An EDQNM model to explore the behavior of stratified turbulence in the high Prandtl number regime*

The mixing of passive scalars driven by an isotropic turbulent flow can be strongly affected by the Prandtl number (Pr), with the scalar dissipation anomaly breaking down for high Pr unless the flow Reynolds number (Re) is sufficiently high (Donzis, Sreenivasan, Yeung, P. K., JFM 2005). State-of-the-art direct numerical simulations (DNS) also reveal striking effects of Pr on mixing in stably stratified turbulence (Riley, Couchman and de Bruyn Kops, JoT 2023), however, our understanding of this is very limited. Moreover, the DNS is limited to relatively low Pr. While a scaling analysis could provide theoretical insight into the problem, this is challenging due to the strongly non-local dynamics of the flow in the regime Pr>>1. Building on the work of Godeferd & Cambon 1994 which was confined to Pr=1, we construct an eddy-damped, quasi-normal Markovian (EDQNM) model for stably stratified turbulence that applies for arbitrary Pr, and also captures the effects of Reynolds (Re) and Froude (Fr) numbers. Predictions from the model are compared with recent DNS data, and the model is then deployed to explore the asymptotic behavior of the flow in regimes of Pr, Re, and Fr that are currently not accessible with DNS.