Sub-filter-scale stress and heat flux in hypersonic Couette flow and a flat-plate boundary layer
A comparative study of sub-filter-scale (SFS) quantities in hypersonic Couette flow and flat-plate boundary layer turbulence under strongly cooled-wall conditions is carried out using filtered direct numerical simulation (DNS) data to characterize the differences in SFS dynamics between internal and external wall-bounded turbulence. The two flows exhibit similar near-wall behaviour in the mean velocity profiles and SFS stress components; however, marked differences emerge in the outer layer and thermal structure. The two configurations also exhibit different thermal fields, leading to different temperature-velocity relations. The SFS behaviour shows strong sensitivity to the filtering operation: the top-hat filter yields larger SFS magnitudes, whereas the sharp spectral filter preserves a distinct spectral separation near the cutoff, leading to characteristic SFS features. Decomposition of the SFS terms shows that the residual component provides the dominant contribution to the mean SFS shear stress and heat flux. Differences between the two flows are primarily associated with the interaction terms between the resolved and residual components, which contribute with opposite signs in the two configurations, consistent with their different thermal structures. The different thermal structures also lead to distinct SFS heat-flux behaviour, including a sign change in the flat-plate boundary layer. Instantaneous SFS fields further reveal that local extrema arise from the combined contributions of multiple decomposed terms. Although these terms exhibit large local fluctuations, their net contributions to the averaged SFS quantities are relatively small. The trace of the SFS stress exhibits local negative values, reflecting local energy redistribution across the filter scale rather than a loss of physical energy.