Two-scale solution for tripped turbulent boundary layer

Recent findings on the Reynolds-number-dependent behaviour of near-wall turbulence in terms ‘foot-printing’ outer large-scale structures call for a new modelling development. A two-scale framework was proposed to couple local fine-mesh solution with global coarse-mesh by He ( Intl J. Numer. Meth. Fluids , vol. 86, 2018, pp. 655–677). The methodology implemented and demonstrated Chen & Fluid Mech 933, 2022, p. A47) canonical turbulent channel flow, where mesh-count scaling Reynolds number is potentially reduced from $O(R{e^2})$ conventional wall-resolved large-eddy simulation (WRLES) $O(R{e^1})$ . present work extends method boundary layers. two-dimensional roughness element used trip layer. It observed that disturbances originating at have much shorter lifetime weaker foot-printing signatures flow compared those long streaky coherent well-developed wall-bounded flows. Modal analyses show impact trip-induced large scales can be adequately captured locally embedded block. For tripped layer, Chebyshev block-spectral mapping adopted propagate source blocks domain, driving target upscaled equations. computed mean statistics energy spectra are good agreement corresponding experimental data, WRLES direct numerical (DNS) results. overall mesh count– $Re$ estimated reduce $O(R{e^{1.8}})$ full LES $O(R{e^{0.9}})$ solution.