Spectral analysis on dissimilarity between turbulent momentum and heat transfers in plane Couette turbulence

Abstract

Nonlinear interaction between different scales in turbulence results in both interscale and spatial transport of turbulent energy, and the role of such scale interactions in turbulent heat transfer mechanism is also of practical importance from the engineering viewpoint. In the present study, we investigate a turbulent plane Couette flow with passive-scalar heat transfer at the Prandtl number 0.71, in order to address the similarity/difference between the scale interactions in the velocity and temperature fields. The constant-temperature-difference boundary condition is used so that the mean velocity and temperature profiles are similar, and then the roles of interscale and spatial transports are compared for the spectral transport budgets of the turbulent energies and temperature-related statistics. We show that turbulent heat transfer occurs at relatively small streamwise length scales compared to momentum transfer, although molecular diffusion is more significant in the temperature field as the Prandtl number is less than 1. Detailed analysis on the transport budgets of the temperature-related spectra shows that scale interactions in temperature field supply more energy to small scales than those in velocity field. Such significant temperature cascade leads to more energetic temperature fluctuation at small scales, which eventually results in the dissimilarity between the spectra of turbulent heat and momentum transfers.