Lagrangian Markovianized Field Approximation for turbulence

TL;DR

This paper develops a Markovian closure model for turbulence that relates to existing approximations, deriving equations for energy and scalar spectra, and validates them through numerical integration across different Schmidt numbers.

Contribution

It introduces a self-consistent Markovian triadic closure for turbulence, connecting it with established closure theories and providing a simplified model for scalar variance.

Findings

Closed equations for energy and scalar spectra are derived.

Numerical results match expected turbulence behaviors.

Model performs well across various Schmidt numbers.

Abstract

In a previous communication (W.J.T. Bos and J.-P. Bertoglio 2006, Phys. Fluids, 18, 031706), a self-consistent Markovian triadic closure was presented. The detailed derivation of this closure is given here, relating it to the Direct Interaction Approximation and Quasi-Normal types of closure. The time-scale needed to obtain a self-consistent closure for both the energy spectrum and the scalar variance spectrum is determined by evaluating the correlation between the velocity and an advected displacement vector-field. The relation between this latter correlation and the velocity-scalar correlation is stressed, suggesting a simplified model of the latter. The resulting closed equations are numerically integrated and results for the energy spectrum, scalar fluctuation spectrum and velocity-displacement correlation spectrum are presented for low, unity and high values of the Schmidt number.