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Double-diffusive transport in multicomponent vertical convection

Christopher J. Howland1,*, Roberto Verzicco2,3,1, and Detlef Lohse1,4,†

  • 1Physics of Fluids Group, Max Planck Center for Complex Fluid Dynamics, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500AE Enschede, Netherlands
  • 2Dipartimento di Ingegneria Industriale, University of Rome “Tor Vergata,” Via del Politecnico 1, 00133 Roma, Italy
  • 3Gran Sasso Science Institute, Viale F. Crispi 7, 67100 L'Aquila, Italy
  • 4Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany

  • *c.j.howland@utwente.nl
  • †d.lohse@utwente.nl
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Phys. Rev. Fluids 8, 013501 – Published 4 January, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.013501

Abstract

Motivated by the ablation of vertical ice faces in salt water, we use three-dimensional direct numerical simulations to investigate the heat and salt fluxes in two-scalar vertical convection. For parameters relevant to ice-ocean interfaces in the convection-dominated regime, we observe that the salinity field drives the convection and that heat is essentially transported as a passive scalar. By varying the diffusivity ratio of heat and salt (i.e., the Lewis number Le), we identify how the different molecular diffusivities affect the scalar fluxes through the system. Away from the walls, we find that the heat transport is determined by a turbulent Prandtl number of Prt≈1 and that double-diffusive effects are practically negligible. However, the difference in molecular diffusivities plays an important role close to the boundaries. In the (unrealistic) case where salt diffused faster than heat, the ratio of salt-to-heat fluxes would scale as Le1/3, consistent with classical nested scalar boundary layers. However, in the realistic case of faster heat diffusion (relative to salt), we observe a transition towards a Le1/2 scaling of the ratio of the fluxes. This coincides with the thermal boundary layer width growing beyond the thickness of the viscous boundary layer. We find that this transition is not determined by a critical Lewis number, but rather by a critical Prandtl number Pr≈10, slightly below that for cold seawater where Pr=14. We compare our results to similar studies of sheared and double-diffusive flow under ice shelves, and discuss the implications for fluxes in large-scale ice-ocean models. By coupling our results to ice-ocean interface thermodynamics, we describe how the flux ratio impacts the interfacial salinity, and hence the strength of solutal convection and the ablation rate.

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Outline

Information

Phys. Rev. Fluids 8, 013501– Published 4 January, 2023
  • Received 19 July 2022
  • Accepted 2 December 2022
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