The origin of jets and vortices in turbulent planetary atmospheres

Thibault JOUGLA ; LEGI ; Oct.2015 - Oct. 2018

Phd student : Thibault JOUGLA ; LEGI ; Oct.2015 - Oct. 2018
Supervision : Jan-Bert Flór (LEGI), David Dritschel (St Andrews University)
Funding : 50% St. Andrews University (UK) / 50% Labex
Doctoral School : Terre-Univers-Environnement ; Grenoble

Abstract

A striking feature of the large-scale turbulent motions of planetary atmospheres and oceans is the presence of well-defined zonal jets, coexisting with a background turbulent flow, often containing coherent long-lived vortices. The jets and vortices are believed to dominate mixing and transport processes in atmospheres and oceans. The observed large-scale organisation and the unsteady smaller-scale turbulent fluid motion are thought to be intimately coupled, with the turbulence feeding the large-scale motion, and the large-scale motion organising the turbulence. Jupiter’s atmosphere is a spectacular example. There, quasi-zonal bands or belts of alternating eastwards and westwards fluid motion are punctuated by a myriad of intense, dynamic storms or vortices like the Great Red Spot.
Turbulence arises through instability of the large-scale circulation, generated by differential solar heating (equatorial regions receive more radiation), and in the case of the giant gas planets, through internal convection. The complex processes at play, and especially how they cooperate to generate ob- served planetary circulations, are fundamental to our understanding of the Earth’s climate and other planetary atmospheres, yet they remain poorly understood due to the vast range of dynamical scales involved.

Scientific Context

Meteorologists and Oceanographers have long noticed recurring weather patterns and meandering eddies (cyclones and anti-cyclones) occurring within a more ponderous, slowly-changing, global-scale background flow. Broad aspects of this ‘general circulation’ are now well understood. Its form depends critically on the planetary rotation rate, the vertical density structure of the fluid (the ‘stratification’), and radiative forcing from the sun. The latter depends on the chemical composition of the fluid, and can lead to cooling as well as heating.
Simplified, single-layer models of the characteristic large-scale flow patterns which naturally arise were pioneered by Rhines in the 1970s [9]. He demonstrated that quasi-zonal jets (typically flowing eastwards) spon- taneously arise in a randomly-stirred turbulent flow when, crucially, there is a large-scale gradient in the mean background ‘planetary vorticity’. He
proposed a characteristic length scale, proportional to the spacing between the jets, now called the ‘Rhines scale’. Since this time, numerous works have sought to verify and extend this theory to less idealised flows, and to apply the theory to observations. The physical mechanism involved was first theorised by McIntyre (1982) [6], and further elucidated in the reviews by Dritschel & McIntyre (2008) [3] and Dunkerton & Scott [4]. These papers show that the gradient in planetary vorticity, when disturbed by turbu- lence, spontaneously forms jets due to inhomogeneous mixing : some regions get well mixed, but between these regions sharp gradients in vorticity develop, and these are coincident with the jets. Scott & Dritschel (2012) [11] showed that this mechanism can lead to vorticity ‘staircases’, the extreme limit of jet formation, when forcing and damping is reduced to realistically small values thought to characterise the giant gas planets. Less idealised single-layer models accounting for variations in the layer thickness show that the structure of the jets depends sensitively on how deformable the layer thickness is. This can be measured by the ratio of the Rhines scale LRh to the Rossby deformation scale LD ; figure 3 demonstrates that jets become increasingly wavy and vortices be- come increasingly more pronounced as LRh/LD increases. Further research is urgently needed to examine more realistic flows, in particular to understand the three-dimensional structure of jets as well as the emergence and persistence of long-lived vortices.

Approach

A major next step in this research would be to investigate nontrivial vertical structure, namely two or more layers. This brings in the competition between barotropic and baroclinic modes, a competition which depends on the precise form of the vertical structure, e.g. the layer depth ratio in a two-layer fluid. We propose a combined numerical/experimental study aimed to delineate the conditions (parameter ranges) leading to the co-existence of jets and vortices in multi-layer and fully three-dimensional rotating stratified flows. The PhD work will be divided equally between the University of St Andrews (School of Mathematics and Statis- tics) under the supervision of Professor David Dritschel, and the Laboratoire des Ecoulements Géophysiques et Industriels in Grenoble under the supervision of Professor Jan-Bert Flór. A systematic study of parameter space has yet to be done in this context, and we believe much can be learned about the fundamental nature of atmospheric and oceanic flows. This is an ambitious project, and one which has only recently become possible. A timely opportunity has arisen from the development of arguably the most advanced, accurate numerical simulation approach for this purpose (CLAM, see Dritschel and Fontane, 2010 [2]). Moreover, the
approach has been refined and tailored to purpose during the internship of Mr Jougla, who has worked closely with Professor Dritschel in this effort. As a result, further extensions have been made considerably more straightforward, giving a head start to the PhD project. The approach comes with a suite of sophisticated diagnostic and graphics tools, enabling in-depth analysis of the results. The numerical results will be compared with state-of-the-art experiments conducted in Grenoble under the supervision of Professor Flo r. Different previous investigations have ́ demonstrated the feasibility of reproducing jets in laboratory experiments subject to small-scale thermal forcing, and mimicking the variation in planetary vorticity with topography (see Bastin & Read, 1997 [1] ; Read et al 2004, 2007 [7, 8] ; Slavin & Afanasyev 2012 [12]). A current problem is that the small-scale turbulence forcing dissipates its energy before reaching the Rhines scale, leaving only weakly laminar jets or no jet formation at all. This has motivated conducting much-larger experiments at the 13m diameter Coriolis platform (Read et al 2004, 2007 [7, 8]) ; these experiments successfully produced jets with a Reynolds number (based on velocity and thickness) of order 1000. However, no quantification of the jets as a function of the dominant parameters was carried out. In the present project, Mr Jougla will conduct experiments in a 1.4m diameter rotating tank, using salt as stratifying agent to create a two-layer fluid. Small sources and sinks at the bottom generate the small-scale turbulence necessary for instability and, ultimately, jet formation (see e.g. [13]). In addition, a large-scale vertical shear will be tested using a rotating lid on the surface (see Flór et al 2011 [5]). Since the shear flow is driven mechanically, a Reynolds number of order 5x104 can be expected (the Reynolds number based on the jet width is likely to be of order 104). To observe the variation in jet properties, a parameter regime as a function of Burger and Rossby numbers will be comprehensively investigated. Advanced experimental techniques will allow one to obtain detailed three-dimensional information about the density and velocity evolution in space and therefore quantification of the results. This will in turn enable benchmarking of the numerical code, and provide a basis for further investigation (in particular of ageostrophic effects) using numerical simulations.

References

[1] M. E. Bastin and P. L. Read. A laboratory study of baroclinic waves and turbulence in an internally heated rotating fluid annulus with sloping endwalls. J. Fluid Mech., 339:173–198, 1997.
[2] D. G. Dritschel and J. Fontane. The combined Lagrangian advection method. J. Comp. Phys., 229:5408– 5417, 2010.
[3] D. G. Dritschel and M. E. McIntyre. Multiple jets as PV staircases : the Phillips effect and the resilience of eddy-transport barriers. J. Atmos. Sci, 65:855–874, 2008. [4]T.J.Dunkerton and R.K. Scott.A barotropic model of the angular momentum conserving potential vorticity staircase in spherical geometry. J. Atmos. Sci., 65:1105–1136, 2008.
[5] J.-B. Flór, H. Scolan, and J. Gula. Frontal instabilities and waves in a differentially rotating fluid. J. Fluid Mech., 685:532–542, 2011.
[6] M. E. McIntyre. How well do we understand the dynamics of stratospheric warmings ? J. Meteorol. Soc. Japan, 60:37–65, 1982. Special issue in commemoration of the centennial of the Meteorological Society of Japan, ed. K. Ninomiya.
[7] P. L. Read, Y. H. Yamazaki, S. R. Lewis, P. D. Williams, K. Miki-Yamazaki, J. Sommeria, H. Didelle, and A. Fincham. Jupiter’s and Saturn’s convectively driven banded jets in the laboratory. Geophys. Res. Lett., 31:L22701, 2004.
[8] P. L. Read, Y. H. Yamazaki, S. R. Lewis, P. D. Williams, R. Wordsworth, K. Miki-Yamazaki, J. Sommeria, and H. Didelle. Dynamics of convectively driven banded jets in the laboratory. J. Atmos. Sci., 64:4031– 4052, 2007.
[9] P. B. Rhines. Waves and turbulence on a beta-plane. J. Fluid Mech., 69:417–443, 1975.
[10] H.Scolan,J.-B.Flo r,andR.Verzicco.Frontalinstabilitiesatadensity-shearinterfaceinrotatingtwo-layer stratified ́ fluid, chapter 11, pages 213–230. Wiley, 2015.
[11] R. K. Scott and D. G. Dritschel. The structure of zonal jets in geostrophic turbulence. J. Fluid Mech., 711:576–598, 2012.
[12] A. G. Slavin and Y.D. Afanasyev. Multiple zonal jets on the polar beta plane. Phys. Fluids, 24:016603,2012.
[13] J. Sommeria, S. D. Meyers & H.L. Swinney. Laboratory model of a planetary eastward jet. Nature 337, 58 – 61 1989