Light is shed upon Eulerian Monte Carlo methods and their application to the simulation of turbulent reactive flows. A rapid decorrelating velocity-field model is used to derive stochastic partial differential equations (SPDE's) stochastically equivalent to the modeled one-point joint probability density function of turbulent reactive scalars. Those SPDE's are shown to be hyperbolic, advection-reaction equations. They are dealt with in a generalized sense, so that discontinuities in the scalar fields can be treated. A numerical analysis is proposed and numerical tests are carried out. In particular, a comparison with the Lagrangian Monte Carlo method is performed.

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When a premixed flame propagates in a turbulent flow, not only does turbulence affect the burning rate (e.g., by wrinkling the flame and increasing its surface area), but also the heat release in the flame perturbs the pressure field, and these pressure perturbations affect the turbulent flow and scalar transport. For instance, the latter effects manifest themselves in the so-called countergradient turbulent scalar flux, which has been documented in various flames and has challenged the combustion community for approximately 35 years. Over the past decade, substantial progress has been made in investigating (a) the influence of thermal expansion in a premixed flame on the turbulent flow and turbulent scalar transport within the flame brush, as well as (b) the feedback influence of countergradient scalar transport on the turbulent burning rate. The present article reviews recent developments in this field and outlines issues to be solved in future research.

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An experimental investigation of the fine-scale structure of turbulence was carried out. Five different shear flows were studied: three in a wind tunnel with an open working section and an elliptical nozzle and two in a wind tunnel of closed working section and square cross-section. The experiments tested two approaches to the theory of fine-scale turbulence structure: one based on the Navier-Stokes equations and the other on some similarity hypotheses. The variability of all fine-scale constants (including exponents in inertial-subrange power laws and the Kolmogorov constant) is revealed. A correlation between all fine-scale constants and the external intermittency coefficient is established.

In this work, we study the large-scale structure of homogeneous flows displaying high density contrasts and small turbulent Mach numbers. Following Batchelor & Proudman [1], we draw an analogy between this configuration and that of a single isolated eddy displaying density non-uniformities. By doing so, we are able to highlight the crucial role played by the solenoidal component of the momentum in the preservation of initial conditions. In particular, we show that the large-scale initial conditions of the spectrum of the solenoidal momentum are preserved provided its infrared exponent is smaller than 4. This condition is reminiscent of the one usually derived in constant density flow, except that it does not apply to the velocity spectrum. The latter is actually shown to be impermanent for infrared exponents larger or equal to 2. The consequences of these properties on the self-similar decay of the flow are discussed. Finally, these predictions are verified by performing large eddy simulations of homogeneous isotropic turbulence.

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