logo CRAS
Comptes Rendus. Physique
Fluid dynamics of a mixed convective/stably stratified system—A review of some recent works
Comptes Rendus. Physique, Volume 21 (2020) no. 2, pp. 151-164.

Part of the special issue: Prizes of the French Academy of Sciences 2019

Numerous fluid systems organise into a turbulent layer adjacent to a stably stratified one, for instance, planetary atmospheres and stellar interiors. Capturing the coupled dynamics of such systems and understanding the exchanges of energy and momentum at the interface between the two layers are challenging, because of the large range of involved time- and length-scales: indeed, the rapid small-scale turbulence excites waves at intermediate scale, which propagate and interact non-linearly to generate large-scale circulations, whose most famous example is the quasi-biennial oscillation of the Earth’s atmosphere. We review here some recent progress on the wave characterisation and on the non-linear mean flow generation, based on the combined experimental and numerical study of a model laboratory system. Applications in climate and stellar modelling are also briefly discussed.

De nombreux systèmes fluides s’organisent en une couche turbulente adjacente à une couche stratifiée stable, comme par exemple les atmosphères planétaires et les intérieurs stellaires. La compréhension des échanges d’énergie et de quantité de mouvement à l’interface entre ces deux couches, et l’appréhension de leur dynamique couplée sont difficiles, en raison de la grande gamme d’échelles de temps et de longueur impliquées : en effet, la turbulence rapide à petite échelle excite des ondes à moyenne échelle, qui se propagent et interagissent non linéairement pour générer des circulations à grande échelle, dont le plus célèbre exemple est l’oscillation quasibiennale de l’atmosphère terrestre. Dans cet article, nous passons en revue quelques progrès récents sur la caractérisation des ondes et sur la génération non-linéaire d’un écoulement moyen, obtenus par l’étude combinée, expérimentale et numérique, d’une configuration modèle au laboratoire. Les conséquences possibles de nos résultats pour la modélisation climatique et stellaire sont aussi brièvement discutées.

Published online:
DOI: 10.5802/crphys.17
Classification: 76-XX
Keywords: Internal gravity waves, Convection, Wave—mean flow interactions, Quasi-biennial oscillation (QBO), Atmospheric and stellar dynamics
Michael Le Bars 1; Louis-Alexandre Couston 1; Benjamin Favier 1; Pierre Léard 1; Daniel Lecoanet 2; Patrice Le Gal 1

1 CNRS, Aix Marseille Univ, Centrale Marseille, IRPHE, Marseille, France
2 Princeton Center for Theoretical Science and Department of Astrophysical Sciences, Princeton, New Jersey 08544, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
@article{CRPHYS_2020__21_2_151_0,
     author = {Michael Le Bars and Louis-Alexandre Couston and Benjamin Favier and Pierre L\'eard and Daniel Lecoanet and Patrice Le Gal},
     title = {Fluid dynamics of a mixed convective/stably stratified {system{\textemdash}A} review of some recent works},
     journal = {Comptes Rendus. Physique},
     pages = {151--164},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {21},
     number = {2},
     year = {2020},
     doi = {10.5802/crphys.17},
     language = {en},
}
TY  - JOUR
AU  - Michael Le Bars
AU  - Louis-Alexandre Couston
AU  - Benjamin Favier
AU  - Pierre Léard
AU  - Daniel Lecoanet
AU  - Patrice Le Gal
TI  - Fluid dynamics of a mixed convective/stably stratified system—A review of some recent works
JO  - Comptes Rendus. Physique
PY  - 2020
DA  - 2020///
SP  - 151
EP  - 164
VL  - 21
IS  - 2
PB  - Académie des sciences, Paris
UR  - https://doi.org/10.5802/crphys.17
DO  - 10.5802/crphys.17
LA  - en
ID  - CRPHYS_2020__21_2_151_0
ER  - 
%0 Journal Article
%A Michael Le Bars
%A Louis-Alexandre Couston
%A Benjamin Favier
%A Pierre Léard
%A Daniel Lecoanet
%A Patrice Le Gal
%T Fluid dynamics of a mixed convective/stably stratified system—A review of some recent works
%J Comptes Rendus. Physique
%D 2020
%P 151-164
%V 21
%N 2
%I Académie des sciences, Paris
%U https://doi.org/10.5802/crphys.17
%R 10.5802/crphys.17
%G en
%F CRPHYS_2020__21_2_151_0
Michael Le Bars; Louis-Alexandre Couston; Benjamin Favier; Pierre Léard; Daniel Lecoanet; Patrice Le Gal. Fluid dynamics of a mixed convective/stably stratified system—A review of some recent works. Comptes Rendus. Physique, Volume 21 (2020) no. 2, pp. 151-164. doi : 10.5802/crphys.17. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.17/

[1] B. R. Sutherland Internal Gravity Waves, Cambridge University Press, Cambridge, UK, 2010 | DOI | Zbl

[2] C. Aerts; J. Christensen-Dalsgaard; D. W. Kurtz Asteroseismology, Springer Science & Business Media, Netherlands, 2010

[3] T. Rogers; D. N. Lin; H. H. B. Lau Internal gravity waves modulate the apparent misalignment of exoplanets around hot stars, Astrophys. J. Lett., Volume 758 (2012) no. 1, p. L6 | DOI

[4] M. Baldwin; L. Gray; T. Dunkerton; K. Hamilton; P. Haynes; W. Randel; J. Holton; M. Alexander; I. Hirota; T. Horinouchi et al. The quasi-biennial oscillation, Rev. Geophys., Volume 39 (2001) no. 2, pp. 179-229 | DOI

[5] C. B. Leovy; A. J. Friedson; G. S. Orton The quasiquadrennial oscillation of Jupiter’s equatorial stratosphere, Nature, Volume 354 (1991) no. 6352, p. 380 | DOI

[6] T. Fouchet; S. Guerlet; D. Strobel; A. Simon-Miller; B. Bézard; F. Flasar An equatorial oscillation in Saturn’s middle atmosphere, Nature, Volume 453 (2008) no. 7192, p. 200 | DOI

[7] R. S. Lindzen; J. R. Holton A theory of the quasi-biennial oscillation, J. Atmos. Sci., Volume 25 (1968) no. 6, pp. 1095-1107 | DOI

[8] J. R. Holton; R. S. Lindzen An updated theory for the quasi-biennial cycle of the tropical stratosphere, J. Atmos. Sci., Volume 29 (1972) no. 6, pp. 1076-1080 | DOI

[9] R. Plumb The interaction of two internal waves with the mean flow: Implications for the theory of the quasi-biennial oscillation, J. Atmos. Sci., Volume 34 (1977) no. 12, pp. 1847-1858 | DOI

[10] A. Renaud; L.-P. Nadeau; A. Venaille Periodicity disruption of a model quasibiennial oscillation of equatorial winds, Phys. Rev. Lett., Volume 122 (2019) no. 21, 214504 | DOI

[11] R. Plumb; A. McEwan The instability of a forced standing wave in a viscous stratified fluid: A laboratory analogue of the quasi-biennial oscillation, J. Atmos. Sci., Volume 35 (1978) no. 10, pp. 1827-1839 | DOI | MR

[12] B. Semin; N. Garroum; F. Pétrélis; S. Fauve Nonlinear saturation of the large scale flow in a laboratory model of the quasibiennial oscillation, Phys. Rev. Lett., Volume 121 (2018) no. 13, 134502 | DOI

[13] F. Lott; L. Guez A stochastic parameterization of the gravity waves due to convection and its impact on the equatorial stratosphere, J. Geophys. Res., Volume 118 (2013) no. 16, pp. 8897-8909 | DOI

[14] N. Butchart; J. Anstey; K. Hamilton; S. Osprey; C. McLandress; A. Bushell; Y. Kawatani; Y.-H. Kim; F. Lott; J. Scinocca et al. Overview of experiment design and comparison of models participating in phase 1 of the SPARC Quasi-Biennial Oscillation initiative (QBOi), Geosci. Model Dev., Volume 11 (2018) no. 3, pp. 1009-1032 | DOI

[15] A. Bushell; J. Anstey; N. Butchart; Y. Kawatani; S. Osprey; J. Richter; F. Serva; P. Braesicke; C. Cagnazzo; C.-C. Chen et al. Evaluation of the Quasi-Biennial Oscillation in global climate models for the SPARC QBO-initiative, Q. J. R. Meteorol. Soc. (2020), pp. 1-31 | DOI

[16] M. Le Bars; D. Lecoanet; S. Perrard; A. Ribeiro; L. Rodet; J. M. Aurnou; P. Le Gal Experimental study of internal wave generation by convection in water, Fluid Dyn. Res., Volume 47 (2015) no. 4, 045502

[17] D. Lecoanet; M. Le Bars; K. J. Burns; G. M. Vasil; B. P. Brown; E. Quataert; J. S. Oishi Numerical simulations of internal wave generation by convection in water, Phys. Rev. E, Volume 91 (2015) no. 6, 063016 | DOI

[18] L.-A. Couston; D. Lecoanet; B. Favier; M. Le Bars Dynamics of mixed convective–stably-stratified fluids, Phys. Rev. Fluids, Volume 2 (2017) no. 9, 094804

[19] L.-A. Couston; D. Lecoanet; B. Favier; M. Le Bars Order out of chaos: slowly reversing mean flows emerge from turbulently generated internal waves, Phys. Rev. Lett., Volume 120 (2018) no. 24, 244505

[20] L.-A. Couston; D. Lecoanet; B. Favier; M. Le Bars The energy flux spectrum of internal waves generated by turbulent convection, J. Fluid Mech., Volume 854 (2018), R3 | MR | Zbl

[21] P. Léard; B. Favier; P. Le Gal; M. Le Bars Coupled convection and internal gravity waves excited in water around its density maximum at 4  C, Phys. Rev. Fluids, Volume 5 (2020) no. 2, 024801 | DOI

[22] J. K. Ansong; B. R. Sutherland Internal gravity waves generated by convective plumes, J. Fluid Mech., Volume 648 (2010), pp. 405-434 | DOI | MR | Zbl

[23] J. W. Deardorff; G. E. Willis; D. K. Lilly Laboratory investigation of non-steady penetrative convection, J. Fluid Mech., Volume 35 (1969) no. 1, pp. 7-31 | DOI

[24] M. Michaelian; T. Maxworthy; L. Redekopp The coupling between turbulent, penetrative convection and internal waves, Eur. J. Mech. B, Volume 21 (2002) no. 1, pp. 1-28 | DOI | Zbl

[25] A. Townsend Natural convection in water over an ice surface, Q. J. R. Meteorol. Soc., Volume 90 (1964) no. 385, pp. 248-259 | DOI

[26] S. Perrard; M. Le Bars; P. Le Gal Experimental and numerical investigation of internal gravity waves excited by turbulent penetrative convection in water around its density maximum, Studying Stellar Rotation and Convection, Springer, Berlin, Heidelberg, Germany, 2013, pp. 239-257 | DOI

[27] L. N. Howard Convection at high Rayleigh number, Applied Mechanics, Springer, New York, USA, 1966, pp. 1109-1115 | DOI

[28] K. J. Burns; G. M. Vasil; J. S. Oishi; D. Lecoanet; B. P. Brown Dedalus: A flexible framework for numerical simulations with spectral methods, Phys. Rev. Res., Volume 2 (2020) no. 2, 023068

[29] P. Fisher; J. Lottes; S. Kerkemeier “Nek5000 v17.0”, http://nek5000.mcs.anl.gov (2017)

[30] D. Lecoanet; M. Cantiello; E. Quataert; L.-A. Couston; K. J. Burns; B. J. Pope; A. S. Jermyn; B. Favier; M. Le Bars Low-frequency variability in massive stars: Core generation or surface phenomenon?, Astrophys. J. Lett., Volume 886 (2019) no. 1, p. L15 | DOI

[31] M. J. Lighthill Waves in Fluids, Cambridge University Press, Cambridge, UK, 2001

[32] P. Goldreich; P. Kumar Wave generation by turbulent convection, Astrophys. J., Volume 363 (1990) no. 2, pp. 694-704 | DOI

[33] D. Lecoanet; E. Quataert Internal gravity wave excitation by turbulent convection, Mon. Not. R. Astron. Soc., Volume 430 (2013) no. 3, pp. 2363-2376 | DOI

[34] D. M. Bowman; S. Burssens; M. G. Pedersen; C. Johnston; C. Aerts; B. Buysschaert; M. Michielsen; A. Tkachenko; T. M. Rogers; P. V. Edelmann et al. Low-frequency gravity waves in blue supergiants revealed by high-precision space photometry, Nat. Astron., Volume 3 (2019) no. 8, pp. 760-765 | DOI

[35] P. Edelmann; R. Ratnasingam; M. Pedersen; D. Bowman; V. Prat; T. Rogers Three-dimensional simulations of massive stars. I. Wave generation and propagation, Astrophys. J., Volume 876 (2019) no. 1, p. 4 | DOI

[36] D. Bowman “What physics is missing in theoretical models of high-mass stars: new insights from asteroseismology”, preprint, arXiv:1912.12653 (2019)

[37] T. Crueger; M. A. Giorgetta; R. Brokopf; M. Esch; S. Fiedler; C. Hohenegger; L. Kornblueh; T. Mauritsen; C. Nam; A. K. Naumann et al. ICON-A, the atmosphere component of the ICON earth system model: II. Model evaluation, J. Adv. Model. Earth Syst., Volume 10 (2018) no. 7, pp. 1638-1662 | DOI

[38] J. A. Anstey; J. F. Scinocca; M. Keller Simulating the QBO in an atmospheric general circulation model: Sensitivity to resolved and parameterized forcing, J. Atmos. Sci., Volume 73 (2016) no. 4, pp. 1649-1665 | DOI

[39] L.-A. Couston; D. Lecoanet; B. Favier; M. Le Bars Shape and size of large-scale vortices: A generic fluid pattern in geophysical fluid dynamics, Phys. Rev. Res., Volume 2 (2020) no. 2, 023143

[40] S. Labrosse Thermal evolution of the core with a high thermal conductivity, Phys. Earth Planet. Inter., Volume 247 (2015), pp. 36-55 | DOI

[41] E. Jaupart; B. Buffett Generation of MAC waves by convection in Earth’s core, Geophys. J. Int., Volume 209 (2017) no. 2, pp. 1326-1336 | DOI

Cited by Sources: