Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session JE: Turbulence: Boundary Layers V |
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Chair: Timothy O'Hern, Sandia National Laboratories Room: Salt Palace Convention Center 151 D-F |
Monday, November 19, 2007 3:35PM - 3:48PM |
JE.00001: Self-consistent high Reynolds number asymptotics based on the log-law for ZPG turbulent boundary layers Peter A. Monkewitz, Hassan M. Nagib, Kapil A. Chauhan The large Reynolds number behavior of flat plate turbulent boundary layers under zero pressure gradient (ZPG) is revisited. Starting from the classical two-layer approach of Millikan and Clauser with a logarithmic velocity profile in the overlap region between ``inner" and ``outer" layer, a fully self-consistent leading-order description of the mean velocity profile, all integral parameters and the downstream evolution of the boundary layer thickness is developed. The latter requires the knowledge of the virtual origin of the boundary layer which is determined from the K\'{a}rm\'{a}n equation. It is demonstrated that this self-consistent description based on the classical log-law fits all the known high Reynolds number data, and in particular their Reynolds number dependence, exceedingly well; i.e. within experimental errors. [Preview Abstract] |
Monday, November 19, 2007 3:48PM - 4:01PM |
JE.00002: Scaling of normal Reynolds stresses in ZPG turbulent boundary layers Hassan M. Nagib, Kapil A. Chauhan, Peter A. Monkewitz An extensive set of experimental data for zero pressure gradient (ZPG) boundary layers over a wide range of Reynolds number is re-evaluated in another attempt to reveal appropriate scaling of the turbulence normal stresses. In view of the lack of well developed theoretical foundations for even the second- order statistics, the task is complex, and rigorous theoretical arguments cannot be made in favor of any of the commonly used non-dimensionalizatios; namely, inner, outer or mixed velocity scales. While the correlation of the data reveals some interesting and sometime contradicting trends, the limitations on measurement accuracy and spatial resolution, particularly in the near wall region, prevent us from reaching definitive conclusions. However, examining the role of the normal Reynolds stress difference (NSD) term in the K\'{a}rm\'{a}n integral equation using recent results from asymptotic theory suggests that the outer velocity scaling is likely not correct, in spite of the better collapse of the available data it produces in the outer part of the boundary layer. While the NSD must be included in any large Reynolds number asymptotics, we conclude that, for any practically relevant Reynolds number, the NSD integral in the K\'{a}rm\'{a}n equation represents a small correction which can be neglected as it has been done up to now. [Preview Abstract] |
Monday, November 19, 2007 4:01PM - 4:14PM |
JE.00003: Two-point correlations and logarithmic layer statistics in wall turbulence over a very large range of Reynolds number Ivan Marusic, Nicholas Hutchins An investigation was conducted of the logarithmic layer structure in turbulent boundary layers spanning three orders of magnitude change in Reynolds number. This was achieved by using two laboratory scale facilities and the atmospheric surface layer at the SLTEST facility in Utah. Several experimental techniques were used including particle image velocimetry in the laboratory, and spanwise and wall-normal arrays of hot-wires and sonic anemometers in the laboratory and atmosphere, respectively. Two-point correlation statistics are found to agree extremely over all Reynolds numbers with outer length scaling. Recent large-scale coherence noted in the logarithmic region of laboratory-scale boundary layers (superstructures) are also found to exist in the atmospheric surface layer flow. [Preview Abstract] |
Monday, November 19, 2007 4:14PM - 4:27PM |
JE.00004: The large-scale structure of turbulent pipe and channel flows Jason Monty, James Stewart, Rob Williams, Min Chong In recent years there has been renewed interest in the large-scale behaviour of wall-turbulence. This is largely due to the insights of Adrian and co-workers (see Adrian, {\it Phys. Fluids}, {\bf 041301}, 2007) and more recently Hutchins \& Marusic ({\it J. Fluid Mech.}, {\bf 579}, 2007). Much of the existing work has centered around turbulent boundary layer measurements, leaving scope for further investigation into pipe and channel flows. Following the work of Hutchins \& Marusic (HM07), the authors sought to study the large-scale structure of duct flows using multi-probe hot-wire arrays. The arrays were custom made to minimise blockage and consisted of up to 15 hot-wires. The results show that `superstructures', identified by HM07 for boundary layers, exist qualitatively similarly in pipes and channels. These coherent structures have lengths of up to 20 pipe radii or channel half-heights. Furthermore, it was found that the spanwise width of the structures was similar in pipes and channels, but much larger than that in a boundary layer. This work forms part of an ongoing investigation into the structural similarities and differences between pipes, channels and boundary layers. [Preview Abstract] |
Monday, November 19, 2007 4:27PM - 4:40PM |
JE.00005: Formation of chaotic packets of hairpin vortices in a channel flow Kyoungyoun Kim, Hyung Jin Sung, Ronald J. Adrian We examine the auto-generation mechanism by which new hairpin vortices are created from sufficiently strong hairpin and they form into a packet. Emphasis is placed on the effects of initial small background noise on the packet formation. The initial conditions are given by conditionally averaged flow fields associated with Q2 event in the fully turbulent channel flow DNS database at $Re_\tau =395$. A small amount of noise is added to the initial field. The nonlinear evolution of the initial vortical structure is tracked by performing a spectral simulation. The initial background noise leads to chaotic development of hairpin packet. The hairpins become asymmetric, leading to much more complicated packet structures than a symmetric hairpin vortex train of the clean background. However, the chaotic packets show the same properties as the clean packet in terms of the growth rate of vertical and spanwise dimensions and the distance between successive vortices. This suggests that the auto-generation mechanism is robust. Conditionally averaged flow fields around tall attached vortices in the hairpin packet show a `downstream wake' structure of low momentum fluids, which is consistent with the fully turbulent DNS results of Del Alamo et al. [J. Fluid Mech. 561, p.329 (2006)]. [Preview Abstract] |
Monday, November 19, 2007 4:40PM - 4:53PM |
JE.00006: Active and Inactive Motions in the Streamwise Reynolds Stress of Boundary Layers. Ronald Panton, Robert McKee The streamwise normal Reynolds stress \textit{$<$uu$>$(y, Re) }
in wall layers does not scale simply
with the friction velocity $u_{\ast}$ as many researchers have
shown
recently. For example, Degraaff and Eaton (JFM, \textbf{422, }p
319) and
Metzger and Klewicki (P of F, \textbf{13}, p 692) propose the
scaling $ |
Monday, November 19, 2007 4:53PM - 5:06PM |
JE.00007: Scaling The Size And Time Interval Of Pocket Events In The Turbulent Boundary Layer Meredith Metzger, Ari Fershtut, Cherie Cambron, Joseph Klewicki Smoke visualization and axial velocity measurements are combined in order to establish the scaling behavior of pocket events in the viscous sublayer of the turbulent boundary layer. The present study is the first to employ an identical analysis methodology over an extensive range of Reynolds numbers based on momentum thickness between $1000 \le R_{\theta} \le 1.5\times{10}^6$. Both the pocket width ($W$) and time interval between pocket events ($T$) increase logarithmically with Reynolds number when normalized by viscous units. Normalization of $W$ and $T$ by the Taylor microscales evaluated at a wall-normal location of about 100 viscous units, however, appears to successfully remove this Reynolds number dependence. The present results are discussed in the context of coherent vortical motions. [Preview Abstract] |
Monday, November 19, 2007 5:06PM - 5:19PM |
JE.00008: Scaling of mixed structure functions in turbulent boundary layers P. Henrik Alfredsson, Boris Jacob, Carlo Massimo Casciola, Alessandro Talamelli The scaling of the anisotropic components of the hierarchy of correlation tensors in the logarithmic region of a flat plate turbulent boundary layer is addressed. We isolate the anisotropic observables by means of a recent theory based on the SO(3) symmetry group of rotations. Employing a dataset made of velocity signals obtained by a multi-probe setup, we demonstrate that the behavior of the anisotropic fluctuations throughout the boundary layer may be understood in terms of the superposition of two distinct regimes, with the transition being controlled by the magnitude of the mean shear and identified with the shear scale. Below the shear scale an isotropy-recovering behavior occurs, characterized by a set of universal exponents which roughly match dimensional predictions based on a first-order expansion in terms of the shear magnitude. Above the shear scale, the competition between energy production and dissipation mechanisms gives rise to a completely different scenario with significant differences in the observed scaling laws. This aspect has profound implications for the correct parameterization of anisotropic behavior in the near-wall region, since approaching the wall, an increasingly larger fraction of the scaling interval tends to conform to the shear-dominated power-laws. [Preview Abstract] |
Monday, November 19, 2007 5:19PM - 5:32PM |
JE.00009: A view of structures in wall-bounded turbulent flow from PIV measurements in three different planes David Dennis, Timothy Nickels High-speed PIV measurements in three different planes (streamwise-wall normal, streamwise-spanwise, and spanwise-wall normal) have been taken in the Cambridge University Engineering Department's turbulent boundary layer water tunnel research facility. This unique facility has been specially designed to produce thick turbulent boundary layers that may be measured with excellent spatial resolution. A boundary layer with $Re_?=4685$, has been examined for the presence of the structures commonly described in the literature (e.g. long, meandering regions of low-momentum fluid, and hairpin vortex packets). The use of high-speed PIV enables the tracking of structures in time, as well as providing measurements that can be used to test the accuracy of Taylor's hypothesis. Once the valid extent of Taylor's hypothesis is known, it can be used to extend the length of the spatial field. The spanwise-wall normal measurements were taken using stereoscopic PIV and therefore provide all three components of the velocity vector. The instantaneous flow fields and the statistics of the flow are examined for evidence of structures. [Preview Abstract] |
Monday, November 19, 2007 5:32PM - 5:45PM |
JE.00010: Physics of the Logarithmic Velocity Mean Profile Joe Klewicki A physical interpretation of the mathematical conditions necessary for a logarithmic (or nearly logarithmic) mean profile is presented. The basis for this interpretation is the analysis of Fife et al., (2005 JFM \textbf{532}, 165) which reveals that the mean momentum balance rigorously admits a hierarchy of scaling layers each having their own characteristic length. These analyses also show that the condition for exact logarithmic dependence exists when the normalized equations of motion (normalized using the local characteristic length) attain a self-similar structure. The physics underlying this are shown to be directly associated with gradient of the turbulent force associated with the Reynolds shear stress gradient, or equivalently the axial component of the Lamb vector. These physics also indicate that the von Karman constant will only truly be invariant when an exact self-similar structure in the gradient of the turbulent force is attained across an interior range of layers comprising the hierarchy. These results are discussed relative to the physics of boundary layer Reynolds number dependence and recent data indicating that the von Karman constant varies for varying mean momentum balance. [Preview Abstract] |
Monday, November 19, 2007 5:45PM - 5:58PM |
JE.00011: Instantaneous streamwise velocity profiles at very high Reynolds number in the neutrally stable atmospheric surface Beverley McKeon, Meredith Metzger We present instantaneous streamwise velocity profiles from the neutrally stable atmospheric surface layer, which we consider as a model for a very high Reynolds number canonical zero pressure gradient boundary layer with $Re_\tau = O(10^6)$. The data were acquired at the SLTEST site in Utah's western desert using 31 logarithmically-spaced single normal hot wires and 9 sonic anemometers spanning $0.001 \le z \le 26$m ($2 < z^+ < 10^5$). Low- and high-pass filters applied to the instantaneous velocity field reveal the relationship between the ``footprint" of large-scale motions (which are thought to originate in the logarithmic overlap layer) reaching down through the buffer layer and the spatial and temporal extent of periods of intense small-scale activity. [Preview Abstract] |
Monday, November 19, 2007 5:58PM - 6:11PM |
JE.00012: The effects of hot-wire spatial resolution on measurements in wall-bounded turbulence. Nicholas Hutchins, Ivan Marusic, Min Chong, Timothy Nickels Reassessment of new and pre-existing data reveal that recorded scatter in the hot-wire measured near-wall peak in viscous- scaled streamwise turbulence intensity is due in large part to the simultaneous competing effects of Reynolds number and viscous scaled wire-length $l^{+}$. These competing factors can explain much of the disparity in existing literature, in particular explaining how previous studies have incorrectly concluded that the inner-scaled near-wall peak is independent of $Re$. We also investigate the appearance of the, so-called, `outer-peak' in the broadband streamwise intensity, found by some researchers to occur within the log-region of high Reynolds number boundary layers. We show that this `outer-peak' is most likely a symptom of attenuation of small-scales due to large $l^{+}$. Fully mapped energy spectra, obtained with a range of $l^{+}$, are presented to demonstrate this phenomena. [Preview Abstract] |
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