Motions In Turbulent Boundary Layer Research Articles

Energy transfer in the formation and evolution of energy-containing motions in turbulent boundary layers

This paper examines using direct numerical simulation (DNS) the recovery of the energy-containing scales of motion (energy-containing motions) when these are removed at the inflow boundary condition of a flat plate zero-pressure gradient turbulent boundary layer (ZPG-TBL). The energy-containing motions are identified from the spanwise spectral energy density of the interscale turbulent transport. Analysis of the resulting spanwise spectral energy densitiy of velocity and vorticity suggests that near-wall streaks are the initial energy-containing motions formed with quasi-streamwise vortices only developing further downstream. This result is in agreement with the previous study on turbulent channel flows by Kannadasan et al. [1].

Convection of multi-scale motions in turbulent boundary layer by temporal resolution particle image velocimetry

Experiments of particle image velocimetry (PIV) in the turbulent boundary layer at have been conducted to investigate the convection characteristic of turbulent structure and the validity of Taylor’s hypothesis. Views of (, the boundary layer thickness) were captured by four streamwise-arranged cameras. Distributions of streamwise turbulent kinetic energy on a streamwise scale were investigated by continuous-wave transform, and scales were found where the portion of streamwise turbulent kinetic energy approaches maximum. Fluctuating velocities (instant velocity minus average velocity on time dimension) were divided into large-scale motion (LSM) and small-scale motion (SSM) portions, bounded by . Convection velocities of LSM and SSM are determined by the spatiotemporal correlation method, and they are larger than local average velocities in near-wall regions, but smaller than local average velocities in wake regions. Statistical characteristics between velocity fields reconstructed by Taylor’s hypothesis and original fields were compared by the autocorrelation method, and the reconstructed field’s patterns are longer than original field’s patterns, while their heights do not have clear distinction. The correlation of original velocity fields and reconstructed fields shows that LSM can hold on over and SSM over in streamwise convection separation for regions of , given a threshold value (correlation coefficient C = 0.6).

Time-resolved sphere and fluid motions in turbulent boundary layers

This paper extends the study by Tee et al. (2020) to investigate the effect of large coherent structures on motion of spheres with specific gravities of 1.006 (P1) and 1.152 (P3) at Reτ = 670 and 1300 (d+ = 56 and 116). The sphere and fluid motions are tracked simultaneously via 3D particle tracking and stereoscopic particle image velocimetry over the streamwise-spanwise plane, respectively. With sufficient mean shear, sphere P1 lifts off of the wall upon release before descending back towards the wall at both Reτ. It typically accelerates strongly over a streamwise distance of less than one boundary layer thickness before approaching an approximate terminal velocity. By contrast, the denser sphere P3 does not lift off upon release but mainly slides along the wall. At lower Reτ where wall friction is stronger, this sphere translates with unsteady velocity, significantly lagging the local fluid. The streamwise velocities of both spheres correlate strongly with the fast- and slow-moving zones that approach and move over them. In most runs, both spheres lag the local coherent structures and travel with either fast- or slow-moving zones throughout the observed trajectories. Vortex shedding, which is most prevalent for sphere P3 at Reτ = 670, is also important. The sphere spanwise motion is prompted by wall friction, spanwise fluid motion, and/or meandering of the coherent structures, and spheres do not appear to migrate preferentially into slow-moving zones.

Large-scale coherent motions in turbulent boundary layers under an adverse pressure gradient up to flow separation

A turbulent boundary layer under the impact of a strong adverse pressure gradient up to flow separation is investigated experimentally at Reynolds numbers up to Reτ=12,000, with the aim to analyse and characterise the interaction between large-scale coherent turbulent structures and a separated flow region. It is shown that the dynamics of the separation line in space and time are strongly modulated by the low frequency large-scale flow motions. Using a conditional comparison of mean flow parameters, it is shown that high-momentum large-scale motions are able to shift the point of separation downstream while the opposite is true for low-momentum large-scale motions. This interaction has a significant impact on the temporal dynamics of the separation line. The spatial frequencies observable along the line of separation on the other hand are determined by the spanwise arrangement of high and low-momentum large-scale motions. Finally, it is demonstrated that the separated region does not have a major influence on the mean boundary layer thickness in contrast to the mean flow velocity and spatial scales of coherent structures which are visibly influenced in the vicinity of the separated region.

Optimal disturbances and large-scale energetic motions in turbulent boundary layers

We examine disturbances leading to optimal energy growth in a spatially developing, zero-pressure-gradient turbulent boundary layer. The slow development of the turbulent mean flow in the streamwise direction is modelled through a parabolized formulation to enable a spatial marching procedure. In the present framework, conventional spatial optimal disturbances arise naturally as the homogeneous solution to the linearized equations subject to a turbulent forcing at particular wavenumber combinations. A wave-like decomposition for the disturbance is considered to incorporate both conventional stationary modes as well as propagating modes formed by non-zero frequency/streamwise wavenumber and representative of convective structures naturally observed in wall turbulence. The optimal streamwise wavenumber, which varies with the spatial development of the turbulent mean flow, is computed locally via an auxiliary optimization constraint. The present approach can then be considered, in part, as an extension of the resolvent-based analyses for slowly developing flows. Optimization results reveal highly amplified disturbances for both stationary and propagating modes. Stationary modes identify peak amplification of structures residing near the centre of the logarithmic layer of the turbulent mean flow. Inner-scaled disturbances reminiscent of near wall streaks, and amplified over short streamwise distances, are identified in the computed streamwise energy spectra. In all cases, however, propagating modes surpass their stationary counterpart in both energy amplification and relative contribution to total fluctuation energy. We identify two classes of large-scale energetic modes associated with the logarithmic and wake layers of the turbulent mean flow. The outer-scaled wake modes agree well with the large-scale motions that populate the wake layer. For high Reynolds numbers, the log modes increasingly dominate the energy spectra with the predicted streamwise and wall-normal scales in agreement with superstructures observed in turbulent boundary layers.

Statistical evidence of anasymptotic geometric structure to the momentum transporting motions in turbulent boundary layers.

The turbulence contribution to the mean flow is reflected by the motions producing the Reynolds shear stress (〈-uv〉) and its gradient. Recent analyses of the mean dynamical equation, along with data, evidence that these motions asymptotically exhibit self-similar geometric properties. This study discerns additional properties associated with the uv signal, with an emphasis on the magnitudes and length scales of its negative contributions. The signals analysed derive from high-resolution multi-wire hot-wire sensor data acquired in flat-plate turbulent boundary layers. Space-filling properties of the present signals are shown to reinforce previous observations, while the skewness of uv suggests a connection between the size and magnitude of the negative excursions on the inertial domain. Here, the size and length scales of the negative uv motions are shown to increase with distance from the wall, whereas their occurrences decrease. A joint analysis of the signal magnitudes and their corresponding lengths reveals that the length scales that contribute most to 〈-uv〉 are distinctly larger than the average geometric size of the negative uv motions. Co-spectra of the streamwise and wall-normal velocities, however, are shown to exhibit invariance across the inertial region when their wavelengths are normalized by the width distribution, W(y), of the scaling layer hierarchy, which renders the mean momentum equation invariant on the inertial domain.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'.

Large-scale motions in turbulent boundary layers subjected to adverse pressure gradients

It is known that large-scale streamwise velocity-fluctuating structures ($u^{\prime }$) are frequently observed in the log region of a zero pressure gradient turbulent boundary layer, and that these motions significantly influence near-wall small-scale $u^{\prime }$-structures by modulating the amplitude (Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28; Mathis et al., J. Fluid Mech., vol. 628, 2009, pp. 311–337). In the present study, we provide evidence that the spatial organization of large-scale structures in the log region is significantly influenced by the strength of adverse pressure gradients in turbulent boundary layers based on a direct numerical simulation dataset. For a mild adverse pressure gradient boundary layer flow, groups of hairpin vortices are coherently aligned in the streamwise direction to form hairpin vortex packets, and streamwise merging events of the induced large-scale $u^{\prime }$-structures create a larger streamwise length scale of structures than that for a zero pressure gradient boundary layer flow. As the pressure gradient strength increases further, however, the formation of hairpin packets is continuously suppressed, and large-scale motions are consequently not concatenated to create a longer motion, resulting in a significant reduction of the streamwise coherence of large-scale structures in the log layer. Although energy spectrum maps for $u^{\prime }$-structures show that the large-scale energy is continuously intensified above the log layer with an increase in the pressure gradient, amplitude modulation of the near-wall small-scale motions is dominantly induced by log region large-scale structures for adverse pressure gradient flows. Conditional averaged flow fields with large-scale Q2 and Q4 events indicate that large-scale counter-rotating roll modes play an important role in organizing the flows under the pressure gradients, and the large-scale roll modes associated with Q4 events are more enhanced in the outer layer than those associated with Q2 events, reducing the streamwise coherence of the vortices in a packet.

Combining time-resolved multi-point and spatially-resolved measurements for the recovering of very-large-scale motions in high Reynolds number turbulent boundary layer

A methodology to recover very-large-scale motions based on the combination of time-resolved multi-point measurements and spatially-resolved full field information is here presented and applied to a high Reynolds number turbulent boundary layer flow developing over a flat plate. These very-large-scale motions are characterised by a large degree of persistence, both in time and space, and are believed to play an active role in the development of turbulence in the near-wall region (Bandyopadhyay and Hussain, 1984; Chung and McKeon, 2010; Hutchins and Marusic, 2007; Marusic et al., 2010). Due to the very large streamwise extent of these structures and of their meandering nature, point-measurement techniques or low time-resolved full field techniques such as Particle Image Velocimetry (PIV) offer a limited view when used alone. In the present paper, a time-resolved estimate of the full velocity vector field in a spanswise/wall-normal plane is obtained by combining low-repetition two-dimensional stereo-PIV measurements and a two-dimensional rake of 143 single hot-wire probes sampled at 30kHz. The latter is used to animate the PIV data at a high sampling rate by implementing an extended version of the complementary technique (Bonnet et al., 1994) which combines Proper Orthogonal Decomposition (POD) and multi-time Linear Stochastic Estimation (mLSE) (Kerhervé, 2012). The results show the potential of the methodology to extract large-scale motions in turbulent boundary layer. This paves the way for further advanced time-resolved description of the spatially developing very-large-scale structures populating the logarithmic region. In addition, the main characteristics of the structures observed are found to be well consistent with that described in literature, validating the methodology and the time-resolved data-set built.

Effects of spanwise spacing on large-scale secondary flows in rough-wall turbulent boundary layers

Large-scale secondary flows can sometimes appear in turbulent boundary layers formed over rough surfaces, creating low- and high-momentum pathways along the surface (Barros & Christensen, J. Fluid Mech., vol. 748, 2014, R1). We investigate experimentally the dependence of these secondary flows on surface/flow conditions by measuring the flows over streamwise strips of roughness with systematically varied spanwise spacing. We find that the large-scale secondary flows are accentuated when the spacing of the roughness elements is roughly proportional to the boundary layer thickness ${\it\delta}$, and do not appear for cases with finer spacing. Cases with coarser spacing also generate ${\it\delta}$-scale secondary flows with tertiary flows in the spaces in between. These results show that the ratio of the spanwise length scale of roughness heterogeneity to the boundary layer thickness is a critical parameter for the occurrence of these secondary motions in turbulent boundary layers over rough walls.

Conditional correlation between a passive scalar and its dissipation in a turbulent boundary layer

A study of the conditional correlation between a passive scalar and its dissipation offers an interesting strategy for understanding turbulence properties associated with both large and small scales. This correlation is investigated with particular emphasis on the dominant coherent motions in turbulent boundary layers; namely, sweeps and ejections, using a local cross-correlation analysis based on the wavelet transform. Contributions to the three temperature derivatives show different features, reflecting clear “local” departures from isotropy. This property of coherent motions is investigated through the conditional cross-spectra inferred from the wavelet analysis, which provides localized scale decomposition of the quantity under consideration, and is translated in the spectral domain. These decompositions indicate the particular coherent motions of the flow which most contribute to the conditional correlation between temperature and its dissipation.

Interferometric study of organized motions in turbulent boundary layers

Double-pulse holographic interferometry has been used to visualize organized structures in zero-pressure-gradient turbulent boundary layers over a flat plate at M=1.8, 2.5, and 3.6 (Re 0 =1.2×10 4 to 2.2×10 4 ) Differential interferograms taken with a pulse interval between 2 to 600 μs at three different Mach numbers show an interesting array of fringe cells that appear inclined downstream in the boundary layers. These fringe cells must be the interferometric images of large-scale outer-layer structures convecting in the main flow direction. On absolute interferograms of the boundary layers, the interferometric images appear as horizontal fringe lines running over the test surface. The wavy fringe pattern frequently exhibits distinct inclined interfaces with a positive upstream density gradient that must be associated with the backs of large-scale outer-layer bulges. Quantitative information of these structures has been extracted from the interferograms that is in agreement with data from other investigators using different experimental techniques. To aid the interpretation of the experimental data, interferograms have been generated numerically with the database from a large-eddy simulation. These interferograms also reveal regular fringe patterns in the boundary layer that are found to be produced by the large-scale structures in the layer

Coherent structures at the ocean surface in convectively unstable conditions

THE turbulent boundary layer at the ocean surface has some dynamical similarities to the atmospheric boundary layer1–4. The atmospheric turbulent boundary layer may exhibit not only random fluctuations but also spatially coherent, organized motion5,6. Thorpe1 conjectured that such organized motion should also be found in the upper ocean boundary layer in convectively unstable conditions. Here I report on observations made in the tropical Atlantic Ocean which confirm this view. Horizontal temperature profiles obtained at a depth of 2 m at night revealed ramp-like structures. Vertical velocity profiles in the upper few metres of the ocean was determined using a free-rising profiler, and exhibited abrupt changes corresponding to sudden changes in temperature. These features are known5,6 to be characteristic of spatially coherent, organized motions in turbulent boundary layers.