Reducing aerodynamic drag is crucial for lowering energy consumption and emissions in industries such asaviation and fluid transport through pipelines. In cruise conditions, skin friction drag is the dominant contributor to aerodynamic resistance and has therefore been the focus of numerous studies. A widely discussed technique for skin friction reduction is active forcing through spatio-temporal spanwise wall oscillations, which has been numerically shown to achieve drag reductions of up to 50%. This technique relies on creating a spanwise wall motion, generating a phase-varying spanwise velocity profile that suppresses near-wall turbulence. However, practical implementation remains challenging due to mechanical complexity and high energy costs, leading to interest in passive alternatives. Among these, dimples and Oblique Wavy Walls (OWW) are examples, as their surface deformations have shown to introduce a spatially varying spanwise shear layer into the flow. Through geometrical surface deformations pressure gradients are formed, which give rise to a spanwise component of the flow in the near-wall region. Although these techniques have demonstrated meandering flow structures, no significant drag reductions have been established previously. This motivates the investigation of sinusoidal undulations as a potential passive method for introducing a spatially periodic spanwise velocity component.

This thesis studies the flow topology of sinusoidal undulations to assess their ability to impose a spanwise shear layer. The geometry is characterised by a streamwise oriented sinusoidal groove, that displaces in the spanwise direction, having a dimple-like cross section. The influence of the geometry is assessed in terms of, spanwise displacement amplitude A, depth-to-diameter ratio d/D, and scale (while retaining geometric similarity). The flow over sinusoidal undulations was visualised by means of Particle Image Velocimetry (PIV) in (i) a stereographic PIV in the streamwise-wall-normal plane to quantify the spanwise velocity amplitude and the penetration depth, and (ii) a planar PIV in the streamwise-spanwise plane in the near-wall region (y = 1 mm) to examine the near-wall flow structure. These experiments were conducted in the M-tunnel of the Delft University of Technology.

Analysis of the experiments confirmed an alternating spanwise movement of the flow that aligns with the geometrical spanwise angle of the sinusoidal undulation. Simultaneously, the windward edges of the geometry act as diffusers, pushing part of the flow over the edge and out of the groove onto the flat area. These combined effects led to the identification of a converging-diverging flow structure, locally resembling dimple flow structure. Additionally, a relation was found between the undulation geometry and flow characteristics such as maximum spanwise velocity and penetration depth. While spanwise velocity oscillations were observed across all geometries, a larger geometrical displacement intensified the diffuser effect of the windward edges. The measured velocity magnitudes were comparable to other passive techniques, but lower than those achieved by active spatially periodic forcing with optimal actuation conditions for drag reduction. Furthermore, these velocities were associated with penetration depths into the buffer layer.

This study demonstrates that sinusoidal undulations are able to introduce a phase-varying spanwise velocity of w⁺≈ 1, or approximately 4% of the freestream velocity, forming a converging-diverging flow topology, bearing resemblance to dimples with comparable spanwise velocity amplitudes (w/U_∞ ∼ 3%). The measured spanwise velocity profiles exhibit similarities to the analytical solution of the spatial Stokes layer, though the penetration depth follows a different definition. The near-wall shear layer in the viscous layer resembles a horizontally mirrored Stokes layer, and is characterised by a secondary deeper penetration resultant from the imposed pressure gradient. To further assess the drag-reduction potential of sinusoidal undulations, drag balance measurements and numerical simulations are recommended.