Challenging Mix Models on Transients to Self-Similarity of Unstably Stratified Homogeneous Turbulence

Abstract

The present work aims at expanding the set of buoyancy-driven unstable reference flows—a critical ingredient in the development of turbulence models—by considering the recently introduced “Unstably Stratified Homogeneous Turbulence” (USHT) in both its self-similar and transient regimes. The previously established accuracy of an anisotropic Eddy-Damped Quasi-Normal Markovian Model (EDQNM) on the USHT has allowed us to: (i) build a data set of well defined transient flows from Homogeneous Isotropic Turbulence (HIT) to late-time self-similar USHT and (ii) on this basis, calibrate, validate, and compare three common Reynolds-Averaged Navier–Stokes (RANS) mixing models (two-equation, Reynolds stress, and two-fluid). The model calibrations were performed on the self-similar flows constrained by predefined long range correlations (Saffman or Batchelor type). Then, with fixed constants, validations were carried out over the various transients defined by the initial Froude number and mixing intensity. Significant differences between the models are observed, but none of them can accurately capture all of the transient regimes at once. Closer inspection of the various model responses hints at possible routes for their improvement.