In assumed probability density function (pdf) methods of turbulent combustion, the shape of the scalar pdf is assumed a priori and the pdf is parametrized by its moments for which model equations are solved. In non-premixed flows the beta distribution has been a convenient choice to represent the mixture fraction in binary mixtures or a progress variable in combustion. Here the beta-pdf approach is extended to variable-density mixing: mixing between materials that have very large density differences and thus the scalar fields are active. As a consequence, new mixing phenomena arise due to 1) cubic non-linearities in the Navier-Stokes equation, 2) additional non-linearities in the molecular diffusion terms and 3) the appearance of the specific volume as a dynamical variable. The assumed beta-pdf approach is extended to transported pdf methods by giving the associated stochastic differential equation (SDE). The beta distribution is shown to be a realizable, consistent and sufficiently general representation of the marginal pdf of the fluid density, an active scalar, in non-premixed variable-density turbulent mixing. The moment equations derived from mass conservation are compared to the moment equations derived from the governing SDE. This yields a series of relations between the non-stationary coefficients of the SDE and the mixing physics. Our treatment of this problem is general: the mixing is mathematically represented by the divergence of the velocity field which can only be specified once the problem is defined. In this paper we seek to describe a theoretical framework to subsequent applications. We report and document several rigorous mathematical results, necessary for forthcoming work that deals with the applications of the current results to model specification, computation and validation of binary mixing of inert fluids.
Exploring 2D turbulent properties in anisotropic and disordered Fourier space: Insights into inverse cascades and universal superdiffusion from randomly sampled triadic interaction
National Research Council, Institute of Atmospheric Pollution Research（国家研究委员会，大气污染研究所）；University of Calabria（卡拉布里亚大学）；Dipartimento di Fisica, University of Calabria（卡拉布里亚大学物理系）
Application of Helmholtz-Hodge decomposition and conditioned structure functions to exploring influence of premixed combustion on turbulence upstream of the flame
Superstatistical Approach to Turbulent Circulation Fluctuations
Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）；Instituto de Física, Universidade Federal do Rio de Janeiro（里约热内卢联邦大学物理研究所）；Department of Mechanical and Aerospace Engineering, New York University（纽约大学机械与航空航天工程系）；Department of Physics and Courant Institute of Mathematical Sciences, New York University（纽约大学物理系与库朗数学科学研究所）；Santa Fe Institute（圣塔菲研究所）；Complexity Science Hub Vienna（维也纳复杂性科学中心）；Dipartimento di Fisica e Astronomia Ettore Majorana, University of Catania（卡塔尼亚大学埃托雷·马约拉纳物理与天文学系）
