Lagrangian Markovianized Field Approximation for turbulence

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.

References in corpus (2)

• Inertial range scaling of scalar flux spectra in uniformly sheared turbulence
• A single-time two-point closure based on fluid particle displacements

Cited by in corpus (3)

• Turbulence and turbulent pattern formation in a minimal model for active fluids
• On the strength of the nonlinearity in isotropic turbulence
• Data Driven Learning of Mori-Zwanzig Operators for Isotropic Turbulence