Energetic structures in the turbulent boundary layer over a spanwise-heterogeneous converging/diverging riblets wall

Abstract

Time-invariant (or mean) secondary flows, in terms of large-scale counter-rotating roll modes filling boundary layer, have been observed in turbulent boundary layer (TBL) flows over various spanwise-heterogeneous rough walls. Recent studies show that these mean secondary flows are inherently connected with instantaneous large-scale structures in TBL flows over such spanwise-heterogeneous rough walls. In this work, the technique of proper orthogonal decomposition (POD) is used to extract dominant energetic (and thus large-scale) structures from TBL flows over the surface with a spanwise-periodic converging/diverging riblets pattern, one of the spanwise-heterogeneous rough walls adopted previously. POD analyses are conducted on the three fluctuating components of velocities, measured by stereoscopic particle image velocimetry at Reθ = 13 000, in a cross-stream plane of the TBL flows over a spanwise section of the converging riblets pattern, where low-momentum eruptions consistently occur. It is found that first two POD modes with large temporal coefficients are linked to large-scale structures oscillating vigorously in the transverse direction within one section of the converging riblets. Superposition of these instantaneous large-scale structures reveals the observed pattern of mean secondary flows. Furthermore, these large-scale structures are associated with enhanced streamwise vortices and spanwise gradients of the streamwise velocity, compared with that in the smooth wall flow, thus rendering profound effects on the spatial correlations of velocities as well as the distributions of Reynolds stresses.