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Layering and vertical transport in sheared double-diffusive convection in the diffusive regime

Published online by Cambridge University Press:  23 December 2021

Yantao Yang Open the ORCID record for Yantao Yang [Opens in a new window] ,
Roberto Verzicco Open the ORCID record for Roberto Verzicco [Opens in a new window] ,
Detlef Lohse Open the ORCID record for Detlef Lohse [Opens in a new window]  and
C.P. Caulfield Open the ORCID record for C.P. Caulfield [Opens in a new window]
Yantao Yang*
Affiliation:
SKLTCS and Department of Mechanics and Engineering Science, BIC-ESAT, College of Engineering, and Institute of Ocean Research, Peking University, Beijing 100871, PR China
Roberto Verzicco
Affiliation:
Physics of Fluids Group, Department of Science and Technology, Mesa+ Institute, Max-Planck Center Twente for Complex Fluid Dynamics, and J. M. Burgers Center for Fluid Dynamics, University of Twente, Twente, 7500 AE Enschede, The Netherlands Dipartimento di Ingegneria Industriale, University of Rome ‘Tor Vergata’, Via del Politecnico 1, 00133 Rome, Italy
Detlef Lohse
Affiliation:
Physics of Fluids Group, Department of Science and Technology, Mesa+ Institute, Max-Planck Center Twente for Complex Fluid Dynamics, and J. M. Burgers Center for Fluid Dynamics, University of Twente, Twente, 7500 AE Enschede, The Netherlands Max Planck Institute for Dynamics and Self-Organisation, 37077 Göttingen, Germany
C.P. Caulfield*
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

A sequence of two- and three-dimensional simulations are conducted for the double-diffusive convection (DDC) flows in the diffusive regime subjected to an imposed shear. For a wide range of control parameters, and for sufficiently strong perturbation of the conductive initial state, staircase-like structures spontaneously develop, with relatively well-mixed layers separated by sharp interfaces of enhanced scalar gradient. Such staircases appear to be robust even in the presence of strong shear over very long times, with early-time coarsening of the observed layers. For the same set of control parameters, different asymptotic layered states, with markedly different vertical scalar fluxes, can arise for different initial perturbation structures. The imposed shear significantly spatio-temporally modifies the vertical transport of the various scalars. The flux ratio $\gamma ^*$ (i.e. the ratio between the density fluxes due to the total salt flux and the total heat flux) is found, at steady state, to be essentially equal to the square root of the ratio of the salt diffusivity to the thermal diffusivity, consistent with the physical model proposed by Linden & Shirtcliffe (J. Fluid Mech., vol. 87, 1978, pp. 417–432) and the variational arguments presented by Stern (J. Fluid Mech., vol. 114, 1982, pp. 105–121) for unsheared double-diffusive convection.

JFM classification

Convection: Double diffusive convection Turbulent Flows: Stratified turbulence Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A30
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Bebieva, Y. & Speer, K. 2019 The regulation of sea ice thickness by double-diffusive processes in the Ross Gyre. J. Geophys. Res. 124, 7068–7081.CrossRefGoogle Scholar
Bebieva, Y. & Timmermans, M.L. 2017 The relationship between double-diffusive intrusions and staircases in the Arctic Ocean. J. Phys. Oceanogr. 47, 867–878.CrossRefGoogle Scholar
Bebieva, Y. & Timmermans, M.L. 2019 Double-diffusive layering in the Canada Basin: an explanation of along-layer temperature and salinity gradients. J. Geophys. Res. 124, 723–735.CrossRefGoogle Scholar
Brown, J.M. & Radko, T. 2019 Initiation of diffusive layering by time-dependent shear. J. Fluid Mech. 858, 588–608.CrossRefGoogle Scholar
Brown, J.M. & Radko, T. 2021 Diffusive staircases in shear: dynamics and heat transport. J. Phys. Oceanogr. 51, 1915–1928.Google Scholar
Caulfield, C.P. 2021 Layering, instabilities and mixing in turbulent stratified flows. Annu. Rev. Fluid Mech. 53, 113–145.CrossRefGoogle Scholar
Ferrari, R. & Wunsch, C. 2009 Ocean circulation kinetic energy: reservoirs, sources, and sinks. Annu. Rev. Fluid Mech. 41, 253–282.CrossRefGoogle Scholar
Garaud, P. 2018 Double-diffusive convection at low Prandtl number. Annu. Rev. Fluid Mech. 50, 275–298.CrossRefGoogle Scholar
Holmboe, J. 1962 On the behaviour of symmetric waves in stratified shear layers. Geofys. Publ. 24, 67–113.Google Scholar
Huisman, S.G., van der Veen, R.C.A., Sun, C. & Lohse, D. 2014 Multiple states in highly turbulent Taylor–Couette flow. Nat. Commun. 5, 3820.CrossRefGoogle ScholarPubMed
Ivey, G.N., Winters, K.B. & Koseff, J.R. 2008 Density stratification, turbulence, but how much mixing? Annu. Rev. Fluid Mech. 40, 169–184.CrossRefGoogle Scholar
Kato, H. & Phillips, O.M. 1969 On the penetration of a turbulent layer into stratified fluid. J. Fluid Mech. 37, 643–655.CrossRefGoogle Scholar
Kelley, D.E., Fernando, H.J.S., Gargett, A.E., Tanny, J. & Ozsoy, E. 2003 The diffusive regime of double-diffusive convection. Prog. Oceanogr. 56, 461–481.CrossRefGoogle Scholar
Linden, P.F. & Shirtcliffe, T.G.L. 1978 The diffusive interface in double-diffusive convection. J. Fluid Mech. 87, 417–432.CrossRefGoogle Scholar
Noguchi, T. & Niino, H. 2010 Multi-layered diffusive convection. Part 1. Spontaneous layer formation. J. Fluid Mech. 651, 443–464.CrossRefGoogle Scholar
Osborn, T.R. 1980 Estimates of the local-rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr. 10, 83–89.2.0.CO;2>CrossRefGoogle Scholar
Ostilla-Mónico, R., Yang, Y., van der Poel, E.P., Lohse, D. & Verzicco, R. 2015 A multiple resolutions strategy for direct numerical simulation of scalar turbulence. J. Comput. Phys. 301, 308–321.CrossRefGoogle Scholar
Portwood, G.D., de Bruyn Kops, S.M. & Caulfield, C.P. 2019 Asymptotic dynamics of high dynamic range stratified turbulence. Phys. Rev. Lett. 122, 194504.CrossRefGoogle ScholarPubMed
Radko, T. 2016 Thermohaline layering in dynamically and diffusively stable shear flows. J. Fluid Mech. 805, 147–170.CrossRefGoogle Scholar
Radko, T. 2019 Thermohaline-shear instability. Geophys. Res. Lett. 46, 822–832.CrossRefGoogle Scholar
Salehipour, H., Caulfield, C.P. & Peltier, W.R. 2016 Turbulent mixing due to the Holmboe wave instability at high Reynolds number. J. Fluid Mech. 803, 591–621.CrossRefGoogle Scholar
Schmitt, R.W. 1994 Double diffusion in oceanography. Annu. Rev. Fluid Mech. 26, 255–285.CrossRefGoogle Scholar
Schmitt, R.W., Ledwell, J.R., Montgomery, E.T., Polzin, K.L. & Toole, J.M. 2005 Enhanced diapycnal mixing by salt fingers in the thermocline of the tropical Atlantic. Science 308, 685–688.CrossRefGoogle ScholarPubMed
Shaw, W.J. & Stanton, T.P. 2014 Dynamic and double-diffusive instabilities in a weak pycnocline. Part 1. Observations of heat flux and diffusivity in the vicinity of Maud Rise, Weddell Sea. J. Phys. Oceanogr. 44, 1973–1991.CrossRefGoogle Scholar
Shibley, N.C. & Timmermans, M.-L. 2019 The formation of double-diffusive layers in a weakly turbulent environment. J. Geophys. Res. 124, 1445–1458.CrossRefGoogle Scholar
Shibley, N.C., Timmermans, M.-L., Carpenter, J.R. & Toole, J.M. 2017 Spatial variability of the Arctic ocean's double-diffusive staircase. J. Geophys. Res. 122, 980–994.CrossRefGoogle Scholar
Stellmach, S., Traxler, A., Garaud, P., Brummell, N. & Radko, T. 2011 Dynamics of fingering convection. Part 2. The formation of thermohaline staircases. J. Fluid Mech. 677, 554–571.CrossRefGoogle Scholar
Stern, M.E. 1960 The ‘salt-fountain’ and thermohaline convection. Tellus 12, 172–175.CrossRefGoogle Scholar
Stern, M.E. 1982 Inequalities and variational principles in double-diffusive turbulence. J. Fluid Mech. 114, 105–121.CrossRefGoogle Scholar
Stern, M.E. & Turner, J.S. 1969 Salt fingers and convecting layers. Deep-Sea Res. 16, 497–511.Google Scholar
Taylor, J.R. & Zhou, Q. 2017 A multi-parameter criterion for layer formation in a stratified shear flow using sorted buoyancy coordinates. J. Fluid Mech. 823, R5.CrossRefGoogle Scholar
Timmermans, M.-L. & Marshall, J. 2020 Understanding arctic ocean circulation: a review of ocean dynamics in a changing climate. J. Geophys. Res. 125, e2018JC014378.CrossRefGoogle Scholar
Timmermans, M.-L., Toole, J., Krishfield, R. & Winsor, P. 2008 Ice-tethered profiler observations of the double-diffusive staircase in the Canada basin thermocline. J. Geophys. Res. 113, C00A02.Google Scholar
Traxler, A., Stellmach, S., Garaud, P., Radko, T. & Brummell, N. 2011 Dynamics of fingering convection. Part 1. Small-scale fluxes and large-scale instabilities. J. Fluid Mech. 677, 530–553.CrossRefGoogle Scholar
Turner, J.S. 1965 The coupled turbulent transports of salt and heat across a sharp density interface. Intl J. Heat Mass Transfer 8, 759–767.CrossRefGoogle Scholar
Turner, J.S. 1985 Multicomponent convection. Annu. Rev. Fluid Mech. 17, 11–44.CrossRefGoogle Scholar
Turner, J.S. 2010 The melting of ice in the arctic ocean: the influence of double-diffusive transport of heat from below. J. Phys. Oceanogr. 40, 249–256.CrossRefGoogle Scholar
Turner, J.S. 2013 Double-Diffusive Convection. Cambridge University Press.Google Scholar
Woods, A.W., Caulfield, C.P., Landel, J.R. & Kuesters, A. 2010 Non-invasive mixing across a density interface in a turbulent Taylor–Couette flow. J. Fluid Mech. 663, 347–357.CrossRefGoogle Scholar
Worster, M.G. 2004 Time-dependent fluxes across double-diffusive interfaces. J. Fluid Mech. 505, 287–307.CrossRefGoogle Scholar
Yang, Y., Chen, W., Verzicco, R. & Lohse, D. 2020 Multiple states and transport properties of double-diffusive convection turbulence. Proc. Natl Acad. Sci. USA 117, 14676–14681.CrossRefGoogle ScholarPubMed
Yang, Y., Verzicco, R. & Lohse, D. 2016 Scaling laws and flow structures of double diffusive convection in the finger regime. J. Fluid Mech. 802, 667–689.CrossRefGoogle Scholar
Zaussinger, F. & Kupka, F. 2018 Layer formation in double-diffusive convection over resting and moving plates. Theor. Comput. Fluid Dyn. 33, 383–409.CrossRefGoogle Scholar

Yang et al. supplementary movie 1

Evolution of layering for Case 1

Download Yang et al. supplementary movie 1(Video)
Video 1.7 MB

Yang et al. supplementary movie 2

Evolution of layering for Case 2

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Video 2 MB

Yang et al. supplementary movie 3

Evolution of layering for Case 3

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Video 2.6 MB

Yang et al. supplementary movie 4

Evolution of layering for Case 4

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Video 8 MB

Yang et al. supplementary movie 5

Evolution of layering for Case 5

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Video 9.3 MB

Yang et al. supplementary movie 6

Evolution of layering for Case 6

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Video 8.2 MB

Yang et al. supplementary movie 7

Evolution of layering for Case 7. The initially slowly growing stage of the single vortical layer is skipped, and the movie starts from the nondimensional time 10000.

Download Yang et al. supplementary movie 7(Video)
Video 8.7 MB