Numerical simulation of scalar mixing from a point source over a wavy wall

The mixing of transported scalars in turbulent flows is a classic topic in turbulence research. The “diffusing power” of turbulent flows was originally recognized, among others, by Taylor (1915) since the beginning of the last century. Later on, Taylor (1921, 1935) also provided the first statistical framework to predict turbulent diffusion in air streams, as well as the scalar mixing in pipe flows (Taylor 1953, 1954). Although such fundamental work still forms the basis for the theoretical analysis of turbulent diffusion, over the last fifty years laboratory experiments and numerical simulations have profoundly advanced the understanding of the mixing process occurring in turbulent flows. An excellent review of this topic has recently been presented by Dimotakis (2005), while the recent achievements in passive scalars mixing, when flow dynamics proceeds independently from the mixing process, can be found in Warhaft (2000). Among the several flow phenomena relevant to the analysis of turbulent mixing, our attention and research efforts are directed towards the modeling of scalar dispersion from localized sources in complex flows (Rossi & Iaccarino 2009b). The present analysis is motivated by the need to obtain a deeper insight into turbulent mixing occurring in the presence of complex flow features, which may severely affect the reliability of simplified theoretical and numerical models. For example (Rossi & Iaccarino 2008), the analysis of scalar dispersion from a line source downstream of a square obstacle has clarified that gradient-transport models based on the Standard Gradient-Diffusion Hypothesis (SGDH) are unable to predict the streamwise component of scalar fluxes. On the other hand, a preliminary evaluation of refined gradient-transport closures for the same flow setup (Rossi & Iaccarino 2009a) suggests that Algebraic Flux Models (AFMs) yield reasonable predictions of the scalar flux anisotropy. However, the limited amount of experimental data for the obstacle flow made it difficult to perform a meaningful and comprehensive validation of algebraic closures. The release of a passive tracer from a point source over a wavy wall is adopted in this work to investigate the scalar mixing over complex topography using Direct Numerical Simulations (DNS). It is worth noting that a comparative analysis of low-order statistics against the present DNS data (Rossi 2009b) established that algebraic flux models are able to capture the complex development of scalar fluxes in the far field over the wavy boundary, but not in the neighborhood of the source. Here, we intend to provide a deeper insight into the physics of the scalar mixing process as well as some of the rationale behind the capabilities and limitations of algebraic closures.