Geophysical fluid flows that are stably-stratified in density, like most of the ocean, can be strongly turbulent at small scales as a result of shear instabilities. The resulting mixing controls the vertical transport of heat and tracers that are key to large-scale layering and circulation patterns, including those crucial to Earth’s climate. However, the physics of sheared stratified turbulence remain poorly understood due to their extraordinary range of scales and spatio-temporal intermittency. This paper reviews a laboratory model, the stratified inclined duct (SID), which encapsulates these fundamental physics and complexity while permitting precise control and measurements, a sweet spot to stimulate fruitful research. We explain how this exchange flow down a modest slope sustains high levels of energy dissipation and mixing while remaining strongly-stratified, thereby accessing the relevant geophysical parameter regime. Emphasising the role of detailed measurements, we highlight key discoveries and unsolved questions around the transition to turbulence, intermittent dynamics and parameterisations of mixing. Dimensional design guidelines show how the optical measurements of the full three-dimensional flow field could be perfected to extrapolate laboratory results to the tantalisingly close regime of the most intense geophysical stratified turbulence.
Les écoulements géophysiques de fluides qui sont stablement stratifiés en densité, comme la plupart de l’océan, peuvent être fortement turbulents à petite échelle en raison d’instabilités de cisaillement. Le mélange qui en résulte contrôle le transport vertical de la chaleur et des traceurs qui sont essentiels pour la stratification et la circulation à grande échelle, et donc pour notre climat. Cependant, la physique de la turbulence stratifiée cisaillée reste mal comprise en raison de sa gamme d’échelles extraordinaire et de son intermittence spatio-temporelle. Cet article passe en revue un modèle de laboratoire, le conduit incliné stratifié (SID), qui capture les fondamentaux de cette physique et sa complexité tout en permettant un contrôle et des mesures précis, une combinaison optimale pour stimuler des recherches fructueuses. Nous expliquons comment cet écoulement d’échange le long d’une pente modeste maintient une dissipation turbulente et un mélange élevés tout en restant fortement stratifié, accédant ainsi au régime géophysique pertinent. En mettant l’accent sur le rôle de mesures détaillées, nous soulignons les découvertes clés et les nombreuses questions non résolues autour de la transition vers la turbulence, des dynamiques intermittentes et des paramétrisations du mélange. Le dimensionnement expérimental montre comment perfectionner les mesures optiques tridimensionnel de l’écoulement pour extrapoler ces résultats au régime le plus intense de la turbulence stratifiée géophysique, qui est enfin à portée de main.
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Mot clés : turbulence, mélange, géophysique, cisaillement, instabilité, intermittence, océan, paramétrage
Adrien Lefauve 1
@article{CRPHYS_2024__25_S3_A4_0, author = {Adrien Lefauve}, title = {Geophysical stratified turbulence and mixing in the laboratory}, journal = {Comptes Rendus. Physique}, publisher = {Acad\'emie des sciences, Paris}, year = {2024}, doi = {10.5802/crphys.196}, language = {en}, note = {Online first}, }
Adrien Lefauve. Geophysical stratified turbulence and mixing in the laboratory. Comptes Rendus. Physique, Online first (2024), pp. 1-29. doi : 10.5802/crphys.196.
[1] How do Internal Waves Create Turbulence and Mixing in the Ocean? (2022) (Preprint, ESS Open Archive) | DOI
[2] The role of ocean mixing in the climate system, Ocean Mixing. Drivers, Mechanisms and Impacts, Elsevier, 2022, pp. 5-34 | DOI
[3] Open questions in turbulent stratified mixing: Do we even know what we do not know?, Phys. Rev. Fluids, Volume 5 (2020), 110518 | DOI
[4] Mixing efficiency in the ocean, Ann. Rev. Mar. Sci., Volume 10 (2018), pp. 443-473 | DOI
[5] Confronting Grand Challenges in environmental fluid mechanics, Phys. Rev. Fluids, Volume 6 (2021) no. 2, 020501 | DOI
[6] Internal Gravity Waves, Cambridge University Press, 2010 | DOI
[7] Layering, instabilities, and mixing in turbulent stratified flows, Ann. Rev. Fluid Mech., Volume 53 (2021), pp. 113-145 | DOI
[8] Length scales of turbulence in stably stratified mixing layers, Phys. Fluids, Volume 12 (2000) no. 6, pp. 1327-1342 | DOI
[9] Sensitivity of stratified turbulence to the buoyancy Reynolds number, J. Fluid Mech., Volume 725 (2013), pp. 1-22 | DOI
[10] Kinetic energy dynamics in forced, homogeneous, and axisymmetric stably stratified turbulence, J. Turbul., Volume 13 (2012), N29 | DOI
[11] Mixing across stable density interfaces in forced stratified turbulence, J. Fluid Mech., Volume 961 (2023), A20 | Zbl
[12] Transition to Turbulence in Pipe Flow, Ann. Rev. Fluid Mech., Volume 55 (2023), pp. 575-602 | DOI
[13] Ultimate turbulent thermal convection, Phys. Today, Volume 76 (2023) no. 11, pp. 26-32 | DOI
[14] Routes to turbulence in Taylor–Couette flow, Philos. Trans. R. Soc. Lond., Ser. A, Volume 381 (2023) no. 2246, 20220114 | DOI
[15] Causality in Rayleigh–Bénard and Taylor-–Couette turbulence, Caust Workshop on Causality in Turbulence and Transition (2022)
[16] Stratified shear flow: experiments in an inclined duct, J. Fluid Mech., Volume 753 (2014), pp. 242-253 | DOI
[17] An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels, Philos. Trans. R. Soc. Lond., Volume 174 (1883), pp. 935-982 | DOI
[18] Experiments on the instability of stratified shear flows: miscible fluids, J. Fluid Mech., Volume 46 (1971) no. 02, pp. 299-319 | DOI
[19] Interfacial mixing in stratified flow, J. Eng. Mech., Volume 87 (1961) no. 5, pp. 55-81 | DOI
[20] Buoyancy effects in fluids, Cambridge University Press, 1973 | DOI
[21] An Experiment on the Stability of Superposed Streams of Fluid, Math. Proc. Camb. Philos. Soc., Volume 23 (1927) no. 6, pp. 730-731 | DOI
[22] Entrainment and mixing in stratified shear flows, J. Fluid Mech., Volume 428 (2001), pp. 349-386 | DOI
[23] Entrainment and mixing in a laboratory model of oceanic overflow, J. Fluid Mech., Volume 746 (2014), pp. 498-535 | DOI
[24] The structure and origin of confined Holmboe waves, J. Fluid Mech., Volume 848 (2018), pp. 508-544 | DOI
[25] Buoyancy-driven exchange flows in inclined ducts, J. Fluid Mech., Volume 893 (2020), A2 | DOI
[26] Data-driven classification of sheared stratified turbulence from experimental shadowgraphs, Phys. Rev. Fluids, Volume 9 (2024), 034603 | DOI
[27] Experimental properties of continuously forced, shear-driven, stratified turbulence. Part 1. Mean flows, self-organisation, turbulent fractions, J. Fluid Mech., Volume 937 (2022), A34 | DOI
[28] Bulk scaling in wall-bounded and homogeneous vertical natural convection, J. Fluid Mech., Volume 841 (2018), pp. 825-850 | DOI
[29] Experiments on gravity currents propagating down slopes. Part 2. The evolution of a fixed volume of fluid released from closed locks into a long, open channel, J. Fluid Mech., Volume 647 (2010), pp. 27-51 | DOI
[30] Laminar-turbulent cycles in inclined lock-exchange flows, Phys. Rev. E, Volume 85 (2012) no. 6, 066308 | DOI
[31] Waves and turbulence in sustained stratified shear flows, Ph. D. Thesis, University of Cambridge, Cambridge, United Kingdom (2018) | DOI
[32] Shadowgraph visualisations of salt-stratified turbulence obtained in a stratified inclined duct (SID) laboratory experiment, dataset, Apollo - University of Cambridge Repository (December 14, 2023). https://doi.org/10.17863/CAM.104471, 2023 | DOI
[33] Research data supporting “Buoyancy-driven exchange flows in inclined ducts”, dataset, Apollo - University of Cambridge Repository (April 17, 2020). https://doi.org/10.17863/CAM.48821, 2020 | DOI
[34] Buoyancy driven counterflow and interfacial mixing, Ph. D. Thesis, University of Cambridge, Cambridge, United Kingdom (1991)
[35] Mixing efficiency in run-down gravity currents, J. Fluid Mech., Volume 809 (2016), pp. 691-704 | DOI
[36] Theoretical considerations on the motion of salt and fresh water, Proceedings Minnesota International Hydraulic Convention, IAHR (1953), pp. 321-333
[37] The hydraulics of two flowing layers with different densities, J. Fluid Mech., Volume 163 (1986), pp. 27-58 | DOI
[38] Hydraulics of exchange flows, J. Hydraul. Eng., Volume 126 (2000) no. 12, pp. 921-928 | DOI
[39] Analytical solution for maximal frictional two-layer exchange flow, J. Fluid Mech., Volume 543 (2005), pp. 1-17 | DOI
[40] Stratified inclined duct: direct numerical simulations, J. Fluid Mech., Volume 969 (2023), A20 | DOI
[41] et al. Stratified inclined duct: two-layers hydraulics and instabilities, J. Fluid Mech., Volume 977 (2023), A25 | DOI | Zbl
[42] A versatile scanning method for volumetric measurements of velocity and density fields, Meas. Sci. Tech., Volume 30 (2019), 055203 | DOI
[43] Research data supporting “Experimental properties of continuously-forced, shear-driven, stratified turbulence”, dataset, Apollo - University of Cambridge Repository (February 7, 2022). https://doi.org/10.17863/CAM.75370, 2022 | DOI
[44] Simultaneous synthetic schlieren and PIV measurements for internal solitary waves, Meas. Sci. Tech., Volume 18 (2007) no. 3, pp. 533-547 | DOI
[45] Research data supporting “Regime transitions and energetics of sustained stratified shear flows”, dataset, Apollo - University of Cambridge Repository (July 22, 2019). https://doi.org/10.17863/CAM.41410, 2019 | DOI
[46] Available potential energy and mixing in density-stratified fluids, J. Fluid Mech., Volume 289 (1995), pp. 115-128 | DOI
[47] Regime transitions and energetics of sustained stratified shear flows, J. Fluid Mech., Volume 875 (2019), pp. 657-698 | DOI
[48] Experimental properties of continuously forced, shear-driven, stratified turbulence. Part 2. Energetics, anisotropy, parameterisation, J. Fluid Mech., Volume 937 (2022), A35 | DOI
[49] Pattern formation outside of equilibrium, Rev. Mod. Phys., Volume 65 (1993) no. 3, pp. 851-1112 | DOI
[50] Theoretical perspective on the route to turbulence in a pipe, J. Fluid Mech., Volume 803 (2016), P1 | DOI
[51] Instability in Geophysical Flows, Cambridge University Press, 2019 | DOI
[52] Instability in stratified shear flow: Review of a physical interpretation based on interacting waves, Appl. Mech. Rev., Volume 64 (2011) no. 6, 060801 | DOI
[53] Weakly nonlinear Holmboe waves, Phys. Rev. Fluids, Volume 6 (2021) no. 2, 024803 | DOI
[54] The effects of spanwise confinement on stratified shear instabilities, Phys. Rev. Fluids, Volume 6 (2021), 103901 | DOI
[55] Turbulent mixing due to the Holmboe wave instability at high Reynolds number, J. Fluid Mech., Volume 803 (2016), pp. 591-621 | DOI
[56] Stratified turbulence and small-scale internal waves above deep-ocean topography, Phys. Fluids, Volume 25 (2013) no. 10, 106604 | DOI
[57] High-Resolution Observations of the North Pacific Transition Layer from a Lagrangian Float, J. Phys. Oceanogr., Volume 51 (2021) no. 10, pp. 3163-3181 | DOI
[58] Indications for the transition of Kelvin-Helmholtz instabilities into propagating internal waves in a high turbid estuary and their effect on the stratification stability, Geo-Mar. Lett., Volume 39 (2019) no. 2, pp. 149-159 | DOI
[59] The ‘zoo’ of secondary instabilities precursory to stratified shear flow transition. Part 1: Shear aligned convection, pairing, and braid instabilities, J. Fluid Mech., Volume 708 (2012), pp. 5-44 | DOI
[60] Long-wave instabilities of sloping stratified exchange flows, J. Fluid Mech., Volume 983 (2024), A12 | DOI
[61] The Significance of Simple Invariant Solutions in Turbulent Flows, Ann. Rev. Fluid Mech., Volume 44 (2012) no. 1, pp. 203-225 | DOI
[62] Exact Coherent States and the Nonlinear Dynamics of Wall-Bounded Turbulent Flows, Ann. Rev. Fluid Mech., Volume 53 (2021), pp. 227-253 | DOI
[63] Recurrent flows: the clockwork behind turbulence, J. Fluid Mech., Volume 726 (2013), pp. 1-4 | DOI
[64] Layer formation in horizontally forced stratified turbulence: connecting exact coherent structures to linear instabilities, J. Fluid Mech., Volume 832 (2017), pp. 409-437 | DOI
[65] The evolution of coherent vortical structures in increasingly turbulent stratified shear layers, J. Fluid Mech., Volume 937 (2022), p. A30 | DOI
[66] Data-driven and operator-based tools for the analysis of turbulent flows, Advanced Approaches in Turbulence, Elsevier, 2021, pp. 243-305 | DOI
[67] An experimental investigation of the instability of a shear flow with multilayered density stratification, Phys. Fluids, Volume 7 (1995) no. 12, pp. 3028-3041 | DOI
[68] Noisy homoclinic pulse dynamics, Chaos, Volume 26 (2016) no. 4, 043104 | DOI
[69] The Estuarine Circulation, Ann. Rev. Fluid Mech., Volume 46 (2014) no. 1, pp. 175-197 | DOI
[70] Processes of Stratification and Destratification During An Extreme River Discharge Event in the German Bight ROFI, J. Geophys. Res. Oceans, Volume 125 (2020) no. 8, e2019JC015987 | DOI
[71] Diurnal shear instability, the descent of the surface shear layer, and the deep cycle of equatorial turbulence, J. Phys. Oceanogr., Volume 43 (2013) no. 11, pp. 2432-2455 | DOI
[72] Pulsating turbulence in a marginally unstable stratified shear flow, J. Fluid Mech., Volume 822 (2017), pp. 327-341 | DOI
[73] Stably Stratified Atmospheric Boundary Layers, Ann. Rev. Fluid Mech., Volume 46 (2014) no. 1, pp. 23-45 | DOI
[74] Self-organized criticality of turbulence in strongly stratified mixing layers, J. Fluid Mech., Volume 856 (2018), pp. 228-256 | DOI
[75] Self-organized criticality, Phys. Rev. A, Volume 38 (1988) no. 1, pp. 364-374 | DOI
[76] Marginal Instability and the Efficiency of Ocean Mixing, J. Phys. Oceanogr., Volume 50 (2020) no. 8, pp. 2141-2150 | DOI
[77] A Marginal Stability Paradigm for Shear-Induced Diapycnal Turbulent Mixing in the Ocean, Geophys. Res. Lett., Volume 49 (2022) no. 2, e2021GL095715 | DOI
[78] A diapycnal diffusivity model for stratified environmental flows, Dyn. Atmos. Oceans, Volume 61-62 (2013), pp. 14-34 | DOI | Zbl
[79] Sensitivity of Deep Ocean Mixing to Local Internal Tide Breaking and Mixing Efficiency, Geophys. Res. Lett., Volume 14 (2019), pp. 14622-14633 | DOI
[80] Stratified Turbulence and Mixing Efficiency in a Salt Wedge Estuary, J. Phys. Oceanogr., Volume 46 (2016) no. 6, pp. 1769-1783 | DOI
[81] Ocean Mixing: Drivers, Mechanisms and Impacts, Elsevier, 2021
[82] Efficiency of turbulent mixing in the abyssal ocean circulation, Geophys. Res. Lett., Volume 44 (2017) no. 12, pp. 6296-6306 | DOI
[83] Prandtl number effects on extreme mixing events in forced stratified turbulence, J. Fluid Mech., Volume 983 (2024), R1 | DOI
[84] Scaling analysis and simulation of strongly stratified turbulent flows, J. Fluid Mech., Volume 585 (2007), pp. 343-368 | DOI
[85] Classical scaling and intermittency in strongly stratified Boussinesq turbulence, J. Fluid Mech., Volume 775 (2015), pp. 436-463 | DOI
[86] Small-scale variation of convected quantities like temperature in turbulent fluid Part 1. General discussion and the case of small conductivity, J. Fluid Mech., Volume 5 (1959) no. 01, pp. 113-133 | DOI
[87] Quantifying vertical mixing in estuaries, Environ. Fluid Mech., Volume 8 (2008) no. 5-6, pp. 495-509 | DOI
[88] Experiments on Differential Scalar Mixing in Turbulence in a Sheared, Stratified Flow, J. Phys. Oceanogr., Volume 44 (2014) no. 10, pp. 2661-2680 | DOI
[89] Asymptotic dynamics of high dynamic range stratified turbulence, Phys. Rev. Lett., Volume 122 (2019), 194504 | DOI
[90] New insights into experimental stratified flows obtained through physics-informed neural networks, J. Fluid Mech., Volume 981 (2024), R1 | DOI
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