Nonlinear diffusion model for Rayleigh-Taylor mixing

TL;DR

This paper introduces a nonlinear eddy diffusivity model based on Prandtl mixing theory that accurately predicts turbulent profiles, heat flux, and Nusselt number in Rayleigh-Taylor convection.

Contribution

The paper develops a novel nonlinear diffusion model that improves predictions of turbulent mixing and heat transfer in Rayleigh-Taylor convection.

Findings

The nonlinear model accurately reproduces turbulent temperature profiles.

It provides precise predictions for heat flux and Nusselt number.

The model aligns well with numerical simulation data.

Abstract

The complex evolution of turbulent mixing in Rayleigh-Taylor convection is studied in terms of eddy diffusiviy models for the mean temperature profile. It is found that a non-linear model, derived within the general framework of Prandtl mixing theory, reproduces accurately the evolution of turbulent profiles obtained from numerical simulations. Our model allows to give very precise predictions for the turbulent heat flux and for the Nusselt number in the ultimate state regime of thermal convection.