Vortex Dynamics - From Physical to Mathematical Aspects
In this contribution, we present a set of procedures developed to identify fluid flow structures ... more In this contribution, we present a set of procedures developed to identify fluid flow structures and characterize their space-time evolution in time-dependent flows. In particular, we consider two different contests of importance in applied fluid mechanics: 1) large-scale almost 2D atmospheric and oceanic flows and 2) flow inside the left ventricle in the human blood circulation. For both cases, we designed an ad hoc experimental model to reproduce and deeply investigate the considered phenomena. We will focus on the post-processing of high-resolution velocity data sets obtained via laboratory experiments by measuring the flow field using a technique based on image analysis. We show how the proposed methodologies represent a valid tool suitable for extracting the main patterns and quantify fluid transport in complex flows from both Eulerian and Lagrangian perspectives.
La plupart des objets astrophysiques, comme les planètes ou les étoiles, produisent leur proprech... more La plupart des objets astrophysiques, comme les planètes ou les étoiles, produisent leur proprechamp magnétique à partir d’une forte agitation d’un fluide conducteur d’électricité comme un métalen fusion ou un plasma ionique. Un champ magnétique de grande échelle est alors crée lorsqueles mouvements de ce fluide génèrent des courants induits suffisamment intenses pour compenserla dissipation Ohmique du système. Ceci est vrai pour des dynamiques à haut nombre de Reynoldsmagnétique Rm = UL/h (U et L sont la vitesse et la longueur caractéristique du système et h la diffusivitémagnétique). Il est connu, que l’écoulement moyen d’un fluide en rotation peut produire unchamp magnétique de grande échelle en cisaillant les lignes d’un champ magnétique déjà présentdans le système. Il s’agit de l’effet Omega. Cependant, un tel processus d’induction ne permet pasd’obtenir une dynamo qui s’auto-entretienne, celle-ci a donc besoin d’un mécanisme d’inductionsupplémentaire pour exister. Ainsi, on fa...
Authors who select OnlineOpen will be charged the standard OnlineOpen fee for your journal, but e... more Authors who select OnlineOpen will be charged the standard OnlineOpen fee for your journal, but excess publication fees will still apply, if applicable. If your paper has generated excess publication fees, please complete and return the form below in addition to completing the OnlineOpen order form online (excess fees are billed separately). If you would like to choose OnlineOpen and you have not already submitted your order online, please do so now.
Saturn's polar regions (polewards of ∼63° planetocentric latitude) are strongly dynamically a... more Saturn's polar regions (polewards of ∼63° planetocentric latitude) are strongly dynamically active with zonal jets, polar cyclones and the intriguing north polar hexagon (NPH) wave. Here we analyze measurements of horizontal winds, previously obtained from Cassini images by Antuñano et al. (2015), https://doi.org/10.1002/2014je004709, to determine the spatial and spectral exchanges of kinetic energy (KE) between zonal mean zonal jets and nonaxisymmetric eddies in Saturn's polar regions. Eddies of most resolved scales generally feed KE into the eastward and westward zonal mean jets at rates between 4.3 × 10−5 and 1.4 × 10−4 W kg−1. In particular, the north polar jet (at 76°N) was being energized at a rate of ∼10−4 W kg−1, dominated by the contribution due to the zonal wavenumber m = 6 NPH wave itself. This implies that the hexagon was not being driven at this time through a barotropic instability of the north polar jet, but may suggest a significant role for baroclinic instab...
The formation of large scale structures in three-dimensional (3D) turbulent flows. How small-scal... more The formation of large scale structures in three-dimensional (3D) turbulent flows. How small-scale dynamics organize in turbulent flows to grow large scale coherent circulation? is at the heart of fundamental studies in fluid dynamics. It appears to be equally important for our understanding of atmospheric dynamics, oceanography, meteorology and more generally geophysical fluid dynamics. Here, we deliver a data collection that <strong>(1)</strong> gathers measurements of 3D turbulent flows that emulate planetary atmospheres of the gas giants. Turbulent flows are explored using three different approaches, laboratory experiments, numerical simulations and direct planetary observations. All data set are computed in order to easily extract flow properties, i.e. high resolution maps of the different velocity components and flow vorticity (useful for further diagnostic). The data collected are fully discribed in Cabanes et al GRL (2020) "Revealing the intensity of turbule...
Background and motivation The longevity of the richly-instrumented Cassini mission permitted an e... more Background and motivation The longevity of the richly-instrumented Cassini mission permitted an exceptionally detailed characterization, and monitoring over the changing seasons, of Saturn’s a) latest Great White Spot1 and associated stratospheric warming2,3; b) mid-latitude convective storms4 and vortices5,6; c) stable hexagonal polar jet7 and central turbulent polar vortex8; d) equatorial stratospheric oscillation of temperature, with jets stacked along the vertical, in Saturn’s stratosphere9 with semi-annual periodicity10; e) possible meridional transport of stratospheric hydrocarbons11,12. Cassini mapping of Jupiter’s and Saturn’s banded tropospheric jets in the cloud layer demonstrated the high rate of conversion of energy from eddies to banded jets13,14 and detailed the structure of macroturbulence and vorticity15,16, which strongly suggests that large-scale tropospheric banded jets emerge from forcing by smaller-scale eddies and waves arising from hydrodynamical instabilities...
Entre los enigmas que plantea Jupiter, la formacion de bandas atmosfericas que se extienden de es... more Entre los enigmas que plantea Jupiter, la formacion de bandas atmosfericas que se extienden de este a oeste intriga desde hace anos a planetologos y expertos en mecanica de fluidos. En una atmosfera turbulenta, tales estructuras deberian ser inestables y desaparecer con rapidez. Dos modelos teoricos aspiran a explicar su origen. Para discriminar entre ellos se emplean simulaciones numericas y experimentos de laboratorio. La sonda Juno, actualmente en orbita alrededor de Jupiter, aportara tambien valiosa informacion.
La plupart des objets astrophysiques, comme les planetes ou les etoiles, produisent leur proprech... more La plupart des objets astrophysiques, comme les planetes ou les etoiles, produisent leur proprechamp magnetique a partir d’une forte agitation d’un fluide conducteur d’electricite comme un metalen fusion ou un plasma ionique. Un champ magnetique de grande echelle est alors cree lorsqueles mouvements de ce fluide generent des courants induits suffisamment intenses pour compenserla dissipation Ohmique du systeme. Ceci est vrai pour des dynamiques a haut nombre de Reynoldsmagnetique Rm = UL/h (U et L sont la vitesse et la longueur caracteristique du systeme et h la diffusivitemagnetique). Il est connu, que l’ecoulement moyen d’un fluide en rotation peut produire unchamp magnetique de grande echelle en cisaillant les lignes d’un champ magnetique deja presentdans le systeme. Il s’agit de l’effet Omega. Cependant, un tel processus d’induction ne permet pasd’obtenir une dynamo qui s’auto-entretienne, celle-ci a donc besoin d’un mecanisme d’inductionsupplementaire pour exister. Ainsi, on fa...
The strong east–west jet flows on the gas giants, Jupiter and Saturn, have persisted for hundreds... more The strong east–west jet flows on the gas giants, Jupiter and Saturn, have persisted for hundreds of years. Yet, experimental studies cannot reach the planetary regime and similarly strong and quasi-steady jets have been reproduced in numerical models only under simplifying assumptions and limitations. Two models have been proposed: a shallow model where jets are confined to the weather layer and a deep model where the jets extend into the planetary molecular envelope. Here we show that turbulent laboratory flows naturally generate multiple, alternating jets in a rapidly rotating cylindrical container. The observed properties of gas giants’ jets are only now reproduced in a laboratory experiment emulating the deep model. In parallel, we adopt the approach of complete three-dimensional Global Climate Models (GCMs) solving for hydrodynamical Navier-Stokes equations and setting a Saturn’s like ”shallow-forcing” climate model. Our findings demonstrate that long-lived jets can exist in o...
The Cassini mission has opened many science questions related to Saturn's atmospheric dynamic... more The Cassini mission has opened many science questions related to Saturn's atmospheric dynamics: jet-streams (including the hexagonal-shaped northern polar jet), giant convective storms, stratospheric equatorial oscillations, interhemispheric transport. This inspired our group to develop a Global Climate Model for Saturn that couples a massively-parallel icosahedral-grid hydrodynamical solver with detailed physical parameterizations (notably correlated-k radiative transfer) for Saturn's troposphere and stratosphere. Multiple test simulations led us to determine the best modeling settings to run simulations in which (amongst other requirements) the conservation of angular momentum is ensured with good accuracy. Multi-year simulations carried out with a spatial resolution of 1/2° in latitude/longitude allowed us to analyze the mechanisms accounting for jet acceleration (and possible latitudinal migration) in the troposphere and the stratosphere of Saturn, the formation of large...
Geophysical & Astrophysical Fluid Dynamics, 2018
We conduct in-depth analysis of statistical flow properties from direct numerical simulations tha... more We conduct in-depth analysis of statistical flow properties from direct numerical simulations that reproduce gas giants macroturbulence, namely large-scale zonal winds. Our numerical model has been specifically designed to simulate a recent laboratory device that reports zonal jets in the configuration of deep turbulent planetary layers (Cabanes et al. 2017). In this framework, the so-called zonostrophic regime is achieved when large topographical variations of the fluid layer combine with rapid rotation in a well developed three-dimensional (3D) turbulent flow. At steady state, strongly energetic, zonally dominated, large-scale axisymmetric structures emerge scaling with Rhines' theoretical scale. This model differs from the shallowlayer scenario where the flow is confined to a quasi-two-dimensional (2D) fluid shell and the anisotropic βeffect arises from latitudinal variation of the Coriolis force. Thus, we aim to reveal, in the specific framework of the deep-layer scenario, signatures of the zonostrophic regime and of a β-topography in statistical flow properties. To do so, we run two large-scale 3D direct numerical simulations in a cylindrical geometry of a highly turbulent and rapidly rotating flow. These two simulations use similar set of parameters but with and without topographical β-effect. We propose a comparative phenomenological description of the temporal and spatial statistics of the three components of the velocity field. Interestingly, we report that peculiar correlations occur between the vertical and radial flow components when a β-topography is imposed and show a feature possibly due to a zonostrophic dynamics in 3D frequency spectra. These results suggest the development of new tools to remotely investigate gas giants zonal winds by extracting statistical flow properties from direct observations. Ultimately our analysis may support the relevance of the deep models in the study of prevalent features of planetary dynamics.
Vortex Dynamics - From Physical to Mathematical Aspects
In this contribution, we present a set of procedures developed to identify fluid flow structures ... more In this contribution, we present a set of procedures developed to identify fluid flow structures and characterize their space-time evolution in time-dependent flows. In particular, we consider two different contests of importance in applied fluid mechanics: 1) large-scale almost 2D atmospheric and oceanic flows and 2) flow inside the left ventricle in the human blood circulation. For both cases, we designed an ad hoc experimental model to reproduce and deeply investigate the considered phenomena. We will focus on the post-processing of high-resolution velocity data sets obtained via laboratory experiments by measuring the flow field using a technique based on image analysis. We show how the proposed methodologies represent a valid tool suitable for extracting the main patterns and quantify fluid transport in complex flows from both Eulerian and Lagrangian perspectives.
La plupart des objets astrophysiques, comme les planètes ou les étoiles, produisent leur proprech... more La plupart des objets astrophysiques, comme les planètes ou les étoiles, produisent leur proprechamp magnétique à partir d’une forte agitation d’un fluide conducteur d’électricité comme un métalen fusion ou un plasma ionique. Un champ magnétique de grande échelle est alors crée lorsqueles mouvements de ce fluide génèrent des courants induits suffisamment intenses pour compenserla dissipation Ohmique du système. Ceci est vrai pour des dynamiques à haut nombre de Reynoldsmagnétique Rm = UL/h (U et L sont la vitesse et la longueur caractéristique du système et h la diffusivitémagnétique). Il est connu, que l’écoulement moyen d’un fluide en rotation peut produire unchamp magnétique de grande échelle en cisaillant les lignes d’un champ magnétique déjà présentdans le système. Il s’agit de l’effet Omega. Cependant, un tel processus d’induction ne permet pasd’obtenir une dynamo qui s’auto-entretienne, celle-ci a donc besoin d’un mécanisme d’inductionsupplémentaire pour exister. Ainsi, on fa...
Authors who select OnlineOpen will be charged the standard OnlineOpen fee for your journal, but e... more Authors who select OnlineOpen will be charged the standard OnlineOpen fee for your journal, but excess publication fees will still apply, if applicable. If your paper has generated excess publication fees, please complete and return the form below in addition to completing the OnlineOpen order form online (excess fees are billed separately). If you would like to choose OnlineOpen and you have not already submitted your order online, please do so now.
Saturn's polar regions (polewards of ∼63° planetocentric latitude) are strongly dynamically a... more Saturn's polar regions (polewards of ∼63° planetocentric latitude) are strongly dynamically active with zonal jets, polar cyclones and the intriguing north polar hexagon (NPH) wave. Here we analyze measurements of horizontal winds, previously obtained from Cassini images by Antuñano et al. (2015), https://doi.org/10.1002/2014je004709, to determine the spatial and spectral exchanges of kinetic energy (KE) between zonal mean zonal jets and nonaxisymmetric eddies in Saturn's polar regions. Eddies of most resolved scales generally feed KE into the eastward and westward zonal mean jets at rates between 4.3 × 10−5 and 1.4 × 10−4 W kg−1. In particular, the north polar jet (at 76°N) was being energized at a rate of ∼10−4 W kg−1, dominated by the contribution due to the zonal wavenumber m = 6 NPH wave itself. This implies that the hexagon was not being driven at this time through a barotropic instability of the north polar jet, but may suggest a significant role for baroclinic instab...
The formation of large scale structures in three-dimensional (3D) turbulent flows. How small-scal... more The formation of large scale structures in three-dimensional (3D) turbulent flows. How small-scale dynamics organize in turbulent flows to grow large scale coherent circulation? is at the heart of fundamental studies in fluid dynamics. It appears to be equally important for our understanding of atmospheric dynamics, oceanography, meteorology and more generally geophysical fluid dynamics. Here, we deliver a data collection that <strong>(1)</strong> gathers measurements of 3D turbulent flows that emulate planetary atmospheres of the gas giants. Turbulent flows are explored using three different approaches, laboratory experiments, numerical simulations and direct planetary observations. All data set are computed in order to easily extract flow properties, i.e. high resolution maps of the different velocity components and flow vorticity (useful for further diagnostic). The data collected are fully discribed in Cabanes et al GRL (2020) "Revealing the intensity of turbule...
Background and motivation The longevity of the richly-instrumented Cassini mission permitted an e... more Background and motivation The longevity of the richly-instrumented Cassini mission permitted an exceptionally detailed characterization, and monitoring over the changing seasons, of Saturn’s a) latest Great White Spot1 and associated stratospheric warming2,3; b) mid-latitude convective storms4 and vortices5,6; c) stable hexagonal polar jet7 and central turbulent polar vortex8; d) equatorial stratospheric oscillation of temperature, with jets stacked along the vertical, in Saturn’s stratosphere9 with semi-annual periodicity10; e) possible meridional transport of stratospheric hydrocarbons11,12. Cassini mapping of Jupiter’s and Saturn’s banded tropospheric jets in the cloud layer demonstrated the high rate of conversion of energy from eddies to banded jets13,14 and detailed the structure of macroturbulence and vorticity15,16, which strongly suggests that large-scale tropospheric banded jets emerge from forcing by smaller-scale eddies and waves arising from hydrodynamical instabilities...
Entre los enigmas que plantea Jupiter, la formacion de bandas atmosfericas que se extienden de es... more Entre los enigmas que plantea Jupiter, la formacion de bandas atmosfericas que se extienden de este a oeste intriga desde hace anos a planetologos y expertos en mecanica de fluidos. En una atmosfera turbulenta, tales estructuras deberian ser inestables y desaparecer con rapidez. Dos modelos teoricos aspiran a explicar su origen. Para discriminar entre ellos se emplean simulaciones numericas y experimentos de laboratorio. La sonda Juno, actualmente en orbita alrededor de Jupiter, aportara tambien valiosa informacion.
La plupart des objets astrophysiques, comme les planetes ou les etoiles, produisent leur proprech... more La plupart des objets astrophysiques, comme les planetes ou les etoiles, produisent leur proprechamp magnetique a partir d’une forte agitation d’un fluide conducteur d’electricite comme un metalen fusion ou un plasma ionique. Un champ magnetique de grande echelle est alors cree lorsqueles mouvements de ce fluide generent des courants induits suffisamment intenses pour compenserla dissipation Ohmique du systeme. Ceci est vrai pour des dynamiques a haut nombre de Reynoldsmagnetique Rm = UL/h (U et L sont la vitesse et la longueur caracteristique du systeme et h la diffusivitemagnetique). Il est connu, que l’ecoulement moyen d’un fluide en rotation peut produire unchamp magnetique de grande echelle en cisaillant les lignes d’un champ magnetique deja presentdans le systeme. Il s’agit de l’effet Omega. Cependant, un tel processus d’induction ne permet pasd’obtenir une dynamo qui s’auto-entretienne, celle-ci a donc besoin d’un mecanisme d’inductionsupplementaire pour exister. Ainsi, on fa...
The strong east–west jet flows on the gas giants, Jupiter and Saturn, have persisted for hundreds... more The strong east–west jet flows on the gas giants, Jupiter and Saturn, have persisted for hundreds of years. Yet, experimental studies cannot reach the planetary regime and similarly strong and quasi-steady jets have been reproduced in numerical models only under simplifying assumptions and limitations. Two models have been proposed: a shallow model where jets are confined to the weather layer and a deep model where the jets extend into the planetary molecular envelope. Here we show that turbulent laboratory flows naturally generate multiple, alternating jets in a rapidly rotating cylindrical container. The observed properties of gas giants’ jets are only now reproduced in a laboratory experiment emulating the deep model. In parallel, we adopt the approach of complete three-dimensional Global Climate Models (GCMs) solving for hydrodynamical Navier-Stokes equations and setting a Saturn’s like ”shallow-forcing” climate model. Our findings demonstrate that long-lived jets can exist in o...
The Cassini mission has opened many science questions related to Saturn's atmospheric dynamic... more The Cassini mission has opened many science questions related to Saturn's atmospheric dynamics: jet-streams (including the hexagonal-shaped northern polar jet), giant convective storms, stratospheric equatorial oscillations, interhemispheric transport. This inspired our group to develop a Global Climate Model for Saturn that couples a massively-parallel icosahedral-grid hydrodynamical solver with detailed physical parameterizations (notably correlated-k radiative transfer) for Saturn's troposphere and stratosphere. Multiple test simulations led us to determine the best modeling settings to run simulations in which (amongst other requirements) the conservation of angular momentum is ensured with good accuracy. Multi-year simulations carried out with a spatial resolution of 1/2° in latitude/longitude allowed us to analyze the mechanisms accounting for jet acceleration (and possible latitudinal migration) in the troposphere and the stratosphere of Saturn, the formation of large...
Geophysical & Astrophysical Fluid Dynamics, 2018
We conduct in-depth analysis of statistical flow properties from direct numerical simulations tha... more We conduct in-depth analysis of statistical flow properties from direct numerical simulations that reproduce gas giants macroturbulence, namely large-scale zonal winds. Our numerical model has been specifically designed to simulate a recent laboratory device that reports zonal jets in the configuration of deep turbulent planetary layers (Cabanes et al. 2017). In this framework, the so-called zonostrophic regime is achieved when large topographical variations of the fluid layer combine with rapid rotation in a well developed three-dimensional (3D) turbulent flow. At steady state, strongly energetic, zonally dominated, large-scale axisymmetric structures emerge scaling with Rhines' theoretical scale. This model differs from the shallowlayer scenario where the flow is confined to a quasi-two-dimensional (2D) fluid shell and the anisotropic βeffect arises from latitudinal variation of the Coriolis force. Thus, we aim to reveal, in the specific framework of the deep-layer scenario, signatures of the zonostrophic regime and of a β-topography in statistical flow properties. To do so, we run two large-scale 3D direct numerical simulations in a cylindrical geometry of a highly turbulent and rapidly rotating flow. These two simulations use similar set of parameters but with and without topographical β-effect. We propose a comparative phenomenological description of the temporal and spatial statistics of the three components of the velocity field. Interestingly, we report that peculiar correlations occur between the vertical and radial flow components when a β-topography is imposed and show a feature possibly due to a zonostrophic dynamics in 3D frequency spectra. These results suggest the development of new tools to remotely investigate gas giants zonal winds by extracting statistical flow properties from direct observations. Ultimately our analysis may support the relevance of the deep models in the study of prevalent features of planetary dynamics.
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