A Reynolds-averaged Navier-Stokes model is presented with the property that it admits self-consistent, high-order spatial profiles in simulations of two-fluid turbulent mixing layers. Whereas previous models have been limited by the assumption of a linear mixing profile, the present paper relaxes this assumption and, as a result, is shown to achieve much better agreement with experimental profiles. Similarity analysis is presented to derive constraints on model coefficients to enforce desired self-similar growth rates that are fully consistent with the high-order spatial profiles. Through this similarity analysis, it is shown that care must be taken in model construction, as it is possible to construct certain terms in such a way as to leave growth rates unconstrained. This model, termed the $k\text{−}\varphi \text{−}L\text{−}a\text{−}V$ model, is then applied in simulations of Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz mixing layers. These simulations confirm that the expected growth parameters are recovered and high-order spatial profiles are maintained.

• Received 23 March 2021
• Revised 4 June 2021
• Accepted 7 July 2021

DOI:https://doi.org/10.1103/PhysRevE.104.015107