Spanwise varying surface temperature generates secondary flows, therefore mimicking a rough surface Bon et al., J. Fluid Mech. 970, A20 (2023). A series of large-eddy simulations (LES) are performed to evaluate the secondary flows generated by thermal heterogeneity for a friction Reynolds number (Reτ=395). Digital filtering method Klein et al., J. Comput. Phys. 186, 652–665 (2003), an artificial inflow generator, is used to generate turbulence and is allowed to convect through the inflow plane by applying Taylor's hypothesis. Thermal heterogeneity is set along the spanwise direction, whereas along the streamwise direction, it is homogeneous. Spanwise thermal heterogeneity is induced by varying two parameters, viz., the temperature ratio of hot strip to cold strip (ϕ=θh/θc) and the aspect ratio (λ=lh/lc). Results indicate that high- and low-momentum pathways are induced in the flow field, analogous to the spanwise heterogeneous rough surfaces. The effect of ϕ and λ on the convective mode of heat transfer close to the wall and its influence on the mean flow structures and anisotropy is studied. The implications of the near-wall behavior on the flow at the channel core are captured through an anisotropic invariant map (Lumley triangle). The buoyancy effect near the wall downplays the fluctuation components, rendering the anisotropy along the axisymmetric expansion limit. The fluid displaced by fluctuating velocity components in the wall-normal direction is analyzed through buoyancy frequency number (N) or Brunt–Väisälä frequency. The flow field characterization facilitated by varying the shear Richardson number in the range 0≤Riτ≤267 demonstrates a vanishing buoyancy flux at the center despite strong temperature and velocity fluctuations.
Bhaskar et al. (Tue,) studied this question.