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Many Dam applications involve phenomena of hydrodynamic mixing instabilities at interfaces between different materials. Simulation codes must include a suitable description of mixing dynamics in order to predict and reconstruct experiments [1]. For the most part, these instabilities rapidly evolve to a developed turbulent regime that can be described by a statistical hydrodynamic Choosing the correct model is to the quality of a simulation.

The statistical equations for the turbulent flow of an incompressible fluid are found in the literature [58], but they are adapted here to the specific needs of mixing flows, using more compact notations detailed in A.

Two‐fluid descriptions often use explicitly separate treatments for the conservation equations in each fluid, along with expressions for exchange terms that can become complicated [82–86]. We will re‐examine the conservation equations (2.1) for a single global fluid with variable properties depending on the position: equation of state, constitutive laws, thermodynamic variables, etc. The various quantities will thus reflect variations due to both flow and composition of the fluid, and the properties of individual fluid components will be selected by taking the product with the local mass fractions c and c = 1 - c. All possible mixing cases can be treated within this formalism (immiscible fluids, molecular interdi.usions, surface tensions, etc.) and, under various closure assumptions, lead to the usual models (such as reviewed in [83–86], for example).

The three major types of “ideal„ instabilities studied here are [92]:

According to the literature, the calibration of coefficients of the incompressible к‐ε model (listed in Table 2.1, p. 14) is based on the reconstruction of a that are not described or are possibly spurious. The content of this set of experiments varies among authors, but there are three main classes:

The self‐similar incompressible “0D„ approach can be used to estimate the performance of Awe's two‐fluid model in the three cases of simple mixing layers. In contrast to what was shown with the single‐fluid к‐ε model, the KH case is now singular compared to the RT and RM cases and will be discussed last. A 1D analytic study of the RT case has been published based on a slightly simplified version of the model [108, 109].

The results of the “0D„ analyses gathered in Tables 5.1 and 6.1 and discussed in Sects. 5.3 and 6.2 provide the basis for comparing Dam's к–ε and Awe's two‐fluid models as outlined in Table 7.1. No further comments will be given on this comparison except for one specific point that is crucial to modeling: the energy dissipation circuits. The representation of these circuits in Table 7.1 is rearranged and simplified from Figs. 5.1 and 6.4.

Before examining the phenomenology of the interaction between a shock and turbulent or material heterogeneities, it is useful to recall that the turbulence of a compressible fluid has that are very different in nature. As is reviewed in B, the velocity fluctuation field can be decomposed into divergent irrotational and nondivergent rotational parts, respectively [147–149]. Only the latter is present for an incompressible fluid. Despite certain formal difficulties and the fact that the two fields evolve in a coupled way, this decomposition provides an intuitive understanding of the nature of compressible turbulence and the effect of shock waves [148, 149]:

Faced with the insufficiencies of the basic single‐fluid models, such as Dam's к‐ε, several authors [13–26,167] have rightly identified the source of the problems as being in the modeling of the turbulent mass flux, „, which appears in the so‐called “Rayleigh–Taylor „ source term.

The relevance of this study stands not in the topics that have been discussed, since most of them have already been explored for many years now, but rather in assembling a broad array of experimental data and hydrodynamic models from the literature under one unified formalism and in subjecting these to a list of evaluation criteria corresponding to the specific needs of the Dam. In this spirit, this study made it possible to define effective approaches for developing and validating new hydrodynamic models for mixing flows.