Role of coherent structures in the transport equation for the vorticity–temperature correlation

Abstract

Understanding scalar transport phenomena is crucial for effective turbulent mixing in various applications. However, this process is complex and challenging to grasp. Coherent structures offer insight into the mechanisms governing scalar dynamics in turbulent flows and can serve as a valuable tool for developing turbulence models. This study presents theoretical and numerical investigations of the transport equation for the vorticity–temperature correlation, known as “scalicity.” The transport equation for scalicity was derived through order estimation. Direct numerical simulations of turbulent-plane Couette flows with passive scalar transport were conducted. A notable spanwise-averaged scalicity fluctuation component was identified in the viscous and buffer layers. This component was analyzed by examining the high correlation between spanwise vorticity and temperature fluctuations, evaluating quadrant contributions, and decomposing the terms. Visualization of the instantaneous field with spanwise scalicity fluctuations highlighted the cyclical relationship between velocity streaks and longitudinal vortices and the unstable wall vorticity layer in turbulent heat transfer. Budget analysis of the transport equation provided insights into the velocity and temperature streaks associated with turbulent eddy structures.