Fluxes through a uniform double-diffusive staircase at low Prandtl number
Abstract
Double-diffusive convection in the diffusive regime is often observed to be in a long-lived layered state, well-known in the Arctic ocean and in volcanic lakes, and thought to exist in the interiors of giant planets. The density profile resembles a `staircase', with stacks of convective layers of uniform density separated by strongly stratified interfaces. The governing parameters are the Prandtl number Pr, diffusivity ratio τ, density ratio Rρ, and Rayleigh number Ra. In this work, we perform direct numerical simulations in triply periodic domains to systematically investigate the properties of statistically stationary double-diffusive staircases with τ≤ Pr ≪ 1. We demonstrate that they can exist for significantly larger density ratios than previously reported, and propose a new criterion for the existence of long-lived layered states. Notably, this criterion depends weakly on Ra. In all simulations, we measure the total fluxes of density Ftotρ, temperature FtotT and composition FtotC, and the flux ratio γ=FtotC/FtotT. We confirm that γ is approximately constant for moderate to large Rρ but also depends weakly on Ra. We show that the Nusselt numbers for composition and temperature scale as Ra1/3 in this limit, which notably differs from the (RaPr)1/3 scaling previously found at lower Rρ. We propose a new model for these findings that is based on the rise and turbulent mixing of density anomalies that form at the edges of the interfaces. The model explains the existing low Pr data with reasonable accuracy.
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BibTeX
@misc{tulekeyev2026fluxes,
title = {{Fluxes through a uniform double-diffusive staircase at low Prandtl number}},
author = {Arstanbek Tulekeyev and Pascale Garaud},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28679},
eprint = {2608.28679},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28679},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fluxes through a uniform double-diffusive staircase at low Prandtl number
AU - Arstanbek Tulekeyev
AU - Pascale Garaud
PY - 2026
DA - 2026/08/26
PB - arXiv
DO - 10.48550/arxiv.2608.28679
UR - https://arxiv.org/abs/2608.28679
AB - Double-diffusive convection in the diffusive regime is often observed to be in a long-lived layered state, well-known in the Arctic ocean and in volcanic lakes, and thought to exist in the interiors of giant planets. The density profile resembles a `staircase', with stacks of convective layers of uniform density separated by strongly stratified interfaces. The governing parameters are the Prandtl number Pr, diffusivity ratio τ, density ratio R_ρ, and Rayleigh number Ra. In this work, we perform direct numerical simulations in triply periodic domains to systematically investigate the properties of statistically stationary double-diffusive staircases with τ≤ Pr ≪ 1. We demonstrate that they can exist for significantly larger density ratios than previously reported, and propose a new criterion for the existence of long-lived layered states. Notably, this criterion depends weakly on Ra. In all simulations, we measure the total fluxes of density F^tot_ρ, temperature F^tot_T and composition F^tot_C, and the flux ratio γ=F^tot_C/F^tot_T. We confirm that γ is approximately constant for moderate to large R_ρ but also depends weakly on Ra. We show that the Nusselt numbers for composition and temperature scale as Ra^1/3 in this limit, which notably differs from the (RaPr)^1/3 scaling previously found at lower R_ρ. We propose a new model for these findings that is based on the rise and turbulent mixing of density anomalies that form at the edges of the interfaces. The model explains the existing low Pr data with reasonable accuracy.
ER -