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Three-dimensional particle tracking experiments were conducted in a turbulent boundary layer with friction Reynolds number $Re_tau$ of 700 and 1300. Two finite size spheres with specific gravities of 1.003 (P1) and 1.050 (P2) and diameters of 60 and 120 wall units were released individually from rest on a smooth wall. The spheres were marked with dots all over the surface to monitor their translation and rotation via high-speed stereoscopic imaging. The spheres accelerated strongly after release over streamwise distances of one boundary layer thickness before approaching an approximate terminal velocity. Initially, sphere P1, which had Reynolds numbers $Re_p$ of 800 and 1900, always lifts off from the wall. Similar behavior was observed occasionally for sphere P2 with initial $Re_p$ of 1900. The spheres that lifted off reached an initial peak in height before descending towards the wall. The sphere trajectories exhibited multiple behaviors including saltation, resuspension and sliding motion with small random bouncing depending on both $Re_tau$ and specific gravity. The lighter sphere at $Re_tau=1300$, which remained suspended above the wall during most of its trajectory, propagated with the fastest streamwise velocity. By contrast, the denser sphere at $Re_tau=700$, which mostly slid along the wall, propagated with the slowest streamwise velocity. After the spheres approached an approximate terminal velocity, many experienced additional lift-off events that were hypothesized to be driven by hairpins or coherent flow structures. Spheres were observed to rotate about all three coordinate axes. While the mean shear may induce a rotation about the spanwise axis, near-wall coherent structures and the spheres wake might drive the streamwise and wall-normal rotations. In all cases where the sphere propagates along the wall, sliding motion, rather than forward rolling motion, is dominant.
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This fluid dynamics video submitted to the Gallery of Fluid motion shows a turbulent boundary layer developing under a 5 metre-long flat plate towed through water. A stationary imaging system provides a unique view of the developing boundary layer as it would form over the hull of a ship or fuselage of an aircraft. The towed plate permits visualisation of the zero-pressure-gradient turbulent boundary layer as it develops from the trip to a high Reynolds number state ($Re_tau approx 3000$). An evolving large-scale coherent structure will appear almost stationary in this frame of reference. The visualisations provide an unique view of the evolution of fundamental processes in the boundary layer (such as interfacial bulging, entrainment, vortical motions, etc.). In the more traditional laboratory frame of reference, in which fluid passes over a stationary body, it is difficult to observe the full evolution and lifetime of turbulent coherent structures. An equivalent experiment in a wind/water-tunnel would require a camera and laser that moves with the flow, effectively `chasing eddies as they advect downstream.
On the basis of (i) Particle Image Velocimetry data of a Turbulent Boundary Layer with large field of view and good spatial resolution and (ii) a mathematical relation between the energy spectrum and specifically modeled flow structures, we show that the scalings of the streamwise energy spectrum $E_{11}(k_{x})$ in a wavenumber range directly affected by the wall are determined by wall-attached eddies but are not given by the Townsend-Perry attached eddy models prediction of these spectra, at least at the Reynolds numbers $Re_{tau}$ considered here which are between $10^{3}$ and $10^{4}$. Instead, we find $E_{11}(k_{x}) sim k_{x}^{-1-p}$ where $p$ varies smoothly with distance to the wall from negative values in the buffer layer to positive values in the inertial layer. The exponent $p$ characterises the turbulence levels inside wall-attached streaky structures conditional on the length of these structures.
The present numerical investigation uses well-resolved large-eddy simulations to study the low-frequency unsteady motions observed in shock-wave/turbulent-boundary-layer interactions. Details about the numerical aspects of the simulations and the subsequent data analysis can be found in three papers by the authors (Theo. Comput. Fluid Dyn., 23:79--107 (2009); Shock Waves, 19(6):469--478 (2009) and J. of Fluid Mech. (2011)). The fluid dynamics video illustrates the complexity of the interaction between a Mach 2.3 supersonic turbulent boundary layer and an oblique shock wave generated by a 8-degree wedge angle. The first part of the video highlights the propagation of disturbances along the reflected shock due to the direct perturbation of the shock foot by turbulence structures from the upstream boundary layer. The second part of the video describes the observed block-like back-and-forth motions of the reflected shock, focusing on timescales about two orders of magnitude longer than the ones shown in the first part of video. This gives a visual impression of the broadband and energetically-significant peak in the wall-pressure spectrum at low frequencies. The background blue-white colouring represents the temperature field (with white corresponding to hot) and one can clearly appreciate why such low-frequency shock motions can lead to reduced fatigue lifetimes and is detrimental to aeronautical applications.
A study of large-scale motions from a new direct numerical simulation database of the turbulent boundary layer up to Re{theta} ~ 2500 is presented. The statistics of large-scale streamwise structures have been investigated using two-dimensional and three-dimensional extraction procedures. The large-scale structures are abstracted using a robust skeletonization method usually applied to other research domains to simplify complex 3D objects. Different structure parameters such as the length, shape or angle are investigated. The features of the detected structures are compared to their mean counterparts extracted from two-point correlations. Structures as large as 10 boundary layer thickness are observed. The streamwise length of these structures follows a -2 power law distribution, similar to the experimental findings at higher Reynolds numbers.
The turbulent boundary layer over a Gaussian shaped bump is computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. The two-dimensional bump causes a series of strong pressure gradients alternating in rapid succession. At the inflow, the momentum thickness Reynolds number is approximately 1,000 and the boundary layer thickness is 1/8 of the bump height. DNS results show that the strong favorable pressure gradient (FPG) causes the boundary layer to enter a relaminarization process. The near-wall turbulence is significantly weakened and becomes intermittent, however relaminarization does not complete. The streamwise velocity profiles deviate above the standard logarithmic law and the Reynolds shear stress is reduced. The strong acceleration also suppresses the wall-shear normalized turbulent kinetic energy production rate. At the bump peak, where the FPG switches to an adverse gradient (APG), the near-wall turbulence is suddenly enhanced through a partial retransition process. This results in a new highly energized internal layer which is more resilient to the strong APG and only produces incipient flow separation on the downstream side. In the strong FPG and APG regions, the inner and outer layers become largely independent of each other. The near-wall region responds to the pressure gradients and determines the skin friction. The outer layer behaves similarly to a free-shear layer subject to pressure gradients and mean streamline curvature effects. Results from a RANS simulation of the bump are also discussed and clearly show the lack of predictive capacity of the near-wall pressure gradient effects on the mean flow.
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