The streamwise and vertical components of the second eigenmode are shown in figures 6(c, d), respectively, and portray a rather different organization. Figure 6(c) shows two large-scale regions of relatively uniform opposed streamwise velocity fluctuations, oriented parallel to the wall and elongated in the streamwise direction. The width of these regions is approximately δ, and they extend the streamwise length of the measurement domain. Note the amplification in fluctuation magnitude throughout the interaction. Such an organization can be viewed as a subspace bifurcation, where the term bifurcation refers to the qualitative changes observed. Bifurcations lead to an increase in the number of spatially extended subspace regions with definite sign. Figure 6(c) therefore shows a region that bifurcates into two large-scale regions of opposite sign. These features can be thought of as subspace representations of the low- and high-speed streamwise-elongated regions observed within the incoming boundarylayer. The superposition of these fluctuations onto the mean flow returns an undulating pattern of the reflected shock foot; a behaviour that can be observed in the instantaneous realizations [e.g., figures 4(a, b)]. Thus, it appears that this eigenmode captures the spanwise rippling component of the observed reflected shock foot patterns. Figure 6(d) shows that the corresponding vertical component exhibits a similar organization to its first mode counterpart. Therefore, the simple model described by the second eigenmode is that streamwise- elongated regions of alternating sign within the incoming boundarylayer correspond to an undulating behaviour of the reflected shock foot.
locity field, or secondary flow, with simple spatial spectral composition in the flow. This mean velocity field interacts nonlinearly with the turbulence of the boundarylayer at a range of other scales to alter the mean quantities of the flow. Due to the large wall-parallel wavelengths compared to the boundarylayer thickness and non-negligible amplitude, the e ff ects of the roughness extend through much of the boundarylayer, and hot wire anemometry can be used to measure the spatial vari- ation in mean quantities, statistics, and power spectra required to trace the e ff ects of the roughness. The non-linear forcing field of the rough wall is modeled in the simplest possible way, as a perturbation to the smooth-wall forcing which involves only the roughness wavenumber and two additional convecting wavenumbers. Real-world roughness is substantially more complicated than the present case of one or two individual sinusoids. It may take as many as 16 modes (Mejia-Alvarez and Christensen ) to accurately reproduce mean-flow quantities of interest for rough-wallboundary layers. Due to the nominally-linear nature of the boundary condition, it is proposed that the e ff ects of a number of these simple roughnesses can be linearly superposed to predict the behavior of a real-world roughness in wall- bounded flow. The validity of such linear superposition is consistent with the results of the R2M case, where the individual scale modulation plots of the streamwise- only mode and of the spanwise-only mode were well predicted by their respec- tive ζ calculations. The lack of fidelity between ζ and scale modulation for static wavenumbers which are not directly imposed does point to a gap in the modelling procedure, but this may not be so significant for real world flows, where roughness exhibits a broad range of wavenumbers. In those circumstances, the mechanism for scale modulation modelled here may dominate the mechanisms for scale modula- tion at harmonic static wavenumbers which are not captured. Roughnesses outside the “wavy-wall” regime have also not been evaluated within this framework. The steeper slopes associated with shorter wavelengths may cause a persistent separa- tion bubble which would introduce more scales into the flow at the wall.
Time sequence signals of instantaneous longitudinal and normal velocity components at different longitudinal and nor- mal positions in a turbulentboundarylayer have been finely measured simultaneously by IFA300 constant temperature anemometer and double-sensor hot-wire probe with sampling resolution higher than the frequency that corresponds to the smallest time scale of Kolmogorov dissipation scale before/after introducing artificial periodic blow/suction pertur- bation. The period-phase-average technique is applied to extract the periodic waveforms of artificial perturbation from instantaneous time sequence signals of longitudinal and normal turbulence background. Experimentalinvestigation is carried out on the attenuation characteristics of periodic perturbation wave with different frequency along longitudinal direction and normal direction in a turbulentboundarylayer. The amplitude distributions of longitudinal and normal disturbing velocity component for different perturbation frequencies are measured at different downstream and normal positions in turbulentboundarylayer. The amplitude growth rate of artificial periodic perturbation wave is calculated according to flow instability theory. The experimental results are compared and in consistent with the theoretical and numerical results.
The blur aspect of the shock wave is the result of the Schlieren spatial integration and demonstrates that the shock is curved, in particular in the foot region of the shock. This feature reflects the three- dimensional nature of the interaction, as confirmed by China clay surface visualizations. Wall corner vortices were clearly detected downstream of the shock wave and, as a result, a quasi-two- dimensional flow region subsists around the centerline of the bump, covering about 30% of the test section bump span. The current investigation focuses on the two-dimensional region of the interaction, and all wall measurements were carried out in the centre line of the bump model. But the strong three-dimensionality of the interaction should be kept in mind as it might be itself a source of unsteadiness, as stressed by Dussauge et al. . 3.2 Optical Shock unsteadiness measurements
Section E.1 provides an introduction to these materials, their actuation mechanism, and a brief review of the literature on IPMCs. The experimental systems used to study these materials are then reviewed in Section E.2. This is followed by the results of a number of experiments. In Section E.3, IPMC samples were actuated in a cantilevered configuration, similar to tests performed in the literature. This was done to understand the repeatability of actuation, hydration requirements, and the response of the IPMC to different voltage inputs. Next, two different methods were used to try and create a dynamic roughness. Section E.4 describes the first setup where a portion of an IPMC surface was rigidly bonded to a base electrode while a small portion was left free to actuate. This sort of actuation was limited to low frequencies, much like the cantilever configuration, but was capable of producing a large peak-to-peak roughness amplitude. In order to try and achieve higher actuation frequencies, the IPMC surface was fully adhered to the base electrode using a conductive gel as described in Section E.5. Here the mechanism for actuation was expected to be a wrinkling or buckling of the surface as described in Section E.1 as opposed to bending, as was the case for the rigidly bonded IPMC in Section E.4. In the end, this second method was only capable of producing small (several micron) variations in the roughness amplitude for frequencies under 10Hz.
RANS simulations and PLS imaging confirmed outer shock strengths in excess of the 2-D oblique limit for the H-I SBLI, which occur due to the combined influence of a streamwise area contraction effect and shock-shock interactions. The severity of these mechanisms scales with a confinement parameter, h/R, as validated by experiments at different ramp heights and constant angle for the H-I interaction. Because the captured streamtube of the H-I interaction is not completely enclosed, the effective confinement parameter reduces with distance away from the midspan due to 3-D relieving. This leads to a circumferential variation in compression strength and a swept outer shock structure. While these negative curvature confinement effects do not significantly alter the static pressure rise across the separation from that of a 2-D case, they do cause a stronger adverse pressure gradient downstream of the compression corner. This increased adverse pressure gradient may necessitate the development of a higher peak velocity on the dividing streamline and a larger separation length, similar to what has been observed for SBLIs in rectangular channels [46, 78]. An additional constriction of the virtual throat at the H-I SBLI exit was also ascertained. The effect of this area reduction is in an increase in the mass being carried toward spillage by the separation bubble, which may also result in larger L sep values given similar wall pressure distributions across the interactions.
The plate has an elliptic leading edge and it is fastened about 0.15 m above lower wall of test section. The transition sandpaper-belt (grits 60; width: 0.05 m) is glued on the plate 0.1 m downstream from the LE as to stabilize the laminar turbulent transition location. A flap (chord: 0.075 m; deviation: 10°) is attached at the plate’s trailing edge as to remove the circulation round the plate. The streamwise pressure gradient is imposed on the flat plate boundarylayer by a displacement body fastened to the upper wall. The flow acceleration begins 0.15m downstream LE. The flow velocity is reaching maximal value 31 m/s in the cross section 0.45 m downstream LE and the flow deceleration starts 0.75 m downstream LE in the section x = 0. The plane diffuser (length 1 m; opening angle: 11.3°) has the deflected wall made from fine woven screen. Suction through this wall prevents flow separation in the diffuser. More details are given in the caption of figure 1. Similar modelling of decelerating flow is still employed e.g. Marxen et al.  and Uruba .
The baseline shock-wave/boundary-layer interaction (SWBLI) revealed a strong interaction with massive mean flow separation. Excellent agreement between LES and experiment in terms of mean wall-pressure evolution has been found, confirming the ability of our LES solver to correctly predict SWBLI at high Reynolds numbers. The pressure plateau within the recirculation zone is perfectly reproduced in the simulation, from which we conclude that the present experimental setup is sufficiently two-dimensional and accessible through simulations with assumed homogeneity in spanwise direction. Unsteady wall-pressure measurements revealed a low-frequency unsteadiness associated to the reflected shock foot. Power spectral densities within the separated zone agree very well with experimental findings. However, the unsteady shock motion is not properly captured in the experiment with the available sensors.
To make tests at different wall temperatures, resistive heaters have been applied to the bottom of the insert to uniformly increase its temperature. The requirements for the heating are high power-density, in order to min- imize the heating period, and minimum thickness, to avoid fitting prob- lems into the nozzle ramp. Considering those specifications, Minco Ther- mofoilTM heaters were chosen. They consist of a flexible etched-foil resis- tive heating element, which is laminated between two Polyimide layers. An aluminum backing foil combined with a layer of acrylic pressure-sensitive adhesive allowed a simple application directly to the bottom of the insert. The maximum operating temperature of this heater configuration is 150 C, but the maximum temperature reachable in testing is determined by the Upilex adhesive properties. According to the company specifications, they should not experience a dramatic degradation if 120 C are exceeded. How- ever, past experience with Upilex sheet has proven that the glue can already form bubbles below the sheet if heated to temperatures much lower than 120 C. These bubbles resulted in deformations of the flat surface, which, in turn, affected the boundarylayer flow. In the end, to avoid such bubbles the heaters power was kept always as low as not to give a wall temperature larger than 50 C. Four heaters have been applied to the bottom of the plate, one big quadratic element on the front, and three rectangular ones on the aft covering as much as possible the surface around six screw holes (Fig. 3.5).
Despite of frequently mentioned applications in the industry, to the best knowledge of authors, no analytical solution has been presented for turbulentboundarylayer flow over a flat plate yet. The only accomplished research in this field is based on direct numerical simulation. This simulation is based on four common turbulence models: algebraic K , K and Reynolds stress modeling [3, 15]. Still there is much debate about similarity solutions of turbulentboundarylayer on the flat plate or pressure gradient. In addition, knowing these solutions is useful for better understanding of turbulence concepts; it helps us to guess an accurate initial scale for the experimental studies using wind tunnel . It should be mentioned that turbulentboundarylayer flow is more complicated than shear flow and turbulent jet flow because of the presence of a solid wall that imposes an additional force to the problem. It is obvious that fluid viscosity exerts no-slip condition to boundarylayer conditions i.e. fluid velocity on a solid surface must be equal to the surface velocity [16, 17]. Ganji et al.  investigated the problem of forced convection over a horizontal flat plate
Single model turbines and miniature wind farms have been experimented with in various scales and arrangements, placed in artificially thickened boundary layers. Chamorro & Porté-Agel have shown that upstream turbines impart a signature of shed tip vortices in the velocity spectra of the wakes of downstream turbines . Wind tunnel experiments from Bossuyt show that there are important temporal correlations in turbine power output from the influence of other turbines in the array . This unsteadiness and variability of the flow can affect wind farm power optimization. Iungo found from wake measurements of a 3 bladed model turbine that the hub vortex oscillates si- nusoidally only in the near wake  in agreement with others [89, 120]. Howard et. al. performed a PIV experiment with two turbines and found that near wake meandering is governed by interac- tion between bluff body hub vortex shedding and higher momentum fluid entrained along the tip vortex shear layer . For a porous disk without a hub, España found that no defined periodic alternations takes place in a flow with high turbulence (12% turbulence intensity) in a simulated atmospheric boundarylayer. The higher turbulence forces a weaker spectral energy peak. Contigu- ous vortices can be shed at different circumferential locations on a disk, and this non-deterministic feature can be affected by upstream turbulence intensity and velocity gradients . This would imply that wake meandering exists, but with no defined periodicity. Medici found that for lower λ (tip speed ratios) the Strouhal number is large and the effective diameter of the turbine becomes smaller when the rotational speed is decreased . In a 3x3 experimental wind farm array set up by Coudou, the Strouhal number was found to be St = f s D
The seminal publications by Kramer (1957, 1960) [37–39] were inspired his obser- vation of wave-like ripples forming on the skin of dolphins as they swam. Kramer hypothesized that, like the dolphins, one could reduce the frictional drag on a ship by applying a compliant coating to its hull, tuned to damp Tollmien-Schlichting (T-S) instabilities and delay transition to turbulence. He created flexible rubber coatings that were filled with silicone oil or other viscous fluids, and applied the coatings to a model that he then towed behind a motor boat in Long Beach Harbor, California. Kramer reported drag reduction in excess of 50% with these coatings, a result which quickly drew the attention of many researchers. Several follow-up studies failed to replicate Kramer’s drag reduction findings, leading to a good deal of controversy to surround the quickly booming field of compliant coatings. It is now appreciated that experimental investigations concerning drag reduction via compliant surfaces require extremely well controlled conditions. Many factors such as freestream turbu- lence and slight geometrical surface defects can adversely affect the drag outcome, and are likely a large part of the inconsistent results in the early literature. Though there was a large body of skeptics, the numerical and analytical studies by Carpenter [5, 6] and Carpenter & Garrad  and the experiments of Gaster  suggested that a Kramer-type surface could indeed delay transition and yield significant drag reduction. Carpenter et al. (2000)  suggested that an optimized coating may in fact play an important role in the efficient swimming of dolphins by maintaining laminar flow along their skin, as envisioned by Kramer.
A supplementary understanding of how the 3-D relief offered by the cylindrical surface influences the SBLI unit was acquired using RANS simulations. The flowfield was inter- rogated with US3D, an unstructured finite-volume Navier-Stokes solver developed at the University of Minnesota [ Nom04; Nom05; Sub09 ] . The upwind, modified Steger-Warming flux due to [ Mac89 ] was used to compute the fluxes. Viscous fluxes were formed using a central, second-order accurate method. An implicit Data Parallel Line Relaxation (DPLR) scheme [ Wri98 ] was used for time integration. Turbulence closure was obtained via the RANS form of the Spalart-Allmaras eddy-viscosity model [ Spa92 ] . Half of the experimental test article (cut about the X Y plane of symmetry) was modeled in the RANS simulation to save on computational resources, ultimately utilizing approximately 5 million cells and L × W × H domain dimensions of 150 mm × 90 mm × 100 mm to fully encapsulate the SBLI. The grid for this fin-cylinder geometry was generated using GridPro, a commercial grid generation software for creating multi-block hexahedral element grids. The cells near the cylinder surface were clustered using GridPro such that the first wall spacing ensured a y + of less than one. RANS simulations were also performed on a grid of roughly 40 million cells (not shown) with no significant differences in the results shown here, providing confidence to the presented results being accurate enough for the comparisons made.
The experimentalinvestigation was undertaken at the Turbulent Shear Flow Laboratory at the North Carolina State University. This facility is a blow down type variable Mach number wind tunnel with a Mach number range of 1.5-4, from Aerolab LLC., that exhausts into ambient air. The test section has a square cross section area of 152.4 mm length and 152.4 mm width and is preceded by a convergent-divergent nozzle and a stagnation chamber. It can be viewed on either sides by windows made of optical grade fused silica which has an approx. cross section area of 454.02 mm length, 152.78 mm width and is 31.75 mm thick. The aluminum frame of the windows has six clearance holes for screws, that are drilled at its base, along its length and are 76.2 mm apart from each other. This is to facilitate set ups that span the width of the wind tunnel and need to be installed on its floor. The wind tunnel was operated through a LabVIEW VI set up on a PC.
Abstract. Drag and mass exchange coefficients are calcu- lated within a self-consistent problem for the wave-induced air perturbations and mean velocity and density fields us- ing a quasi-linear model based on the Reynolds equations with down-gradient turbulence closure. This second part of the report is devoted to specification of the model el- ements: turbulent transfer coefficients and wave number- frequency spectra. It is shown that the theory agrees with laboratory and field experimental data well when turbulent mass and momentum transfer coefficients do not depend on the wave parameters. Among several model spectra better agreement of the theoretically calculated drag coefficients with TOGA (Tropical Ocean Global Atmosphere) COARE (Coupled Ocean–Atmosphere Response Experiment) data is achieved for the Hwang spectrum (Hwang, 2005) with the high frequency part completed by the Romeiser spectrum (Romeiser et al., 1997).
Choi  carried out an experimental study in a wind tunnel over trapezoidal riblets with groove height (h) 1.5 mm and peak-to-peak spacing (s) of 2.5 mm. The wall pressure fluctuations were measured in a modified turbulentboundarylayer with riblets and the results were compared with smooth surface. It was found that the riblets reduce the root mean square amplitude of pressure fluctuation by about 4% as also the turbulence near the wall. It seems that the riblets create pools of laterally constrained slow viscous flow in the valleys, and thereby modify the interaction of the wall flow with outer flow. The vertical gradients are thus smeared out, leading to a reduction in skin friction. An investigation was conducted by Dean & Bhushan  on the effect of riblets in internal rectangular duct flow. The flow cell has 1 m in overall length from inlet to outlet. It was fabricated in a way could change the duct’s width to either 3cm or 4cm. Blade riblets with groove height (h) of 254 µm with three ratios of height to space equal to 0.3, 0.5, and 0.7 were fabricated. Their results showed increasing in pressure drop for all tasted rib surfaces comparing to smooth surface and no drag reduction recorded. Dean& Bhushan concluded that the reason of rib surface did not show overall benefit in reducing the drag, due to riblets dimensions as presented in their paper not beneficial in duct flow of that nature and dimensional characteristic.
The effect of wave-induced perturbations on the momentum transfer in MABL has been investigated in numerous theo- retical (e.g., Janssen, 1989; Makin et al., 1995; Reutov and Troitskaya, 1996; Jenkins, 1992), numerical (e.g., Sullivan et al., 2000, 2008; Yang and Shen, 2010; Druzhinin et al., 2012) and experimental (e.g., Hsu et al., 1981; Hsu and Hsu, 1983; Troitskaya et al., 2011) studies. For the wind waves, decreas- ing turbulent flux of momentum near the water surface causes decreasing wind speed at the reference level (the wind waves decelerate wind due to the wind-to-wave momentum flux) and, as follows from Eq. (1), increasing the drag coefficient. Alternatively, field experiments show that swell can acceler- ate airflow due to delivery of momentum from wave to wind (see, e.g., Semedo et al. (2009) and references therein).
called a plane wall jet (Pig. 2.1). In 195& Glauert (Ref. 1) presented a theoretical analysis of the wall jet. By using Prandtl’s hypothesis for the outer layer and Blasius' shear stress relation for the inner layer, he deduced that complete similarity was not possible. Glauert also determined that Um«x and ym/2ax . A number of investigators have