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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

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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