Turbulent boundary layer response to large-scale wavy topographies

Flat-plate turbulent boundary layer adjustment to large-scale 2D and 3Dwavy topographieswas experimentally studied using high-resolution particle image velocimetry in a refractive-index-matching flume. The flowwas characterized at a Reynolds number Re = 4×10⁴, based on the channel half height and incoming free-stream velocity. Two ratios of amplitude (a) to incoming boundary layer thickness (δ₀) were considered for each topography (a/δ₀ = 0.12 and 0.81). The 2D topography is described by a sinusoidal wave in the streamwise direction with an amplitude to wavelength ratio a/λ_x = 0.05, while the 3D topography is defined with an additional wave superimposed in the spanwise direction. The results show that the spanwise variability of the topography leads to a much milder response in both a/δ₀ ratios. The regions of strong acceleration and deceleration over the crests and troughs of the topography are reduced over the 3D topography due to the alternate flow path around the 3D elements. Furthermore, the boundary layer thickness and integral parameters experienced milder variations over the 3D topography for both a/δ₀. The Reynolds shear stress shows distinctive evolution with downstream distance. In the 3D case, maximum Reynolds stress similar to those in the developed region is achieved within the first three wavelengths past the topographic change indicating that the dynamics of the downstream evolution is dominated by vertical diffusion and redistribution. This is in contrast with the 2D case with a/δ₀ = 0.12 where the Reynolds stress did not achieve the levels observed in the developed region.