Role of large scale motions on passive scalar transport in a turbulent channel

The prominence of passive scalar transport in turbulent flows is accentuated by the number of applications and the fundamental significance of the problem. The concept of organized motions has provided a new view point to tackle the conundrum of turbulence. It has been found that organized motions are pervasive in all classes of turbulent flows. Besides its inherent complexity, wall-bounded turbulent flows has received the most attention in the history due to the practical significance of the problem. Therefore, organized motions in wall-bounded turbulent flows have been investigated extensively. Recently, large scale organized motions which are mostly populated above the buffer region were identified. They are commonly known as large scale motions (LSMs). Significance of LSMs in transporting turbulence kinetic energy as well as Reynolds stresses has been extensively studied. However, the importance of LSMs in scalar transport has not yet been investigated at least to the best of the author's knowledge. Hence, the present study aims to fill this gap in the existing literature. This study uses a direct numerical simulations (DNS) database of a fully developed turbulent channel flow at friction Reynolds number Re_τ of $394$ with temperature as a passive scalar. Molecular Prandtl number Pr is set to $0.71$. Both walls are isothermal, however, the lower wall of the channel is maintained at a higher temperature than that of the upper wall. Periodic boundary condition is imposed in both homogeneous directions of the channel. Two widely used techniques have been exploited in analyzing the problem: two-point correlations and proper orthogonal decomposition (POD). Three-dimensional two-point correlations were computed based on three reference points along the inhomogeneous wall-normal direction. The reference points are located at y^+=20, y^+=69, and y^+=170 representing buffer layer, log-layer, and wake region of the channel respectively. Two-point correlation analysis reveals that the structure which is dominant in transporting the streamwise component of the turbulence kinetic energy and turbulence scalar variance resembles a hairpin vortex packet. Three-dimensional scalar POD was computed to identify the most energetic modes that are responsible for three components of the turbulence kinetic energy and the turbulence scalar variance. It was found that the most energetic modes of u^'2 are responsible for the most of the turbulence kinetic energy. Integral length scales of modes for all the variables were computed to examine whether energy containing modes constitute large scale structures. The analysis revealed that the dominant modes in transporting streamwise component of the turbulence kinetic energy are accountable for LSMs with 3-4 channel half heights long. Moreover, the dominant modes that carry scalar variances constitute LSMs with streamwise length scale of 2-4 channel half heights long.