Scale Interactions in Flow Overlying Spanwise-, Streamwise-, and Obliquely-Varying Surface Roughness*

Flow overlying streamwise-elongated ridge-type (spanwise heterogeneous) roughness features the formation of turbulent secondary flow of streamwise aligned counter rotating vortex cells flanking and centering on individual ridges. This flow phenomenon alters the momentum transfer and turbulence production relative to smooth-wall turbulence. In practical applications, the predominant direction of roughness variability can change relative to the oncoming flow direction. In the extreme case, when the flow orientation is perpendicular to the ridges, the flow is dominated by streamwise repeating wakes tripped by the ridges when the spacing of the ridges is fully separated and the height of the ridges is not very small relative to the boundary layer thickness. In more scenarios, the flow is likely to orientate in an oblique angle to the ridge-type roughness, and it is observed that in this case the flow reflects a mixture of pure secondary flow and wake shedding from upstream ridges. In this work, high-frame-rate stereo PIV data and high-frame-rate dual-camera big/small field of view planar PIV data are used to study the scale interactions in turbulent flow overlying spanwise-, streamwise-, and oblique-ridge-type roughness, and to investigate how orientation angle influences the dominant flow characteristics. A pointwise method of modulation analysis is used to quantify the degree of interaction between inner and outer scales. The spatio-temporal nature of PIV data further enables a conditional average method to extract scale interactions in a spatio-temporal sense.