

To address the central question arise with JUMP, we designed the first mixed laboratory-numerical-observational platform to explore physical ingredients that govern the formation of zonal jets in the gas giant’s atmospheres. We deliver, in open access, a package of theoretic statistical tools to extract properties of Jupiter-like flows reproduced with the numerical and laboratory platform and observe from direct measurement in the planets. The theoretic statistical tools aim to disclose the dynamical mechanisms that lead to the formation of zonal jets. Using these tools, we show that zonal jets in planetary envelopes results from upscale transfer of kinetic energy from the small scale turbulent eddies up to the large scale jets. We show that this upscale transfer result of rapid planetary rotation in planet such as Jupiter and Saturn. Finally we evidence that large scale hydrodynamic features become zonal jets because of the curvature of the spherical planetary fluid layer. These successive dynamical parameters, namely the formation of turbulent eddies, rotation and spherical curvature, are responsible for the banding of Jupiter’s and Saturn’s atmospheres. In the Earth's atmosphere and oceans, jets are also present but they are so weak and meandering that they are virtually undetectable without some deep analysis of the flow. Nonetheless, jets formation in all planetary envelopes, of the Earth, gas giants and other exoplanets, are likely to result from the same planetary parameters.

These results, being obtained using a new climate model named DYNAMICO, we integrated today collaborative efforts of numerous scientific communities that aim to model and understand climate changes. Indeed, Jupiter and Saturn reference simulations that have been run to reproduce the planetary jets, can be considered as crucial tests for the new model DYNAMICO before it becomes a widespread model for the Earth’s atmosphere. Therefore, the next step will be to apply JUMP dynamical diagnostic to the most recent and future models of the Earth’s atmosphere and ocean.

To address the central question arise with JUMP, we designed the first mixed laboratory-numerical-observational platform to explore physical ingredients that govern the formation of zonal jets in the gas giant’s atmospheres. We deliver, in open access, a package of theoretic statistical tools to extract properties of Jupiter-like flows reproduced with the numerical and laboratory platform and observe from direct measurement in the planets. The theoretic statistical tools aim to disclose the dynamical mechanisms that lead to the formation of zonal jets. Using these tools, we show that zonal jets in planetary envelopes results from upscale transfer of kinetic energy from the small scale turbulent eddies up to the large scale jets. We show that this upscale transfer result of rapid planetary rotation in planet such as Jupiter and Saturn. Finally we evidence that large scale hydrodynamic features become zonal jets because of the curvature of the spherical planetary fluid layer. These successive dynamical parameters, namely the formation of turbulent eddies, rotation and spherical curvature, are responsible for the banding of Jupiter’s and Saturn’s atmospheres. In the Earth's atmosphere and oceans, jets are also present but they are so weak and meandering that they are virtually undetectable without some deep analysis of the flow. Nonetheless, jets formation in all planetary envelopes, of the Earth, gas giants and other exoplanets, are likely to result from the same planetary parameters.

These results, being obtained using a new climate model named DYNAMICO, we integrated today collaborative efforts of numerous scientific communities that aim to model and understand climate changes. Indeed, Jupiter and Saturn reference simulations that have been run to reproduce the planetary jets, can be considered as crucial tests for the new model DYNAMICO before it becomes a widespread model for the Earth’s atmosphere. Therefore, the next step will be to apply JUMP dynamical diagnostic to the most recent and future models of the Earth’s atmosphere and ocean.

In practical terms, JUMP was initially planned to explore three physical ingredients to answer the central questions: How zonal jets form and how deep they extend within planetary interiors? The physical ingredients originally identified were: (i) the atmospheric layer depth, (ii) the nature of the β-effect, i.e. a parameter related to planetary spherical curvature, and (iii) energy dissipation at the bottom boundary of the atmospheric layers.

After two years of JUMP, ingredients (i) and (ii) have been deeply explored and ingredient (iii) is ready to be implemented and will be in a near future. We show Figure 2 the 1st version of JUMP’s device, which is a square tank of 30cm height by 68cm long, mounted on a rotating table and containing 4 cm heigh of salty water. Once rotated, the water’s free surface takes the shape of a paraboloid modeling the effect of planetary curvature, namely the β-effect. By exploring (i) the atmospheric layer depth and (ii) the nature of the β-effect, we show in the laboratory that zonal jets result from the coupled action of rotation and water’s free surface curvature (i.e. β-effect). We also run global climate models of gas giant’s atmosphere. The model names the Jupiter/Saturn DYNAMICO and make use of a three-dimensional hydrodynamical solver well-suited for massively parallel computations. By conducting an in depth analysis of statistical flow properties calculated from the reference Jupiter and Saturn simulations, we confirm that zonal jets form in rapidly rotating flows with a spherical curvature.

During the implementation of JUMP, the fellow brought out a new physical ingredient of relevance and an unexpected dynamical phenomenon that revealed to be of crucial interest for the understanding of planetary zonal jets and momentarily deviated JUMP’s roadmap from its last ingredient (iii). Thus, the fourth, unplanned, physical ingredient (iv) is potential vorticity, a conservative quantity in planetary atmospheres. It has been demonstrated that potential vorticity can be used to probe the intensity of turbulent motions that sustain the formation of zonal jets. The fifth, unplanned, discovery (v) is the formation, in our laboratory device, of a wavy structure that resembles Saturn’s polar hexagon. JUMP’s results and discoveries have been continuously disseminated and made understandable to a society at large, with a web-platform dedicated to the project.

After two years of JUMP, ingredients (i) and (ii) have been deeply explored and ingredient (iii) is ready to be implemented and will be in a near future. We show Figure 2 the 1st version of JUMP’s device, which is a square tank of 30cm height by 68cm long, mounted on a rotating table and containing 4 cm heigh of salty water. Once rotated, the water’s free surface takes the shape of a paraboloid modeling the effect of planetary curvature, namely the β-effect. By exploring (i) the atmospheric layer depth and (ii) the nature of the β-effect, we show in the laboratory that zonal jets result from the coupled action of rotation and water’s free surface curvature (i.e. β-effect). We also run global climate models of gas giant’s atmosphere. The model names the Jupiter/Saturn DYNAMICO and make use of a three-dimensional hydrodynamical solver well-suited for massively parallel computations. By conducting an in depth analysis of statistical flow properties calculated from the reference Jupiter and Saturn simulations, we confirm that zonal jets form in rapidly rotating flows with a spherical curvature.

During the implementation of JUMP, the fellow brought out a new physical ingredient of relevance and an unexpected dynamical phenomenon that revealed to be of crucial interest for the understanding of planetary zonal jets and momentarily deviated JUMP’s roadmap from its last ingredient (iii). Thus, the fourth, unplanned, physical ingredient (iv) is potential vorticity, a conservative quantity in planetary atmospheres. It has been demonstrated that potential vorticity can be used to probe the intensity of turbulent motions that sustain the formation of zonal jets. The fifth, unplanned, discovery (v) is the formation, in our laboratory device, of a wavy structure that resembles Saturn’s polar hexagon. JUMP’s results and discoveries have been continuously disseminated and made understandable to a society at large, with a web-platform dedicated to the project.

JUMP’s project final achievement has been completed thanks to the direct confrontation of three independent sources of zonal jets, coming from three different datasets, i.e. laboratory, numerical and observational flows. The three datasets together with a package of theoretic statistical tools are in open access on JUMP’s webpage and form the laboratory-numerical-observational platform. Thanks to this platform, we succeeded in theorizing a new statistical tool, planetary potential vorticity, to explore the intensity of turbulence in planetary atmospheres. This tool will likely be re-used by other scientific communities for future planetary exploration.

Indeed, quantifying the intensity of planetary turbulent motions was up to now inaccessible to conventional tools, however, since they require large quantities of spatially-and temporarily-resolved data. JUMP presented a new and universal diagnostic that can estimate the intensity, of the energy exchanged between all scales of motion in planetary atmospheres. This diagnostic is based on the conservation of potential vorticity in rotating system from which we defined a length scale, LM, representing a typical distance over which potential vorticity is mixed by planetary turbulence. The length scale LM is represented in Figure 1.

Using this new tool, we estimated the length scale L M within Jupiter’s and Saturn’s troposphere, showing for the first time that turbulent energy transfer in Saturn’s atmosphere is four times less intense than Jupiter’s. We can speculate that part of this difference simply reflects the fact that Saturn is nearly twice as far from the sun as Jupiter, and hence receives a quarter of the solar energy input. Because it is universal, this new tool can be used to diagnose the intensity of the turbulent mixing in many other natural settings, such as the Earth’s ocean and newly discovered exoplanets.

Indeed, quantifying the intensity of planetary turbulent motions was up to now inaccessible to conventional tools, however, since they require large quantities of spatially-and temporarily-resolved data. JUMP presented a new and universal diagnostic that can estimate the intensity, of the energy exchanged between all scales of motion in planetary atmospheres. This diagnostic is based on the conservation of potential vorticity in rotating system from which we defined a length scale, LM, representing a typical distance over which potential vorticity is mixed by planetary turbulence. The length scale LM is represented in Figure 1.

Using this new tool, we estimated the length scale L M within Jupiter’s and Saturn’s troposphere, showing for the first time that turbulent energy transfer in Saturn’s atmosphere is four times less intense than Jupiter’s. We can speculate that part of this difference simply reflects the fact that Saturn is nearly twice as far from the sun as Jupiter, and hence receives a quarter of the solar energy input. Because it is universal, this new tool can be used to diagnose the intensity of the turbulent mixing in many other natural settings, such as the Earth’s ocean and newly discovered exoplanets.