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Zonal jets at the laboratory scale: hysteresis and Rossby waves resonance. (English) Zbl 07298967
Summary: The dynamics, structure and stability of zonal jets in planetary flows are still poorly understood, especially in terms of coupling with the small-scale turbulent flow. Here, we use an experimental approach to address the questions of zonal jets formation and long-term evolution. A strong and uniform topographic \(\beta\)-effect is obtained inside a water-filled rotating tank thanks to the paraboloidal fluid free upper surface combined with a specifically designed bottom plate. A small-scale turbulent forcing is performed by circulating water through the base of the tank. Time-resolving particle image velocimetry measurements reveal the self-organization of the flow into multiple zonal jets with a strong instantaneous signature. We identify a subcritical bifurcation between two regimes of jets depending on the forcing intensity. In the first regime, the jets are steady, weak in amplitude, and directly forced by the local Reynolds stresses due to our forcing. In the second one, we observe highly energetic and dynamic jets of width larger than the forcing scale. An analytical modelling based on the quasi-geostrophic approximation reveals that this subcritical bifurcation results from the resonance between the directly forced Rossby waves and the background zonal flow.
MSC:
76 Fluid mechanics
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[1] Afanasyev, Y.D. & Ivanov, L.M.\(2019 \beta \)-plume mechanism of zonal jet creation by a spatially localized forcing. In Zonal Jets: Phenomenology, Genesis, and Physics (ed. B. Galperin & P.L. Read), pp. 266-283. Cambridge University Press.
[2] Afanasyev, Y.D., O’leary, S., Rhines, P.B. & Lindahl, E.2012On the origin of jets in the ocean. Geophys. Astrophys. Fluid Dyn.106 (2), 113-137.
[3] Afanasyev, Y.D. & Wells, J.2005Quasi-two-dimensional turbulence on the polar beta-plane: laboratory experiments. Geophys. Astrophys. Fluid Dyn.99 (1), 1-17. · Zbl 1206.86003
[4] Arnold, N.P., Tziperman, E. & Farrell, B.2011Abrupt transition to strong superrotation driven by equatorial wave resonance in an idealized GCM. J. Atmos. Sci.69 (2), 626-640.
[5] Aubert, J., Jung, S. & Swinney, H.L.2002Observations of zonal flow created by potential vorticity mixing in a rotating fluid. Geophys. Res. Lett.29 (18), 23-1-23-4.
[6] Bakas, N.A. & Ioannou, P.J.2013Emergence of large scale structure in barotropic \(\beta \)-plane turbulence. Phys. Rev. Lett.110 (22), 224501.
[7] Barbosa Aguiar, A.C., Read, P.L., Wordsworth, R.D., Salter, T. & Hiro Yamazaki, Y.2010A laboratory model of Saturn’s North Polar Hexagon. Icarus206 (2), 755-763.
[8] Bastin, M.E. & Read, P.L.1997A laboratory study of baroclinic waves and turbulence in an internally heated rotating fluid annulus with sloping endwalls. J. Fluid Mech.339, 173-198.
[9] Bastin, M.E. & Read, P.L.1998Experiments on the structure of baroclinic waves and zonal jets in an internally heated, rotating, cylinder of fluid. Phys. Fluids10 (2), 374-389.
[10] Bellani, G. & Variano, E.A.2013Homogeneity and isotropy in a laboratory turbulent flow. Exp. Fluids55 (1), 1646.
[11] Benzi, R., Malguzzi, P., Speranza, A. & Sutera, A.1986The statistical properties of general atmospheric circulation: observational evidence and a minimal theory of bimodality. Q. J. R. Meteorol. Soc.112 (473), 661-674.
[12] Berloff, P., Kamenkovich, I. & Pedlosky, J.2009A mechanism of formation of multiple zonal jets in the oceans. J. Fluid Mech.628, 395-425. · Zbl 1181.76071
[13] Bouchet, F., Nardine, C. & Tangarife, T.2019a Kinetic theory and quasi-linear theories of jet dynamics. In Zonal Jets: Phenomenology, Genesis, and Physics (ed. B. Galperin & P.L. Read), pp. 368-379. Cambridge University Press.
[14] Bouchet, F., Rolland, J. & Simonnet, E.2019bRare event algorithm links transitions in turbulent flows with activated nucleations. Phys. Rev. Lett.122 (7), 074502.
[15] Bouchet, F. & Venaille, A.2012Statistical mechanics of two-dimensional and geophysical flows. Phys. Rep.515 (5), 227-295.
[16] Bouchet, F. & Venaille, A.2019 Zonal flows as statistical equilibria. In Zonal Jets, 1st edn. (ed. B. Galperin & P.L. Read), pp. 347-359. Cambridge University Press.
[17] Burin, M.J., Caspary, K.J., Edlund, E.M., Ezeta, R., Gilson, E.P., Ji, H., Mcnulty, M., Squire, J. & Tynan, G.R.2019Turbulence and jet-driven zonal flows: secondary circulation in rotating fluids due to asymmetric forcing. Phys. Rev. E99 (2), 023108.
[18] Cabanes, S., Aurnou, J., Favier, B. & Le Bars, M.2017A laboratory model for deep-seated jets on the gas giants. Nat. Phys.13 (4), 387-390.
[19] Cabanes, S., Favier, B. & Le Bars, M.2018Some statistical properties of three-dimensional zonostrophic turbulence. Geophys. Astrophys. Fluid Dyn.112 (3), 207-221.
[20] Chan, J.C.L. & Williams, R.T.1987Analytical and numerical studies of the beta-effect in tropical cyclone motion. Part I: Zero mean flow. J. Atmos. Sci.44 (9), 1257-1265.
[21] Charney, J.G. & Devore, J.G.1979Multiple flow equilibria in the atmosphere and blocking. J. Atmos. Sci.36 (7), 1205-1216.
[22] Charney, J.G., Shukla, J. & Mo, K.C.1981Comparison of a barotropic blocking theory with observation. J. Atmos. Sci.38 (4), 762-779.
[23] Chemke, R. & Kaspi, Y.2016The effect of eddy-eddy interactions on jet formation and macroturbulent scales. J. Atmos. Sci.73 (5), 2049-2059.
[24] Condie, S.A. & Rhines, P.B.1994A convective model for the zonal jets in the atmospheres of Jupiter and Saturn. Nature367 (6465), 711-713.
[25] Connaughton, C.P., Nadiga, B.T., Nazarenko, S.V. & Quinn, B.E.2010Modulational instability of Rossby and drift waves and generation of zonal jets. J. Fluid Mech.654, 207-231. · Zbl 1193.76059
[26] Cornillon, P.C., Firing, E., Thompson, A.F., Ivanov, L.M., Kamenkovich, I., Buckingham, C.E. & Afanasyev, Y.D.2019 Oceans. In Zonal Jets: Phenomenology, Genesis, and Physics (ed. B. Galperin & P.L. Read), pp. 46-71. Cambridge University Press.
[27] Coumou, D., Petoukhov, V., Rahmstorf, S., Petri, S. & Schellnhuber, H.J.2014Quasi-resonant circulation regimes and hemispheric synchronization of extreme weather in boreal summer. Proc. Natl Acad. Sci. USA111 (34), 12331-12336.
[28] Cravatte, S., Kessler, W.S. & Marin, F.2012Intermediate zonal jets in the tropical pacific ocean observed by argo floats. J. Phys. Oceanogr.42 (9), 1475-1485.
[29] Davey, M.K. & Killworth, P.D.1989Flows produced by discrete sources of buoyancy. J. Phys. Oceanogr.19 (9), 1279-1290.
[30] De Verdiere, A.C.1979Mean flow generation by topographic Rossby waves. J. Fluid Mech.94 (1), 39-64.
[31] Di Nitto, G., Espa, S. & Cenedese, A.2013Simulating zonation in geophysical flows by laboratory experiments. Phys. Fluids25 (8), 086602.
[32] Dritschel, D.G. & Mcintyre, M.E.2008Multiple jets as PV staircases: the Phillips effect and the resilience of eddy-transport barriers. J. Atmos. Sci.65 (3), 855-874.
[33] Espa, S., Bordi, I., Frisius, T., Fraedrich, K., Cenedese, A. & Sutera, A.2012Zonal jets and cyclone-anticyclone asymmetry in decaying rotating turbulence: laboratory experiments and numerical simulations. Geophys. Astrophys. Fluid Dyn.106 (6), 557-573.
[34] Firing, E. & Beardsley, R.C.1976The behavior of a barotropic eddy on a \(\beta \)-plane. J. Phys. Oceanogr.6 (1), 57-65.
[35] Flierl, G.R.1977The application of linear quasigeostrophic dynamics to Gulf stream rings. J. Phys. Oceanogr.7 (3), 365-379.
[36] Früh, W.-G. & Read, P.L.1999Experiments on a barotropic rotating shear layer. Part 1. Instability and steady vortices. J. Fluid Mech.383, 143-173. · Zbl 0941.76531
[37] Galperin, B., Hoemann, J., Espa, S. & Di Nitto, G.2014aAnisotropic turbulence and Rossby waves in an easterly jet: an experimental study. Geophys. Res. Lett.41 (17), 6237-6243.
[38] Galperin, B. & Read, P.L.2019Zonal Jets: Phenomenology, Genesis, and Physics. Cambridge University Press.
[39] Galperin, B., Sukoriansky, S. & Dikovskaya, N.2010Geophysical flows with anisotropic turbulence and dispersive waves: flows with a \(\beta \)-effect. Ocean Dyn.60 (2), 427-441.
[40] Galperin, B., Sukoriansky, S., Dikovskaya, N., Read, P.L., Yamazaki, Y.H. & Wordsworth, R.2006Anisotropic turbulence and zonal jets in rotating flows with a \(\beta \)-effect. Nonlinear Process. Geophys.13 (1), 83-98.
[41] Galperin, B., Sukoriansky, S., Young, R.M.B., Chemke, R., Kaspi, Y., Read, P.L. & Dikovskaya, N.2019 Barotropic and zonostrophic turbulence. In Zonal Jets: Phenomenology, Genesis, and Physics (ed. B. Galperin & P.L. Read), pp. 220-237. Cambridge University Press.
[42] Galperin, B., Young, R.M.B., Sukoriansky, S., Dikovskaya, N., Read, P.L., Lancaster, A.J. & Armstrong, D.2014bCassini observations reveal a regime of zonostrophic macroturbulence on Jupiter. Icarus229, 295-320.
[43] Gill, A.E.1974The stability of planetary waves on an infinite beta-plane. Geophys. Fluid Dyn.6 (1), 29-47.
[44] Gillet, N., Brito, D., Jault, D. & Nataf, H.C.2007Experimental and numerical studies of convection in a rapidly rotating spherical shell. J. Fluid Mech.580, 83-121. · Zbl 1113.76002
[45] Guervilly, C. & Cardin, P.2016Subcritical convection of liquid metals in a rotating sphere using a quasi-geostrophic model. J. Fluid Mech.808, 61-89. · Zbl 1383.76546
[46] Guervilly, C. & Cardin, P.2017Multiple zonal jets and convective heat transport barriers in a quasi-geostrophic model of planetary cores. Geophys. J. Intl211 (1), 455-471.
[47] Held, I.M.1983 Stationary and quasi-stationary eddies in the extratropical troposphere: theory. In Large-Scale Dynamical Processes in the Atmosphere (ed. B. Hoskins & R. Pearce), pp. 127-168. Academic Press.
[48] Herbert, C., Caballero, R. & Bouchet, F.2020Atmospheric bistability and abrupt transitions to superrotation: wave-jet resonance and hadley cell feedbacks. J. Atmos. Sci.77 (1), 31-49.
[49] Hide, R.1968On source-sink flows in a rotating fluid. J. Fluid Mech.32 (4), 737-764. · Zbl 0157.57403
[50] Hide, R. & Mason, P.J.1975Sloping convection in a rotating fluid. Adv. Phys.24 (1), 47-100.
[51] Hide, R. & Titman, C.W.1967Detached shear layers in a rotating fluid. J. Fluid Mech.29 (1), 39-60.
[52] Ingersoll, A.P., Dowling, T.E., Gierasch, P.J., Orton, G.S., Read, P.L., Sánchez-Lavega, A., Showman, A.P., Simon-Miller, A.A. & Vasavada, A.R.2007Dynamics of Jupiter’s atmosphere. In Jupiter: The Planet, Satellites and Magnetosphere (ed. F. Bagenal, T.E. Dowling & W.B. McKinnon), vol. 1, pp. 105-128. Cambridge University Press.
[53] Ivanov, L.M., Collins, C.A. & Margolina, T.M.2009System of quasi-zonal jets off California revealed from satellite altimetry. Geophys. Res. Lett.36 (3), L03609.
[54] Kaplan, E.J., Schaeffer, N., Vidal, J. & Cardin, P.2017Subcritical thermal convection of liquid metals in a rapidly rotating sphere. Phys. Rev. Lett.119 (9), 094501.
[55] Kaspi, Y., et al.. 2018Jupiter’s atmospheric jet streams extend thousands of kilometres deep. Nature555 (7695), 223-226.
[56] Kaspi, Y., Galanti, E., Showman, A.P., Stevenson, D.J., Guillot, T., Iess, L. & Bolton, S.J.2020 Comparison of the deep atmospheric dynamics of Jupiter and Saturn in light of the Juno and Cassini gravity measurements. Space Sci. Rev.216 (5), 84.
[57] Lorenz, E.N.1972Barotropic instability of rossby wave motion. J. Atmos. Sci.29 (2), 258-265.
[58] Malguzzi, P., Speranza, A., Sutera, A. & Caballero, R.1996Nonlinear amplification of stationary rossby waves near resonance. Part I. J. Atmos. Sci.53 (2), 298-311.
[59] Malguzzi, P., Speranza, A., Sutera, A. & Caballero, R.1997Nonlinear amplification of stationary Rossby waves near resonance. Part II. J. Atmos. Sci.54 (20), 2441-2451.
[60] Manfroi, A.J. & Young, W.R.1999Slow evolution of zonal jets on the beta plane. J. Atmos. Sci.56 (5), 784-800.
[61] Matulka, A.M. & Afanasyev, Y.D.2015Zonal jets in equilibrating baroclinic instability on the polar beta-plane: experiments with altimetry. J. Geophys. Res.: Oceans120 (9), 6130-6144.
[62] Maximenko, N.A., Bang, B. & Sasaki, H.2005Observational evidence of alternating zonal jets in the world ocean. Geophys. Res. Lett.32 (12), L12607.
[63] Maximenko, N.A., Melnichenko, O.V., Niiler, P.P. & Sasaki, H.2008Stationary mesoscale jet-like features in the ocean. Geophys. Res. Lett.35 (8), L08603.
[64] Mcewan, A.D., Thompson, R.O.R.Y. & Plumb, R.A.1980Mean flows driven by weak eddies in rotating systems. J. Fluid Mech.99 (3), 655-672. · Zbl 0433.76024
[65] Meunier, P. & Leweke, T.2003Analysis and treatment of errors due to high velocity gradients in particle image velocimetry. Exp. Fluids35 (5), 408-421.
[66] Nezlin, M.V. & Snezhkin, E.N.1993 Experimental configurations. In Rossby Vortices, Spiral Structures, Solitons: Astrophysics and Plasma Physics in Shallow Water Experiments (ed. M.V. Nezlin & E.N. Snezhkin), pp. 67-79. Springer.
[67] Niino, H. & Misawa, N.1984An experimental and theoretical study of barotropic instability. J. Atmos. Sci.41 (12), 1992-2011.
[68] Pedlosky, J.1981Resonant topographic waves in barotropic and baroclinic flows. J. Atmos. Sci.38 (12), 2626-2641.
[69] Petoukhov, V., Rahmstorf, S., Petri, S. & Schellnhuber, H.J.2013Quasiresonant amplification of planetary waves and recent Northern Hemisphere weather extremes. Proc. Natl Acad. Sci. USA110 (14), 5336.
[70] Porco, C.C., et al.. 2003Cassini imaging of Jupiter’s atmosphere, satellites, and rings. Science299 (5612), 1541-1547.
[71] Read, P.L., Yamazaki, Y.H., Lewis, S.R., Williams, P.D., Miki-Yamazaki, K., Sommeria, J., Didelle, H. & Fincham, A.2004Jupiter’s and Saturn’s convectively driven banded jets in the laboratory. Geophys. Res. Lett.31 (22), L22701.
[72] Read, P.L.2019 Zonal jet flows in the laboratory: an introduction. In Zonal Jets: Phenomenology, Genesis, and Physics (ed. B. Galperin & P.L. Read), pp. 119-134. Cambridge University Press.
[73] Read, P.L., Jacoby, T.N.L., Rogberg, P.H.T., Wordsworth, R.D., Yamazaki, Y.H., Miki- Yamazaki, K., Young, R.M.B., Sommeria, J., Didelle, H. & Viboud, S.2015An experimental study of multiple zonal jet formation in rotating, thermally driven convective flows on a topographic beta-plane. Phys. Fluids27 (8), 085111.
[74] Read, P.L., Yamazaki, Y.H., Lewis, S.R., Williams, P.D., Wordsworth, R., Miki-Yamazaki, K., Sommeria, J. & Didelle, H.2007Dynamics of convectively driven banded jets in the laboratory. J. Atmos. Sci.64 (11), 4031-4052.
[75] Rhines, P.B.1975Waves and turbulence on a beta-plane. J. Fluid Mech.69 (03), 417.
[76] Rogers, J.H.1995The Giant Planet Jupiter, vol. 6. Cambridge University Press.
[77] Sánchez-Lavega, A., et al.. 2019 Gas giants. In Zonal Jets: Phenomenology, Genesis, and Physics (ed. B. Galperin & P.L. Read), pp. 72-103. Cambridge University Press.
[78] Sansón, L.Z. & Van Heijst, G.J.F.2000Nonlinear Ekman effects in rotating barotropic flows. J. Fluid Mech.412, 75-91. · Zbl 0961.76088
[79] Schneider, T.2006The general circulation of the atmosphere. Annu. Rev. Earth Planet. Sci.34, 655-688.
[80] Scott, R.K.2010 The structure of zonal jets in shallow water turbulence on the sphere. In IUTAM Symposium on Turbulence in the Atmosphere and Oceans (ed. D. Dritschel), vol. 28, pp. 243-252. Springer.
[81] Scott, R.K. & Dritschel, D.G.2012The structure of zonal jets in geostrophic turbulence. J. Fluid Mech.711, 576-598. · Zbl 1275.76132
[82] Scott, R.K. & Dritschel, D.G.2019 Zonal jet formation by potential vorticity mixing at large and small scales. In Zonal Jets: Phenomenology, Genesis, and Physics (ed. B. Galperin & P.L. Read), pp. 238-246. Cambridge University Press.
[83] Semin, B., Garroum, N., Pétrélis, F. & Fauve, S.2018Nonlinear saturation of the large scale flow in a laboratory model of the quasibiennial oscillation. Phys. Rev. Lett.121 (13), 134502.
[84] Slavin, A.G. & Afanasyev, Y.D.2012Multiple zonal jets on the polar beta plane. Phys. Fluids24 (1), 016603.
[85] Smith, C.A., Speer, K.G. & Griffiths, R.W.2014Multiple zonal jets in a differentially heated rotating \(annulus^{*,+}\). J. Phys. Oceanogr.44 (9), 2273-2291.
[86] Solomon, T.H., Holloway, W.J. & Swinney, H.L.1993Shear flow instabilities and Rossby waves in barotropic flow in a rotating annulus. Phys. Fluids A5 (8), 1971-1982.
[87] Sommeria, J., Meyers, S.D. & Swinney, H.L.1989Laboratory model of a planetary eastward jet. Nature337 (6202), 58-61.
[88] Stommel, H.1982Is the South Pacific helium-3 plume dynamically active?Earth Planet. Sci. Lett.61 (1), 63-67.
[89] Sukoriansky, S., Dikovskaya, N. & Galperin, B.2007On the arrest of inverse energy cascade and the rhines scale. J. Atmos. Sci.64 (9), 3312-3327.
[90] Sukoriansky, S., Dikovskaya, N. & Galperin, B.2008Nonlinear waves in zonostrophic turbulence. Phys. Rev. Lett.101 (17), 178501.
[91] Sukoriansky, S., Dikovskaya, N., Grimshaw, R. & Galperin, B.2012Rossby waves and zonons in zonostrophic turbulence. AIP Conf. Proc.1439 (1), 111-122.
[92] Sukoriansky, S., Galperin, B. & Dikovskaya, N.2002Universal spectrum of two-dimensional turbulence on a rotating sphere and some basic features of atmospheric circulation on giant planets. Phys. Rev. Lett.89 (12), 124501.
[93] Thompson, R.O.R.Y.1980A prograde jet driven by Rossby waves. J. Atmos. Sci.37 (6), 1216-1226.
[94] Tian, Y., Weeks, E.R., Ide, K., Urbach, J.S., Baroud, C.N., Ghil, M. & Swinney, H.L.2001Experimental and numerical studies of an eastward jet over topography. J. Fluid Mech.438, 129-157. · Zbl 1062.76505
[95] Tollefson, J., et al.. 2017Changes in Jupiter’s zonal wind profile preceding and during the Juno mission. Icarus296, 163-178.
[96] Vallis, G.K.2006Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. Cambridge University Press. · Zbl 1374.86002
[97] Vasavada, A.R. & Showman, A.P.2005Jovian atmospheric dynamics: an update after Galileo and Cassini. Rep. Prog. Phys.68 (8), 1935-1996.
[98] Weeks, E.R., Tian, Y., Urbach, J.S., Ide, K., Swinney, H.L. & Ghil, M.1997Transitions between blocked and zonal flows in a rotating annulus with topography. Science278 (5343), 1598-1601.
[99] Whitehead, J.A.1975Mean flow generated by circulation on a \(\beta \)-plane: an analogy with the moving flame experiment. Tellus27 (4), 358-364.
[100] Wordsworth, R.D., Read, P.L. & Yamazaki, Y.H.2008Turbulence, waves, and jets in a differentially heated rotating annulus experiment. Phys. Fluids20 (12), 126602. · Zbl 1182.76830
[101] Yarom, E. & Sharon, E.2014Experimental observation of steady inertial wave turbulence in deep rotating flows. Nat. Phys.10 (7), 510-514.
[102] Young, R.M.B. & Read, P.L.2017Forward and inverse kinetic energy cascades in Jupiter’s turbulent weather layer. Nat. Phys.13 (11), 1135-1140.
[103] Youssef, A. & Marcus, P.S.2003The dynamics of jovian white ovals from formation to merger. Icarus162 (1), 74-93.
[104] Zhang, Y. & Afanasyev, Y.D.2014Beta-plane turbulence: experiments with altimetry. Phys. Fluids26 (2), 026602.
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