Session HA: Turbulent Boundary Layers: Experimental Studies II

Vortex properties in turbulent boundary layers

Swirl strength was used to identify vortices in turbulent boundary layers. Dual-plane PIV data at Re$_{\tau }\approx$ \$1100 with coarser (Ganapathisubramani et al., 2006) and finer resolution (Saikrishnan et al., 2007) as well as DNS data at Re$_{\tau }$=590 (Moser et al., 1999) and Re$_{\tau }$=934 (del \'Alamo et al., 2004) were analyzed. A new core-combination algorithm was developed to improve identification of in- and out-of-plane vortices. Core orientation was determined by the eigenvector of the velocity gradient tensor, and core radii were characterized. The effects of wall normal location, Reynolds number, and spatial resolution were studied. In general, the PDF of swirl magnitude is affected by both in- and out-of-plane spatial resolution as well as the wall normal location. Scaling of swirl will be discussed in the presentation. The results show that, in the logarithmic region, the mean angle between the eigenvector and the vorticity vector decreases and the mean core radius increases with wall normal distance. Joint PDFs show linear increases in circulation with core radius, as well as correlations between core inclination angle and circulation. Convection velocities of strong cores are typically smaller than the local mean velocity.   

Holographic Microscopy Reveals Buffer Layer Structures Generating Wall Stress Extremes in a Turbulent Boundary Layer

3-D velocity distributions and wall stresses are measured concurrently in the inner part of a turbulent boundary layer in a smooth square channel using digital holographic microscopy. With over 750 realizations analyzed, mean velocity and Reynolds stress profiles agree well with published data. Conditional sampling based on local shear stress maxima and minima reveals two types of dominant buffer layer structures. The first develops as spanwise vorticity lifts abruptly from the wall, creating initially a vertical arch, which is then stretched and forms a pair of inclined, counter rotating vortices with ejection-like flow between them. A wall-stress minimum occurs under the point of initial detachment, while stress maxima develop 35 wall units downstream, due to vortex-induced entrainment during early stages of vortex rollup. This structure exists in 16.4{\%} of the samples. The second structure is a slightly inclined, single, predominantly streamwise vortex. It appears in 20{\%} of the instantaneous realizations and generates an elongated, strong stress maximum on one side, and a weak minimum on the other.   

Investigation of the Turbulent Bursting Period over a Very Large Reynolds Number Range

The present study examines Reynolds number scaling of the average bursting period, $T_b$, over a Reynolds number range spanning three orders of magnitude, using hot-wire anemometry measurements from combined wind tunnel and field experiments. Wind tunnel data were obtained from the study of Klewicki and Falco (1990) at Reynolds numbers based on momentum thickness of $Re_\theta=1010$, $2870$, $4850$; while the field data were acquired at the Surface Layer Turbulence and Environmental Test (SLTEST) facility at $Re_\theta =5\times10^6$. Ejection events were detected from streamwise velocity time series using the U-Level algorithm of Lu and Wilmarth (1973). Events appearing in close succession were grouped into multiple event bursts using a statistical iterative approach based on pattern clustering. Four different Reynolds number scalings of $T_b$ were investigated, namely: inner, outer, mixed, and intermediate. Data reveal that, of these four types of scalings, the Taylor microscale performs the best in removing Reynolds number dependencies in $T_b$. In addition, the present data reveal that outer scaled values of $T_b$ decrease by two orders of magnitude over the range of Reynolds numbers; while inner scaled values of $T_b$ increase by one order of magnitude.   

Scales Interaction in Wall Turbulence

Recently, the role of very large scale motions in turbulent boundary layer has been significantly re-evaluated, in terms of kinetic energy and Reynolds stress contribution, (e.g. Guala et al. 2006), and as a source of strong scale interactions across the wall region (e.g. Hutchins \& Marusic, 2007). Simultaneous hotwire measurements, across the vertical direction, at $Re_\tau = \delta u_\tau /\nu \simeq 10^6$ in the atmospheric surface layer, in near-neutral conditions, are analyzed by means of linear and non linear techniques to quantify interactions among turbulent scales, from the very large scale motions (of order of $6 - 10 \delta$) to the dissipative scales. Results show that the ``signature'' of very large scale oscillations can be found in conditioned statistics of dissipation and high pass filtered velocity. Premultiplied spectra and joint PDF allows for a spectral and probabilistic description of the interaction between the various scales, while wavelet analysis and cross correlations provide information of time dependency and phase delays. We regard very large scale motions as active, with respect to their effect onto any scale, from the energy containing eddies, to the Kolmogorov scale. Data were collected at the SLTEST site, Utah (Metzger et al. 2007).   

Variation of the Karman Constant in a Highly Accelerated Turbulent Boundary Layer

In this paper the response of an initially canonical turbulent boundary layer on a flat plate to the imposition of a favorable streamwise pressure gradient sufficient to cause relaminarization is investigated experimentally. In anticipation of the loss of standard log-law behavior, the local wall shear stress is measured directly using the oil film interferometry technique. It is shown that a logarithmic region is maintained even for the largest flow accelerations encountered in the experiment although the slope $1/\kappa $ and additive constant B exhibit a systematic streamwise variation from standard zero-pressure gradient values. The variation of the Karman and additive constants with applied pressure gradient is not explicitly associated with the relaminarization process. Systematic variation of the constants from their standard zero-pressure-gradient value occurs even for the comparably small favorable pressure gradient upstream of the contraction. This measured variation in $\kappa $and B is fully consistent with the empirical correlation proposed by Nagib {\&} Chauhan (2008) for a wide variety of turbulent boundary layer experiments in favorable and adverse pressure gradients. However, the measurements obtained in this study extend the available data set to much larger values of $\kappa \,B$and B associated with strong favorable pressure gradients and relaminarization.   

Flow-Dependence and Non-Universality of the von K\'{a}rm\'{a}n ``Constant"

The overlap parameters of the logarithmic region in turbulent pipe, channel, and boundary-layer flows are established using a composite profile approach which incorporates the influence of the outer part. The composite profile incorporates $\kappa$, $B$ and $\Pi$ as the varying parameters and their resulting behavior with Reynolds number is examined and compared for these flows. The $Re$-specific von K\'{a}rm\'{a}n coefficient for channel flows decreases with Reynolds number to a level below the well defined value of $\kappa_{BZ}~=~0.384$ for ZPG TBLs. The proper limiting value of $\kappa_C$ for the channel flow could not be established with a high confidence because of the limited range of available Reynolds numbers, but the best projected value is near $\kappa_C\sim 0.37$. For the pipe flow, reprocessing of the Superpipe data indicates that $\kappa_P\sim0.41$, which is on the opposite side of the boundary layer value compared to the channel flow. This collective ``non-universal" behavior of $\kappa$ in boundary layers, pipes and channels suggests that the von K\'{a}rm\'{a}n coefficient is not universal, and exhibits dependence on not only the pressure gradient but also on the flow geometry, thereby raising fundamental questions regarding turbulence flow theory and modeling for all wall-bounded flows. In contrast, a wide range of data from such canonical flows reveals a universal relation between the overlap parameters; i.e., the von K\'{a}rm\'{a}n coefficient and the intercept B.   

Correlation structure of the Lamb vector in the outer region of a turbulent boundary layer

The streamwise component of the Lamb vector ($T$) acts as a momentum source (for $T > 0$) or sink ( for $T < 0$) in the mean-momentum balance of turbulent boundary layers. In this study, the spatial structure of $T$ in the outer region of a turbulent boundary layer is examined by using dual-plane particle image velocimetry data. Two-point correlations of $T$ indicate that size of source motions remain relatively constant while the size of sink motions increases with increasing wall-normal distance. Source-like motions are correlated with elongated low momentum zones that possess regions of up wash embedded within it. Momentum sinks appear to be located within low-speed regions that are within larger high momentum zones. The velocity fluctuations undergo rapid transitions between quadrants in the vicinity of sinks (i.e., both streamwise and wall normal velocity fluctuations change sign). The length scales, over which the fluctuations change sign, are larger farther away from the wall.   

Modulation of the near-wall cycle due to large-scale log-region events

Previous observations made by Hutchins and Marusic (\emph{Phil. Trans. R. Soc. A}, {\bf 365}, 2007) have shown a close relationship between the small inner-region motions and large-scale structures in high Reynolds number turbulent boundary layers. Here, we study this effect more fully employing Hilbert transformations of the spectrally filtered small-scale component of fluctuating velocity signals. The results show strong evidence that the near-wall cycle resides under a non-linear influence, very close to a pure amplitude modulation, of the large-scale log-region motions. The modulation effect is seen to increase with increasing Reynolds number. Experimental data is considered over three orders of magnitude in Reynolds number.   

A conditioned volumetric view of ``superstructure'' events in turbulent boundary layers

A conditionally averaged view of ``superstructure'' type events is presented for the case of zero pressure gradient turbulent boundary layers at friction Reynolds number, $Re_{\tau} \approx 14\,000$. Detailed boundary layer traverses are acquired above a simultaneously sampled spanwise rake of 10 flush-mounted hot-film sensors, affixed to the tunnel wall with a spanwise spacing of approximately $0.08$ boundary layer thicknesses ($\delta$). The data from the traversing probes are conditioned on the occurrence of superstructure-type footprints sensed by the wall array. The resulting data give a more complete volumetric view of the large-scale meandering log-region features than has previously been afforded by hot-wire rake and PIV measurements. Such detailed views are used to further investigate the existence of an amplitude modulation effect, in which the footprints of large $\delta$- scaled structures (that typify the logarithmic region) have been observed to modulate the viscous-scaled near-wall cycle.   

Experimental determination of the von K\'{a}rm\'{a}n constant in turbulent two dimensional soap film flows

We report measurements in both the viscous layer and in the log region of a two dimensional (2D) flowing soap film. The turbulence is created by a horizontal grid (a comb) and decays downstream where measurements are made. We report a sequence of measurements at film width Reynolds numbers of 10${^4}$ -10${^5}$, and fit our velocity profile data to a putative law of the wall form which is a reasonable representation of our data at the higher Reynolds numbers studied. We report our results for the von K\'{a}rm\'{a}n constant, and compare with calculations from theory and numerical simulation. Our findings indicate that the von K\'{a}rm\'{a}n constant in 2D is less than the accepted value in 3D.