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Abstract
Quantifying transport by strongly stratified turbulence in low Prandtl number ( $Pr$ ) fluids is critically important for the development of better models for the structure and evolution of stellar and planetary interiors. Motivated by recent numerical simulations showing strongly anisotropic flows suggestive of a scale-separated dynamics, we perform a multiscale asymptotic analysis of the governing equations. We find that, in all cases, the resulting slow–fast systems take a quasilinear form. Our analysis also reveals the existence of several distinct dynamical regimes depending on the emergent buoyancy Reynolds and Péclet numbers, $Re_b = \alpha ^2 Re$ and $Pe_b = Pr Re_b$ , respectively, where $\alpha$ is the aspect ratio of the large-scale turbulent flow structures, and $Re$ is the outer-scale Reynolds number. Scaling relationships relating the aspect ratio, the characteristic vertical velocity and the strength of the stratification (measured by the Froude number $Fr$ ) naturally emerge from the analysis. When $Pe_b \ll \alpha$ , the dynamics at all scales is dominated by buoyancy diffusion, and our results recover the scaling laws empirically obtained from direct numerical simulations by Cope et al. (J. Fluid Mech., vol. 903, 2020, A1). For $Pe_b \ge O(1)$ , diffusion is negligible (or at least subdominant) at all scales and our results are consistent with those of Chini et al. (J. Fluid Mech., vol. 933, 2022) for strongly stratified geophysical turbulence at $Pr =O(1)$ . Finally, we have identified a new regime for $\alpha \ll Pe_b \ll 1$ , in which slow, large scales are diffusive while fast, small scales are not. We conclude by presenting a map of parameter space that clearly indicates the transitions between isotropic turbulence, non-diffusive stratified turbulence, diffusive stratified turbulence and viscously dominated flows, and by proposing parameterisations of the buoyancy flux, mixing efficiency and turbulent diffusion coefficient for each regime.
Department
Mechanical Engineering
Publication Date
11-5-2024
Journal Title
Journal of Fluid Mechanics
Publisher
Cambridge University Press (CUP)
Digital Object Identifier (DOI)
Document Type
Article
Recommended Citation
Shah K, Chini GP, Caulfield CP, Garaud P. Regimes of stratified turbulence at low Prandtl number. Journal of Fluid Mechanics. 2024;998:A60. doi:10.1017/jfm.2024.678
Rights
© The Author(s), 2024.
Comments
This is an open access article published by Cambridge University Press (CUP) in Journal of Fluid Mechanics in 2024, available online: https://dx.doi.org/10.1017/jfm.2024.678