Effect of Reynolds number on a high-speed cold-wall turbulent boundary layer

Direct numerical simulation (DNS) of a Mach 4. 9 zero-pressure-gradient turbulent boundary layer spatially developing over a cooled flat plate at wall-to-recovery temperature Tw/Tᵣ = 0. 60 is performed. Very long, streamwise contiguous domains are used in the DNS to achieve a wide continuous range of ‘useful’ friction Reynolds numbers of 1000 Re_ 2500. The DNS datasets have been analysed to assess state-of-the-art compressibility scaling relations and turbulence modelling assumptions. The DNS data show a notable distinction in Reynolds number dependence between thermal and velocity fields. Although Reynolds stress and the budgets of turbulent kinetic energy have reached Reynolds number independence in the inner layer under semi-local scaling by Re_ 1000, the budget terms for temperature variance and turbulent heat flux retain a clear Reynolds number dependence near the wall over a broader range up to Re_ 1900. Such a stronger dependence of the thermal field on the Reynolds number may lead to inaccuracy in turbulence models that are calibrated on the basis of low-Reynolds-number data. Spectral and structural analysis suggests a more significant reduction in the prevalence of alternating positive and negative structures and an increase in the streamwise uniformity of streaks in the wall heat flux qw than in the wall shear stress w when the Reynolds number increases.