The logarithmic and power law behaviors of the accelerating, turbulent thermal boundary layer

Abstract

Direct numerical simulation of spatially evolving thermal turbulent boundary layers with strong favorable pressure gradient (FPG) shows that the thermal fluctuation intensity, θ′+ and the Reynolds shear stress, u′v′¯+ exhibit a logarithmic behavior spanning the meso-layer (e.g., 50≤y+≤170). However, the mean thermal profile is not logarithmic even in the zero pressure gradient (ZPG) region; instead, it follows a power law. The maxima of u′2¯+ and v′θ′¯+ change little with the strength of acceleration, while v′+, w′+, and u′v′¯+ continue to decay in the flow direction. Furthermore, θ′+ and u′θ′¯+ surprisingly experience changes from constants in ZPG to sharp rises in the FPG region. Such behavior appears to be due to squashing of the streaks which decreases the streak flank angle below the critical value for “transient growth” generation of streamwise vortices, shutting down production [W. Schoppa and F. Hussain, “Coherent structure generation near-wall turbulence,” J. Fluid Mech. 453, 57–108 (2002)]. The streamwise vortices near the wall, although shrink because of stretching, simultaneously, also become weaker as the structures are progressively pushed farther down to the more viscous region near the wall. While the vortical structures decay rapidly in accelerating flows, the thermal field does not—nullifying the myth that both the thermal and velocity fields are similar.