Session H7: Turbulent Boundary Layers V

Organization of very-long coherent structures in a turbulent pipe DNS with long domain

Regions of negative velocity fluctuation are extracted from a turbulent pipe simulation at $Re_\tau=685$. The lengths of these regions are characterized for a range of thresholds. The organizational patterns of these structures are analyzed using a linear stochastic estimate of a negative velocity fluctuation event. Instantaneous examples of these events are compared with the patterns in the estimate to understand the relationship between structure organization and the two-point spatial correlation. Close examination of the very long motions reveal distinct forms of smaller motions with different characteristic scales. Studying these structural elements provides insight into how the smaller motions compose the very long motions. Cross-sections in various planes are compared to features observed in experimental investigations, including vortical motions. Three-dimensional vortical structures are extracted using several methods, and their geometries and relationships with the velocity motions are examined.   

Properties of Wide Spanwise or Azimuthal Velocity Modes in Turbulent Boundary Layers, Channels, and Pipes

While the motions that exist after instantaneously spanwise averaging a plane turbulent channel or boundary layer would vanish as spanwise domain size is increased, the motions from azimuthally averaging a pipe have clearer physical significance due to the constrained geometry. These averages also arise as the spanwise $k_z=0$ and azimuthal $k_\theta=0$ modes in a Fourier (or POD) decomposition. The $k_{z}$/$k_\theta=0$ modes of velocity contain 3.0, 3.5, and 7.2\% of the streamwise, wall-normal, and spanwise turbulent kinetic energy at $0.25h$ above the wall for a $Re_\tau=590$ channel DNS with $\pi h$ wide domain (Moser, Kim, \& Mansour, Phys. Fluids, 1999), and 1.5, 2.3, and 4.2\% for a $Re_\tau=685$ pipe DNS at $0.25R$ above the wall. These increase to 9--11\% for each component at the channel centerline. These modes are studied for channel and boundary layer DNSs with several domain widths and a pipe. Time evolution and traveling wave behavior of these modes are explored. The modes are characterized with proper orthogonal decomposition, and the results are compared to 2D POD modes for planes without spanwise/azimuthal averaging.   

Large-scale coherent motion in turbulent pipe flow

Fully-developed turbulent pipe flow at bulk Reynolds numbers ranging from Re = 10 000 to 44 000 has been investigated experimentally using high-speed PIV in a plane perpendicular to the mean flow. A stereoscopic setup was used to enable the reconstruction of all three components of the entire azimuthal velocity field. The application of Taylor's hypothesis allowed to reconstruct the quasi-instantaneous streamwise extension of the flow field. Individual recording sequences cover more than 150 bulk scales based on the bulk velocity and the pipe radius such that even the largest expected streamwise extends of the flow structures are captured. The azimuthal flow field scaling was found to be consistent with results reported in previous studies. A steep decrease of azimuthal width towards values found in turbulent boundary layers could be observed at low Reynolds number indicating the near-wall region to be unaffected by the confinement of the pipe geometry. At wall distances $0.5 < y/R < 0.8$ azimuthal growth nearly stagnates. The large-scale coherent flow field at different wall-normal positions exhibits a very high instantaneous similarity. Streak-width distributions exhibit a flattening of the present azimuthal streak extensions throughout the logarithmic and wake region.   

Time-resolved PIV in fully developed turbulent pipe flow

Stereoscopic particle image velocimetry was used to study the three-component velocity field in fully developed turbulent pipe flow, to investigate the structure and behavior of the large and very large scale motions in the outer layer. The data was acquired with a high speed camera, making it possible to resolve the velocity field in time for Reynolds numbers ranging from 1.3$\times $10$^{4}$ to 3.6$\times $10$^{4}$. Proper Orthogonal Decomposition was performed on the data to extract the most energetic modes in the flow, which are believed to correspond to the very large scale motions. We show that a small number of modes may be used to reconstruct these structures. The procedure can be used as a VLSM filter to further investigate their behavior.   

On the generation and growth of hairpin vortex packets in wall turbulence

We demonstrate that the critical layer framework of McKeon \& Sharma (JFM, 2010) which was previously shown to capture aspects of the statistics of wall turbulence, also gives insight into the appearance and organization of vortical structure. The model reconciles aspects of the statistical and structural pictures of wall turbulence. Choosing suitable scales, the superposition of left- and right-going propagating modes which are attached to the wall reproduces the development of a periodic array of pro- and retro-grade hairpin vortices. The addition of mean shear associated with the turbulent mean velocity profile suppresses the retrograde vortices and enhances the prograde vortices. Further, superposition of attached modes with differing convection velocities produces packets of hairpins that evolve in both space and time. Characteristics of these vortical structures and a comparison with the vortex signatures observed in experiments will be described.   

The lifetime and evolution of vortical structures in the turbulent boundary layer

The evolution and persistence of vortices in wall normal and wall parallel planes of a zero-pressure gradient turbulent boundary layer are investigated using time resolved 2D-2C particle image velocimetry at a moderate Reynolds number ($Re_\tau=470$). Measurements are performed with a large field of view: $5\delta \times 1.2\delta$ (streamwise x wall normal) in the wall normal plane and both $10\delta \times 5\delta$ and $4.3\delta \times 2.2\delta$ (streamwise x spanwise) in the wall parallel planes. Given that the data provides information in both the streamwise direction and time simultaneously, not only can the vortices be tracked as they convect downstream, but the evolution of the surrounding flow structures can be studied in the reference frame of the vortex. In addition to investigating statistics associated with the lifetime and convection velocity of vortices at various wall normal locations, the effects of spatial and/or temporal filters on the identification and shape of vortices will be investigated and an interpretation of vortices in such a filtered velocity field will be given. Support for this work from the AFOSR under award\# FA9550-09-1-0701 is gratefully acknowledged.   

Convection Velocities of Coherent Structures in a Thermally Perturbed Turbulent Boundary Layer

Increasing use of airborne laser-based communication systems has led to a need to understand the effects of turbulent boundary layers on the performance of such systems. As a beam of coherent light passes through a variable density flow, it is degraded as a result of changes in the index of refraction associated with the density fluctuations. In order to study this phenomenon, a zero-pressure gradient flat plate is subjected to a thermal perturbation, causing an internal, heated layer to form within the boundary layer. A Malley probe is used downstream of the perturbation to measure the Optical Path Difference of a laser traversing the flow. This probe consists of two parallel laser beams which deflect as heated turbulent structures convect through the beams. Cross-correlating the deflection angle spectrum of the two beams provides convective velocity information. The mean convective velocity is compared to the free stream velocity and estimates of structure convection velocities in the literature obtained using other diagnostics.   

Very large-scale motions in a turbulent pipe flow

Direct numerical simulation of a turbulent pipe flow with \textit{Re}$_{D}$=35000 was performed to investigate the spatially coherent structures associated with very large-scale motions. The corresponding friction Reynolds number, based on pipe radius $R$, is $R^{+}$=934, and the computational domain length is 30$R$. The computed mean flow statistics agree well with previous DNS data at \textit{Re}$_{D}$=44000 and 24000. Inspection of the instantaneous fields and two-point correlation of the streamwise velocity fluctuations showed that the very long meandering motions exceeding 25R exist in logarithmic and wake regions, and the streamwise length scale is almost linearly increased up to $y$/R$\sim $0.3, while the structures in the turbulent boundary layer only reach up to the edge of the log-layer. Time-resolved instantaneous fields revealed that the hairpin packet-like structures grow with continuous stretching along the streamwise direction and create the very large-scale structures with meandering in the spanwise direction, consistent with the previous conceptual model of Kim {\&} Adrian (1999).   

Why do large and small scales couple in a turbulent boundary layer?

Correlation measurement, which is not definitive, suggests that large and small scales in a turbulent boundary layer (TBL) couple. A TBL is modeled as a jungle of interacting nonlinear oscillators to explore the origin of the coupling. These oscillators have the inherent property of self-sustainability, disturbance rejection, and of self-referential phase reset whereby several oscillators can phase align (or have constant phase difference between them) when an ``external'' impulse is applied. Consequently, these properties of a TBL are accounted for: self-sustainability, return of the wake component after a disturbance is removed, and the formation of the 18o large structures, which are composed of a sequential train of hairpin vortices. The nonlinear ordinary differential equations of the oscillators are solved using an analog circuit for rapid solution. The post-bifurcation limit cycles are determined. A small scale and a large scale are akin to two different oscillators. The state variables from the two disparate interacting oscillators are shown to couple and the small scales appear at certain regions of the phase of the large scale. The coupling is a consequence of the nonlinear oscillatory behavior. Although state planes exist where the disparate scales appear de-superposed, all scales in a TBL are in fact coupled and they cannot be monochromatically isolated.   

Behavior captured by Lagrangian coherent structures near the wall in a turbulent boundary layer

In this study, Lagrangian coherent structures (LCS) are identified in a plane that is 50 viscous lengths from the wall in a turbulent boundary layer. To locate the LCS, the criteria introduced by Haller (2011)\footnote{Haller, G. Physica. D 240 7. (2011)}, which is based on a variational approach to optimizing normal repulsion (or attraction), is applied. The flow map is constructed by using time resolved velocity fields, obtained from high speed (1.5 kHz) PIV measurements, to compute trajectories (Integration time $\sim y^{+}\delta_{\nu}/u_{\tau}$ and time steps $\sim \delta_{\nu}/u_{\tau}$). The various turbulent behaviors captured by the repelling and attracting LCS are examined. In particular, the computed LCS are compared with plots of streamwise momentum, velocity fluctuations, dissipation, and various Eulerian fields that highlight vortical structures. It is found that different LCS depict structures corresponding to different Eulerian criteria. For instance, some LCS are boundaries between high and low momentum regions, while others surround vortical structures and/or exhibit high dissipation.