Scale-space energy transport in anisotropic inhomogeneous buoyancy-driven turbulent flows

TL;DR

This paper introduces a new mathematical framework with exact transport equations for turbulence kinetic energy and heat transfer in anisotropic, inhomogeneous buoyancy-driven flows, enabling detailed analysis across physical and scale spaces.

Contribution

The paper derives novel exact transport equations for turbulence energy and heat flux in inhomogeneous, anisotropic flows, extending turbulence analysis to combined physical and scale spaces.

Findings

Quantified inhomogeneity contributions in Rayleigh-Bénard convection

Evaluated production, dissipation, and interscale transport terms

Demonstrated the framework's application to complex turbulent flows

Abstract

In this article, we introduce a new mathematical framework that can describe the budget of turbulence kinetic energy and heat transfer in both physical space and scale space of turbulence. We derived two exact transport equations for inhomogeneous and anisotropic buoyancy-driven incompressible turbulent flow. The two equations are the turbulent kinetic energy transport equation and the turbulent heat flux density transport equation. These equations are derived from the governing Navier-Stokes equation and two-point correlations. Analogous to the energy spectrum and heat flux spectrum for homogeneous isotropic turbulence, energy density, and heat flux density introduced in this paper describe the energy and heat flux corresponding in various scales and the transport across physical and scale space for inhomogeneous anisotropic turbulent flows. The proposed equations are used to post-process a turbulent Rayleigh-B\'enard convection flow dataset. Specifically, production, dissipation, interscale transport, and buoyancy terms are evaluated, and the contribution from inhomogeneity is quantified.