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Quantifying structural uncertainty in the BHR model for variable-density flows

In this brief, we try to develop a comprehensive framework to identify, quantify, isolate, and reduce the uncertainties in the original BHR model \citep {Besnard1992} for variable-density flows. Because the eigenspace perturbation of Reynolds stress successfully accounts for the structural uncertainty in many flows, we first extend this methodology to the BHR model for variable-density flows with different $At$. The philosophy of eigenspace perturbation in Reynolds stress, i.e., quantifying the states of maximizing and minimizing the production mechanism, has led to the proposals of the structural uncertainty quantification strategy in the BHR model for variable-density flows. Several canonical flows, including one-dimensional (1D) Rayleigh-Taylor instability (1DRT), Rayleigh-Taylor mixing in a tilted rig (TR) and turbulent jet mixing flow, are investigated.