Effects of pressure gradients and roughness on transfer entropy in wall turbulence

Using DNS of a turbulent boundary layer with heat transfer, we pursue transfer entropy approach to study causality among various instantaneous variables in wall turbulence perturbed by pressure gradients (due to a smooth bump) and organized roughness (longitudinal grooves). We investigate the origin of low-frequency oscillations of the separation bubble (SB) downstream of the bump, and the connection between the flow separation induced by mean streamline curvature upstream of the bump and the downstream SB dynamics. The causal link between negative production in the accelerating flow and the coherent structures in the flow is established. The spinning streamwise jets generated by longitudinal grooves are quantitatively connected to the modified turbulence intensity within the shear layer resulting from their interaction with spanwise vortices (as well as the altered reattachment dynamics of the SB). The complicated shear layer dynamics are linked to the upstream moving minibubbles embedded within the SB. Preliminary findings suggest a strong relationship between the flow dynamics near the wall upstream of the bump—where intermittent separation occurs on a smooth bump or steady separation with grooves—and the unsteady behavior of the SB and its reattachment region. A particular focus is the explanation of the the failure of the Reynolds analogy between heat and momentum transports, assessing the causal relationship between heat flux, shear stress, coherent structures, pressure gradients and roughness. Employing transfer entropy measures of pressure (gradient), velocity, and vorticity to temperature and wall heat flux is pivotal for pinpointing the precise reasons why the Reynolds analogy fails at distinct locations.