* Turbulence intensities and shear stress using X-array hot-wire probe. An appreciable modulation of all the flow quantities, imposed by the wavy boundary. is obser[r]

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The main objective of the present study was to generate an **experimental** database with well-documented inlet and **boundary** conditions that will enable an assessment of our ability to predict flow separation location and complex flow behavior in the separated region **over** a model with simple geometry. The approach was to conduct a set of wind tunnel and water channel experiments on a small wind tunnel model known as FAITH (Fundamental Aero Investigates The Hill; figure 1-3) that would contribute towards understanding of the separating and reattaching flow characteristics associated with a **wall**-mounted axisymmetric hill immersed in a subsonic **boundary** **layer**. Three model parameters were considered to be of significance to the FAITH project: the generating function for the shape, the ratio of model height to base radius (H/R), and the ratio of model height to **boundary** **layer** thickness (H/δ). In addition it was considered important that the flow remain qualitatively similar **over** a large Reynolds number range and that the model should protrude through a fully-developed **turbulent** **boundary** **layer**. (It was expected that these last two factors would simplify the CFD problem.) The cosine function shape was chosen to eliminate surface discontinuities and thus make the model easy to grid for CFD simulation. The height-to-radius ratio was chosen to reliably induce flow separation **over** the downstream side of the model. Based on the authors’ engineering judgment H/R = 1/3 appeared to be appropriate and this proved to be the case. The height-to-**boundary** **layer** thickness ratio was set partially by facility considerations. It was desired to have the model height and **boundary** **layer** thickness be the same order of magnitude, as this would provide the most interesting problem for CFD. In addition it was desired to do the majority of the tests in the Fluid Mechanics Laboratory’s Test Cell #2 wind tunnel, which has a **wall** **boundary** **layer** thickness of about 5 cm. Ideally, the model would be as large as possible for the wind tunnel because the flow **over** a large model could be characterised in finer spatial detail. At this point the Fluid Mechanics Laboratory’s water channel facility proved very valuable. Within the water channel models can be placed at different positions along a splitter plate corresponding to different values of **boundary** **layer** thickness; thus the ratio H/δ can be easily varied. A small model was quickly fabricated and equipped for dye flow visualization. Multiple runs at varying distances along the splitter plate indicated that H/δ = 3 resulted in a good interaction between the model and **boundary** **layer** while allowing a reasonable model size.

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This study aims at the mechanism of drag reduction in **turbulent** **boundary** **layer** (TBL) with superhy- drophobic surface. Comparing the time-resolved particle image velocimetry (TRPIV) measurement results with that of hydrophilic surface, the drag reduction rate **over** a superhydrophobic surface is approximately 10%. To investigate the characteristics of coherent structure in a drag-reduced TBL with superhydropho- bic surface, a modified multi-scale spatial locally-averaged structure function is proposed for detecting coherent structure. The conditional sampling and spatial phase-lock average methods are employed to obtain the topology of physical quantities like the velocity fluctuation, spanwise vorticity, and Reynolds stress during eject and sweep process. The results indicate that the suppression of coherent structure burst in the near-**wall** region is the key mechanism in reducing the skin friction drag for TBL **over** super- hydrophobic surface.

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From the detailed analysis of Kolmogorov and others in the mid 1900’s three key regions of the velocity spectra can be identified as being critical to the behavior of turbulence [14].
First, the very low wave numbers represent the largest spatial scales, i.e. the integral scale, or largest eddies in the **turbulent** flow. As the figure shows, these eddies contain the largest magnitude in the power spectra and are named the “energy-containing eddies”. These eddies are primarily responsible for extracting kinetic energy from the mean flow, i.e. tur- bulence production. Due to their large size integral scale eddies are relatively una ffected by viscous forces. Smaller eddies extract energy from the energy-containing eddies. These eddies occupy the middle part of the spectra with a slope of ≈ − 5 3 known as the “inertial subrange”, which constitutes the second region. Continuing onward, even smaller eddies extract energy from the eddies in the inertial subrange. These eddies are known as dissi- pative eddies that produce the ≈ −7 slope of the dissipation range in the spectral at high wave numbers. Dissipative eddies are extremely small and described using the Kolmogorov length scale. At this length scale viscous forces are dominant causing kinetic energy to dis- sipate through molecular or viscous dissipation. This behavior is reflected in the Reynolds number which is known to be unity at this length scale, representing an equal magnitude of flow inertia and viscous force.

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could then be applied to give the particle phase velocities. By constructing a mask from the filtered large particle images, the large particles could be removed from the original combined images, to isolate the tracer field. These tracer images could then be processed by standard PIV algorithms to yield the fluid velocity field. Because of particle image broadening by the optical systems used, a reasonably large difference in size is necessary between the two parti- cle phases, but the problems of expensive multi-colour illumination systems, multiple camera setups and multiple image registration associated with alternative systems are avoided. Follow- ing this demonstration, Kiger and Pan ( 2002 ) applied the technique to measure two-phase flow in an open water channel with a Reynolds number Re τ = (u τ h /µ) = 570, based on channel half height, h. A conventional low-repetition digital PIV system was used, and so only instan- taneous measurements could be made. Having verified that the channel floor **boundary** **layer** characteristics for clear water flow were in good agreement with the DNS data of Mosser et al. ( 1999 ), glass beads of mean diameter 195 µm and specific gravity 2.6 were added as inertial particles, with a bulk mass loading ratio of 6 × 10 −4 . The results showed that even at this mass loading the presence of the relatively “heavy” inertial particles did modify the fluid mean ve- locity profile, and produced a 7% increase in the **wall** friction velocity u τ . Normal and shear Reynolds stresses showed an increase of between 8 and 10% in the outer region of the bound- ary **layer**. Mean particle velocities were shown to lag the mean fluid velocity, whereas local instantaneous particle and fluid velocities were virtually identical, a phenomenon also noted by Kaftori et al. ( 1995b ). Kiger and Pan ( 2002 ) conditionally sampled particles moving away from and towards the **wall** with the Willmarth perturbation quadrant, and confirmed Kaftori’s suggestion that the apparent particle lag was associated with upward moving particles being preferentially found within Q2 or ejection events with reduced streamwise velocity. **Wall**-ward moving particles, however, showed little preference between Q3 and Q4 events, and hence had streamwise velocities similar to the mean fluid velocity.

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Abstract
Tomographic particle image velocimetry and proper orthogonal decomposition are used to investigate the three-dimensional instantaneous flow organization of an incident shock wave/**turbulent** **boundary** **layer** interaction at Mach 2.1. The results show that the incoming **boundary** **layer** contains large- scale coherent motions, in the form of streamwise-elongated regions of low- and high-speed fluid, similar to what has been observed in incompressible **turbulent** **boundary** layers. The instantaneous reflected shock foot pattern appears to respond to these regions as they enter the interaction, conforming to the low- and high-speed regions. Its behaviour can be qualitatively decomposed into two types of patterns: an overall streamwise translation and a spanwise rippling. These observations are substantiated by the global eigenmodes of the proper orthogonal decomposition, which contain subspace representations of this phenomenology.

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ABSTRACT
Time sequence signals of instantaneous longitudinal and normal velocity components at different longitudinal and nor- mal positions in a **turbulent** **boundary** **layer** 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. **Experimental** **investigation** is carried out on the attenuation characteristics of periodic perturbation wave with different frequency along longitudinal direction and normal direction in a **turbulent** **boundary** **layer**. The amplitude distributions of longitudinal and normal disturbing velocity component for different perturbation frequencies are measured at different downstream and normal positions in **turbulent** **boundary** **layer**. 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.

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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 [44]) to accurately reproduce mean-flow quantities of interest for rough-**wall** **boundary** 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**.

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are shown in Figures 10-12. Prediction of the phase shift is satisfactory. The predicted magnitude of the perturbed skin friction is twice as large as that measured. As [r]

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The no-relaxation model predicts the correct qualitative behavior for the phase shift of the surface normal stress for a wide range of positive and negative wave [r]

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For the numerical **investigation**, an efficient numerical procedure based on solving a Poisson’s equation and a model for synthetic turbulence was developed. The Poisson’s equation was solved in the wavenumber domain according to Hockney’s method. The source terms on the right-hand side of the Poisson’s equation were realized by synthetic turbulence which is generated by the Fast Random Particle-Mesh Method (FRPM). The kinetic energy was well reconstructed except for the near-**wall** region, especially for < 0.1δ. This is acceptable for the purpose which is orientated to practical applications, because the region close to the **wall** impacts mostly the high frequencies but not the main features for the **wall** pressure fluctuations. Moreover, the high frequencies are generally irrelevant to the vibration due to the poor transmission efficiency for the structural response. Both the mean-shear turbulence term and the turbulence-turbulence term were considered. The results demonstrated that the **wall** pressure fluctuations contributed from both terms are of the same order of magnitude if anisotropic turbulence is considered. For isotropic turbulence the mean-shear term is the dominant term. In contrast to the spectra with a peak at medium frequencies for the mean-shear term, the spectra for the turbulence- turbulence term show a maximum plateau at lower frequencies. The calculated one-point spectrum for the mean-shear term is verified by comparing to the theoretical prediction using the turbulence statistics provided by FRPM. Compared to the spectral models from the literature a stronger decay at high frequencies was found which is mainly because of the limited grid resolution which was not fine enough to resolve the small turbulence structures close to the **wall**. The two-point correlation properties were consistent with the database from other investigators. It was found that the small eddies in the inner region could affect the one-point spectra and the two-point correlation properties at low frequencies due to the temporal turbulence decay. The convection velocities were well estimated. The wavenumber-frequency spectra were also calculated. The convective ridge can be clearly determined. Furthermore, a calculation using the developed numerical procedure for the experiment presented in this work was also performed. The calculated **wall** pressure features show good agreement with the **experimental** results.

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Figure 3 shows the pressure readings at Reynolds number
= 5.3 × 10 4 for triangular grooves. The resultant results shows that the pressure drop readings that were performed on the surface are more stable, and that also its turbulence frequency is low as compared to other surfaces. Moreover, most of the pressure drop point lies below the smooth surface pressure drop line with higher irregular or less smooth readings. The structured surfaces tends to portray pressure readings that have higher amplitude, as well as the readings where the smooth surface is tested but their average readings when taken into consideration tends to be a little lower. Statistically, the structured surfaces portrays on an average basis pressure drops that are a little bit lower even though the figures show certain points with higher pressure drop values. This can then be explained by the fact that the reason for the structure surfaces displaying; the low-pressure drop readings is that on the initial phase the pressure drops had to stabilize for a certain period of time before proceeding to return to the same smooth surface readings. The same pattern is reaped for **over** many period of time explaining the low-pressure drops that are shown on an average basis.

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5 Conclusions
This paper is the first part of our report on the momentum and buoyancy transfer in MABL **over** **wavy** water surface.
Here we constructed a model based on a self-consistent prob- lem for the wave-induced air perturbations and mean veloc- ity and density fields. We explored the simplest case of har- monic waves propagating along the wind. It is shown within the model that a drag coefficient may either decrease or in- crease, depending on the wave length. Surface drag decrease is expected in the presence of swell, which can deliver mo- mentum to wind. Drag decrease is more pronounced in un- stable stratification. This is the result of exchange intensity reduction in stably stratified flow due to suppression of the **turbulent** pulsations. The case of a harmonic wave propagat- ing along the wind considered in this paper is an idealization, but it is essential for analysis of peculiarities of air–sea inter- action.

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In spite of the complicated time-dependent geometry (as compared with the plain quasi-stationary one in the model), the sharp density gradients in the TBL, and the limitations in the model grid size, etc., we have shown that a substantial number of the TBL turbulence features can be understood by comparison of the **experimental** data with the model of ki- netic reconnected current sheet at the nonlinear state. Proba- bly, the evolution of nonlinear structures in the hot inhomo- geneous plasma weakly depends on the initial disturbances after exceeding some amplitude or scale thresholds. For ex- ample, Chmyrev et al. (1988) have shown that after thinning to the ion gyroradius scale, current sheets tend to split into the vortex streets, since this state has lower energy as com- pared with the homogeneous planar current sheet. The char- acteristic scales of the TBL turbulence are shown to reach the scales of a few km, i.e. several electron inertial lengths c/ω pe (Savin et al., 1998b). This infers violation of the frozen-in field condition and could also be treated as a feature of the local reconnection near the cusp. The operation of the bursty reconnection for the locally anti-parallel fields **over** the cusp is in agreement with a number of studies, and the experimen- tal evidences for the permanent by-product reconnection of the TBL is strongly fluctuating fields are seen as well (see e.g. Savin et al., 1998b, 2001, 2002a, b; Merka et al., 2000;

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This study reports on experimentally observed rare near-**wall** reverse flow events in a fully developed **turbulent** flat plate **boundary** **layer** at zero pressure gra- dient with Reynolds numbers between Re θ ≈ 2500 and Re θ ≈ 8000 (Re τ ≈ 800 − 2400). The reverse flow events are captured using high magnification particle image velocimetry sequences with record lengths varying from 50 000 to 126 000 samples. Time resolved particle image sequences allow singular re- verse flow events to be followed **over** several time steps whereas long records of nearly statistically independent samples provide a variety of single snapshots at a higher spatial resolution. The probability of occurrence lies in the order of 0.012 – 0.018% which matches predictions from direct numerical simulations (DNS). The typical size of the reverse flow bubble is about 30 **wall** units in length and 5 **wall** units in height which agrees well with similar observations made in existing DNS data.

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Pressure Gradient **Turbulent** **Boundary** **Layer**
Christian E. Willert 1
Submitted July 3, 2015
Abstract This study reports on experimentally observed near-**wall** reverse flow events in a fully developed flat plate **boundary** **layer** at zero pressure gradient with Reynolds numbers between Re τ = 1000 and Re τ = 2700. The reverse flow events are captured using high magnification particle image velocimetry sequences with record lengths varying from 50,000 to 126,000 samples. Time resolved particle image sequences allow singular reverse flow events to be followed **over** several time steps whereas long records of nearly statistically independent samples provide a variety of single snapshots at a higher spatial resolution. The probability of occurrence lies in the range of 0.01% to 0.1% which matches predictions made with direct numerical simulations (DNS). The self-similar size of the reverse flow bubble is about 30-50 **wall** units in length and 5 **wall** units in height which also agrees well to DNS data provided by Lenaers et al. (ETC13, Journal of Physics: Conference Series 318 (2011) 022013).

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In the present work we suggest a self-consistent model of stratified **turbulent** **boundary** **layer** **over** waved water sur- face. The model is based on the system of Reynolds-averaged Navier–Stokes equations in the basic formulation with the first-order closure hypothesis, where coefficients of **turbulent** transport were verified experimentally. Comparisons with the **experimental** data enabled us to choose the eddy viscosity and heat conductivity coefficients scaled by the total tangen- tial stress in the **boundary** **layer**. Wind–wave momentum and mass exchange within the model is considered in the quasi- linear approximation. This approach, when the linear approx- imation is prescribed for the wave-induced disturbances and nonlinear effects are concerned only with the mean flow, is often used in plasma physics. For the wind–wave interaction with homogeneous MABL, it was applied by Janssen, 1991;

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The movement of the interface becomes even more essential in the determination of the **turbulent** parameters of the airflow above the water surface. There seems to be no straightforward way to decouple the velocity fluctuations that are intrinsic to the **turbulent** airflow, from variations related to the random water surface movement. First, as mentioned above, the elevation of the sensor relative to the instantaneous local surface position varies in time and may cause fluctuations in the measured velocity. Second, the **wavy** motion observed in water also exists in air. The corresponding airflow orbital velocities have a wide spectrum related to the spectrum of the surface elevation in the presence of wind waves; the phases of those fluctuations are random. The fluctuations associated with waves in airflow decay exponentially with height above the mean surface. These two phenomena result in the characteristic fluctuations of the horizontal, u 2 1 /2 , and vertical, w 2 1 /2 , velocity components, that at low elevations are notably higher than the corresponding values measured in **boundary** layers **over** smooth and rough surfaces (Zavadsky & Shemer 2012). An additional but less important complication is related to the drift current induced by wind shear as well as by the water waves’ nonlinearity.

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favourable to adverse conditions. This hierarchy was visible in the LES results, even if the grid cut-off entailed a more rapid fall. As a consequence, some energy was lost in the calculations in the high-frequency range. This is not critical since the behaviour of viscous scales can be considered as quasi-universal. It was possible to reconstruct the lost energy by matching a model of Goody ( 2004 ), and we found a correction of 9 % of the averaged pressure fluctuations in the ZPG case. The integrated value scaled by the **wall** shear stress increased from FPG to APG conditions. This is consistent with experiments, but there is a lack of data to see an emerging trend with the value of a pressure-gradient parameter. The influence of the pressure gradient on the convective velocity of pressure fluctuations on the **wall** was not very conclusive. The view of Schloemer ( 1967 ) or Burton ( 1973 ) of a lower convection speed for APG flows and a higher one for FPG flows was not supported by the present numerical experiments, where Mach and Reynolds numbers are roughly constant for nearly equilibrium TBLs. Instead, the conclusion here was that the mean convective velocity from space–time correlations is weakly affected by the pressure gradient, except that the range of longitudinal separations scaled by the **boundary** **layer** thickness was reduced for APG flows due to the thickening of the TBL. The **investigation** of frequency-dependent convection velocities from cross-spectral measurements would help to establish a clearer trend. Furthermore, high-resolution wavenumber–frequency spectra were obtained and made clear the features of the convective ridge, which is the imprint of hydrodynamic pressure fluctuations associated with vortical motions, and of the acoustic domain, corresponding to **boundary**-**layer** noise. In particular, it was found that the **boundary**-**layer** thickness δ was the best length scale to compare the different gradient cases, even if an enlargement was visible for APG conditions in the frequency and streamwise wavenumber directions. As a result, the convective ridge was more isotropic in adverse conditions, which is consistent with the picture of hairpin structures that lift off the **wall**. The decay rate toward the subconvective wavenumbers revealed a large dynamical range, which is hardly reproduced in available modelling or in experiments. The trace of acoustic wavenumbers was clearly identifiable and showed slightly higher acoustic activity for APG **boundary** layers, at least when scaled with outer properties. This is consistent with the levels of direct radiation outside the TBL. The radiation patterns were similar for the five gradient cases and were significantly marked by mean flow propagation effects, which will be further analysed in a future paper.

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