Thermally-driven secondary flows in turbulent channel flow: Prandtl's secondary flow of the third kind

Turbulent secondary flows are classified as Prandtl's secondary flow of the first or second kind, where the former is produced by stretching and/or tilting of vorticity while the latter is produced by spatial heterogeneity in the Reynolds stresses. While previous studies have focused on spanwise variability in surface roughness, which can produce heterogeneity in Reynolds stresses (Prandtl's secondary flow of the second kind), turbulent secondary flows driven by thermal gradients have received less attention. Using large eddy simulations of unstably-stratified turbulent channel flow with uniform aerodynamic roughness, but spanwise-variable surface heat flux, we demonstrate that spanwise thermal heterogeneity can produce turbulent secondary flows, defined hereafter as Prandtl's secondary flow of the third kind. Shear and buoyancy production over elevated heat flux regions necessitates lateral entrainment of low-TKE fluid, inducing mean counter-rotating cells aligned such that upwelling and downwelling occur over high and low heat flux regions, respectively. This result illustrates that buoyancy production of TKE alters aggregate flow response and thus is a distinctly different mechanism responsible for sustenance of secondary flows than others identified previously.