Structure Of Turbulent Boundary Layer Research Articles

Understanding Coherent Turbulence and the Roll‐Cell Transition With Lagrangian Coherent Structures and Frame‐Indifferent Fluxes

AbstractWe present the first analysis of frame‐indifferent (objective) fluxes and material vortices in Large Eddy Simulations of atmospheric boundary layer turbulence. We extract rotating fluid features that maintain structural coherence over time for near‐neutral, transitional, and convective boundary layers. In contrast to traditional analysis of coherent structures in turbulent boundary layers, we provide the first identification of vortex boundaries that are mathematically defined to behave as tracer transport barriers. Furthermore, these vortices are indifferent to the choice of observer reference frame and can be identified without user‐dependent velocity field decompositions. We find a strong agreement between the geometric qualities of the coherent structures we extract using our new method and classical descriptions of horizontal rolls and convective cells arising from decades of observational studies. We also quantify trends in individual vortex contributions to turbulent and advective fluxes of heat under varying atmospheric stability. Using recently developed tools from the theory of transport barrier fields, we compare diffusive momentum and heat barrier fields with the presence of rolls and cells, and determine a strong connection between heat and momentum orthogonality with the physical drivers of roll‐cell transformation. This newly employed frame‐indifferent characterization of coherent turbulent structures can be directly applied to numerical model output, and thus provides a new Lagrangian approach to understand complex scale‐dependent processes and their associated dynamics.

Mean-flow structures of the turbulent boundary layers bounding a two-dimensional separation bubble

Understanding the mean-flow structures of a separated turbulent boundary layer (TBL) is crucial for turbulence modeling. This study investigates the spatial scaling properties of the total shear stress and mixing length in the TBLs bounding a two-dimensional (2D) separation bubble, aiming to derive analytical descriptions for the entire mean-velocity profiles of the TBLs. For the adverse pressure gradient (APG) TBL upstream of the separation bubble, the total shear stress possesses a two-layer structure with an inner layer adhering to a linear law and an outer layer conforming to a defect power law. In contrast, the mixing length profile consists of four layers, namely the viscous sublayer, the buffer layer, the overlap layer, and the wake region. Each of the layers exhibits a power law or a defect power law relationship with the spatial coordinate normal to the wall. In the four-layer structure, three parameters are sensitive to the variation of the APG: the buffer-layer thickness, the relative magnitude of the mixing length at the boundary layer edge, and a defect power law exponent quantifying the extent of the wake region. For the reattached TBL downstream of the separation bubble, the total shear stress consists of two parts. One part is induced by the pressure gradient and retains the two-layer structure, while the other, engendered by the intense turbulence advected from the separated shear layer, exhibits a dual-power-law distribution. The advected turbulence also significantly alters the four-layer structure of the mixing length, resulting in an augmented buffer layer, a diminished overlap layer, and a wake region that mimics a turbulent mixing layer. Via a dilation ansatz to describe the scaling transition between adjacent layers, the study formulates the complete profiles of the total shear stress and mixing length. The formulation leads to the derivation of novel analytical expressions for the entire mean-velocity profiles of the TBLs. The expressions are in precise accord with the direct numerical simulations of an incompressible 2D separation-bubble flow and a 2D impinging shock wave/TBL interaction. The elucidation of the mean-flow structures through this study is anticipated to facilitate the analysis of turbulence models, thereby enhancing their performance in simulating separated TBLs. The construction of the mean-flow descriptions by inspecting the spatial scaling properties of turbulence paves a promising way for theoretical exploration of complex nonequilibrium TBLs.

Turbulent boundary layer structures downstream of a square cylinder

Particle image velocimetry is used to investigate the coherent structures within a turbulent boundary layer (TBL) perturbed by a slender square cylinder. A moderate Reynolds number of Reτ=3691 is considered. The cylinder is immersed in different vertical regions of the TBL, from the viscous sublayer to the logarithmic layer, depending on the value of the cylinder–wall gap ratio within the range of G/D=0.0−2.0. Here, G is the distance between the wall and the lower surface of the cylinder, and D is the cross-section size of the square cylinder. The results reveal a substantial influence of the TBL statistics and structures. Utilizing velocity correlation and proper orthogonal decomposition (POD), we highlight the intriguing influence of large-/very large-scale turbulent structures induced by the cylinder. When the cylinder is positioned on or in close proximity to the wall, periodic shedding of vortices is not apparent. In the presence of a cylinder, the large-/very large-scale turbulent structures are reduced in size compared with those in the undisturbed TBL, owing to the interaction between the flow around the cylinder and the boundary layer turbulence. The lower modes of the POD in the disturbed TBL are similar to those of the undisturbed flow field. However, the large-/very large-scale turbulent structures are increasingly affected by the strengthening of the shedding vortices with increasing G/D when the cylinder is located in the logarithmic region. As a result, the Kármán vortex street becomes the dominant structure associated with the higher POD modes at sufficiently high cylinder–wall gap ratios.

Kármán Street-Boundary Layer Interactions In Turbulent Flow

Understanding the intricate interplay between turbulent boundary layers and wake structures caused by obstacles in the flow is key to assessing the local shear stress fields as well as the drag. These types of flows can be relevant to natural phenomena including sediment and nutrient transport. While existing literature predominantly explores the flow downstream of cylinders mounted perpendicular to bounding surfaces or downstream of cylinders positioned outside the boundary layer region, this work experimentally studies the turbulent boundary layer passing over a cylindrical obstacle positioned near and parallel to the surface of an underlying solid wall. Planar particle image velocimetry (PIV) was performed in an open recirculating water channel for three test cases at a friction Reynolds number Reτ = 1320. Key parameters investigated include the cylinder diameter relative to the boundary layer thickness (D/δ = 0.09 and 0.01) and the gap between the cylinder and the wall (G/δ = 0.09), where the range of D/δ used is smaller than most examples found in the literature. Instantaneous and averaged velocity and vorticity fields are examined based on the PIV measurements. The results in Fig. 1 show how von Kármán vortex streets and turbulent boundary layer structures interact to form unique flow features. The larger cylinder generates a clear separation downstream of its axis as well as a wake that remains coherent over a distance δ downstream. The smaller cylinder with D/δ = 0.01 generates a much narrower and weaker wake, but still shows a clear influence on time-averaged velocity profile. Future experiments will evaluate flow conditions further downstream as well as additional values of G/δ for the same D/δ values.

Detecting the high/low-speed large-scale structures by a machine learning perspective in turbulent boundary

The current developments in machine learning have facilitated the application of data-driven strategies for predicting the evolution of vortex structures in turbulent boundary layers. This study combines the attached eddy hypothesis with the extreme gradient boosting model to forecast large-scale high/low-speed motion based on a series of input signals. The performance of the trained model, as quantified by the percentage of accurately predicted high/low-speed regions, exhibits variability concerning the deviation between the input velocity fluctuation and the predicted output value at z/δ=0.016, where ‘z’ represents the wall-normal height and ‘δ’ indicates the boundary layer thickness. Our findings underscore the significant potential of machine learning in predicting high/low-speed regions within large-scale motion.

Investigation of coherent structures in low-speed turbulent boundary layers controlled by AC-DBD plasma actuators

The dielectric barrier discharge (DBD) actuator has the advantages of being lightweight, having no moving parts, ease of use, and fast response, and has received widespread attention in flow control applications. Turbulence boundary layer drag reduction is one of many applications of DBD flow control, but the mechanism of DBD actuator turbulence drag reduction needs further investigation. The effect of DBD excitation on the skin-friction drag of a turbulent boundary layer on a flat plate at different flow speeds was investigated experimentally. The change in skin-friction drag was measured using oil film interferometry, and the velocity distribution within the boundary layer was obtained using a particle image velocimetry system. The results showed that under the action of the plasma actuator, the local skin-friction coefficient was measured to decrease by 49%. Through dynamic mode decomposition, plasma actuators can increase the thickness of the low-velocity region in the boundary layer, reduce the intensity of Q2 and Q4 events, and inhibit the development of coherent structures, thereby achieving drag reduction.

Effects of porous substrates on the structure of turbulent boundary layers

Three different porous substrates (with different pore sizes, $s$ , and permeabilities, $K$ ) are used to examine their effect on the structure of boundary layer flow over them. The flow is characterised with single-point hot-wire measurements as well as planar particle image velocimetry. In order to elucidate differences in shallow and deep flows past porous substrates, foams with two different thicknesses ( $h$ ) are used (for all three substrates). A wide range of friction Reynolds numbers ( $2000< Re_\tau <13\,500$ ) and permeability-based Reynolds numbers ( $1< Re_K< 50$ ) are attained. For substrates with $Re_K \sim 1$ , the flow behaviour remains similar to flow over impermeable smooth walls and as such Townsend's hypothesis remains valid. Very large-scale motions are observed over permeable foams even when the $Re_K > 1$ . In contrast, a substantial reduction in velocity disturbances and associated length scales is achieved for permeable foams with intermediate values of pore density and relative foam thickness ( $h/s$ ), which affects outer-layer similarity. As permeability is increased by increasing pore size, the foam becomes sparse relative to viscous scales at high Reynolds numbers. For such foams, the flow conforms to outer-layer similarity and is more akin to flow over rough surfaces. Permeability attenuates the wavelengths associated with the outer-layer peak.

Experimental study of coherent structures and bed shear stress on a smooth bed under a solitary wave

The coherent structures induced by a solitary wave on a smooth bed were studied in a wave flume. The solitary wave was near the point of incipient breaking and the wave Reynolds number was in the intermittent turbulent regime. The velocity field inside the bottom boundary layer was measured using a Particle Image Velocimetry (PIV) system. The bed shear stress was obtained from the measured velocities in the viscous sublayer by employing the Newton's law of viscosity. It was found that the generation and maintenance of turbulent coherent structures in a solitary wave boundary layer was like that observed in oscillatory flow boundary layers at similar wave Reynolds numbers, a process that was first described as the bursting phenomenon in the wall boundary layer of steady flows. The effect of coherent structures on the instantaneous velocity profile and bed shear stress was examined. Ejections and sweeps were found to play a crucial role in producing large bed shear stress fluctuations. Quadrant analysis and probability distribution plots of the bed shear stress showed that sweep (Q4) events were responsible for producing instantaneous bed shear stress values as high as four to five times the standard deviation above the mean, while ejection (Q2) events produced bed shear stress values mostly below the mean. Both types of events were more numerous than outward interaction (Q1) and inward interaction (Q3). It was also found that a high proportion of the measured velocity profiles that did not follow the law of the wall were associated with large vortices in the boundary layer. It was shown that the instantaneous velocities did not conform to a law-of-the-wall velocity profile unless the measured velocity field was averaged over an area large compared to the vortices.

Experimental investigation of particle dynamics in particle-laden turbulent boundary layer

In a horizontal wind tunnel, experiments were performed on both particle-free and particle-laden flows at the same incoming velocity. Glass micro-spheres were carried by air along the turbulent boundary layer at a high Reynolds number (Reτ=3200). The Stokes numbers of the solid particles considered were O(10) and O(102). Under a similar volume fraction, Φv=O(10−5), the velocity and spatial distribution of solid inertial particles were investigated using simultaneous particle image/tracking velocimetry measurements and time-resolved particle imaging. This allowed for the exploration of particle dynamics and their corresponding spatial structure in the particle-laden turbulent boundary layer. The results showed that particle–wall (P-W) interaction occurs in both types of particle-laden flows. However, the particle Stokes number directly affects the intensity of the P-W interaction, significantly altering the behavior and spatial organization of particles. The results from the Voronoi tessellation technique confirmed that preferential clustering still happens for the small particle case. In particular, the premultiplied spectra for the particle concentration showed that the temporal pattern of particle clustering presents a similar time-scale to very large-scale motion (around 22δ, where δ is the boundary layer thickness) in the near-wall region.

Polymer drag reduction: A review through the lens of coherent structures in wall-bounded turbulent flows

The current work qualitatively surveys the phenomenon of polymer drag reduction from the standpoint of the salient coherent motions in the near-wall region of wall-bounded turbulent flows. In an attempt to make the work self-containing, turbulence is introduced phenomenologically in terms of the scale separation concept. In concert with this theme, the idea of drag crisis is then developed in terms of reduction in this scale separation. Leveraging such a perspective, it is explained how the polymer chain dynamics spatiotemporally modulate the near-wall structure of turbulent boundary layers to affect drag reduction. To this end, a sea of literature pertaining to coherent motions in Newtonian wall-bounded flows is juxtaposed with the turbulence-inhibiting characteristics of polymer chains to develop a polymer-modified version for the near-wall cycle of turbulence generation and its sustenance. The future of polymer drag reduction, in light of the current state of knowledge and contemporary challenges, is also discussed.

Coherent structures and turbulent model refinement in oblique shock/hypersonic turbulent boundary layer interactions

In the present study, we investigate the evolution of turbulent statistics and coherent structures in hypersonic turbulent boundary layers at the Mach number of 5 impinged by oblique shock waves generated by the wedge with the angles of 14°, 10°, and 6°, inducing strong, mild, and incipient flow separation, by exploiting direct numerical simulation databases, for the purpose of revealing the underlying flow physics that are of significance to turbulent modeling. We found that the large-scale structures are amplified within the interaction zone, manifested in the form of large-scale low- and high-speed streaks with the spanwise length scale of boundary layer thickness, and gradually decay downstream, the process of which is extremely long. The abrupt variation in the characteristic length, time, and velocity scales as well as the incompatible viscous dissipation of the mean and turbulent kinetic energy results in the incorrect predictions by the Reynolds-Averaged Navier–Stokes (RANS) equation simulations, provided the models are established based on solving the transport equations of the turbulent kinetic equation and its viscous dissipation (k−ε or k−ω models, for instance). To amend this issue, we propose to refine the parameters in the model as the functions of wall pressure, the flow quantities related to multiple flow features. The RANS simulations with the k−ω SST model utilizing the proposed refinement improve greatly the accuracy of the skin friction, wall heat flux, and Reynolds shear stress downstream of the interaction zone, and the wall pressure distributions in hypersonic turbulence over compression ramp, suggesting its promising prospect in engineering applications.

Wind turbine wake: bridging the gap between large eddy simulations and wind tunnel experiments

The wind industry has experienced rapid growth over the past two decades and wind energy is expected to continue leading the way in the global energy transition. Additional wind farms are expected to be installed in the coming years, both offshore and onshore. In view of exploiting any suitable terrain, an increased number of turbines are installed in close proximity to existing structures, thus exposing these to the wake turbulence. For instance, electrical cables are regularly exposed to those higher levels of turbulence compared to design loads, potentially leading to premature failure of the power line. It is hence essential to have a good understanding of these phenomena to be able to mitigate their effects. Scale-resolving investigations using Large Eddy Simulation (LES) can provide insight into site-specific loading conditions when combined with an Actuator Line Model (ALM), which reproduces the reaction force of each blade on the flow while still using a relatively coarse grid. The ALM used in this framework was newly-implemented in the spectral element code Nek5000, a highly efficient code with reduced cost per degree of freedom and exponentially fast convergence. The present work aims to bridge the gap between LES and a well controlled wind tunnel test of a scaled wind turbine, for validation purposes.First, a small scale wind turbine of diameter 80 cm is designed and tested in a well controlled wind tunnel environment. Experimental data are gathered ahead of it and in its wake, and the mean velocity and turbulence intensity profiles are presented.Although blockage effects are kept to a minimum, they will be accounted for in the simulations to ensure a better comparison with the measurements. In this work, we focus on a single inflow velocity field and on a fixed rotation speed.Simulating the produced wake using LES combined with ALM remains challenging as the results are very sensitive to the turbulent inflow conditions and also to the airfoil aerodynamics used in the ALM. In the experiment, the incoming profile is also that of a developing flow and accurately reproducing its main characteristics is required for proper inflow to the LES. A “Recycle and Rescale Method” (R2M) will be hence be used as it is well suited for such case. The method will allow for the relevant turbulent boundary layer structures to be properly reproduced numerically, hence ensuring that the wind turbine is exposed to similar inflow conditions than in the experiment.With the developed framework, the comparison between the wake produced in the experiment and that obtained using LES with ALM will provide the necessary data to further adjust the parameter and grid size used for the LES and the polar model used in the ALM.

Drag Reduction Performance of Triangular (V-groove) Riblets with Different Adjacent Height Ratios

Surface structure is used to interfere with the turbulent boundary layer in the groove drag reduction, which is important to the endurance and stability of high-speed and ultrahigh-speed aircraft. The size of the groove structure directly affects the flow in the turbulent boundary layer and changes the drag reduction effect. The drag reduction characteristics of bionic triangular (V-groove) riblets were studied through Particle Image Velocimetry (PIV) experiment and Finite Volume Method (FVM) simulation. Triangular riblets with adjacent height ratios (AHR) of 1.00, 1.74, and 3.02 were considered in this research, and the influence of these groove structures on the flow characteristics of turbulence near the wall is compared with those of the smooth plates. The distribution of time-averaged velocity, turbulence intensity, and coherent structures of turbulent boundary layer on the riblet surface is analyzed to document the effects of the geometric parameters of various groove structures on drag reduction rates. Results showed that the best drag reduction is obtained using the V-groove riblets with adjacent height ratio of 1:1 under the low free-stream velocity. The results can be used as a reference for further optimization of drag reduction structures with surface grooves.

Large-Scale Coherent Turbulence Structures in the Atmospheric Boundary Layer over Flat Terrain

Abstract We investigate characteristics of large-scale coherent motions in the atmospheric boundary layer using field measurements made with two long-range scanning wind lidars. The joint scans provide quasi-instantaneous wind fields over a domain of ∼50 km2, at two heights above flat but partially forested terrain. Along with the two-dimensional wind fields, two-point statistics and spectra are used to identify and characterize the scales, shape, and anisotropy of coherent structures—as well as their influence on wind field homogeneity. For moderate to high wind speeds in near-neutral conditions, most of the observed structures correspond to narrow streaks of low streamwise momentum near the surface, extending several hundred meters in the streamwise direction; these are associated with positive vertical velocity ejections. For unstable conditions and moderate winds, these structures become large-scale rolls, with longitudinal extent exceeding the measuring domain (>∼5 km); they dominate the conventional surface-layer structures in terms of both physical scale and relative size of velocity-component variances, appearing as quasi-two-dimensional structures throughout the entire boundary layer. The observations shown here are consistent with numerical simulations of atmospheric flows, field observations, and laboratory experiments under similar conditions. Significance Statement Coherent structures have attracted the interest of researchers for decades, being viewed as the closest to “order” that we can find within the chaos of turbulence. In the turbulent atmospheric boundary layer, micro- and mesoscale coherent structures come in many shapes and sizes, such as convective cells, rolls, or streaks. In this study we used dual lidars (remote sensing measurements), developing analysis of their tandem usage to characterize in detail some of the large-scale coherent structures generated over flat terrain. This allowed us to better understand the mechanisms that generate such structures and describe their influence on the morphology of the turbulent atmospheric boundary layer across a good deal of its depth.

Meandering features of wall-attached structures in turbulent boundary layer

In wall turbulence, meandering behaviors of large-scale structures observed in the logarithmic layer is a crucial spatial feature for understanding the spatial organization of these structures and improving the structure-based turbulence model. These structures extend from the near-wall region to the edge of boundary layers. Their meandering motions leave an imprint on the two-point turbulence statistics across the flow, especially in the logarithmic region. Here, we demonstrate the influence of the meandering motions of wall-attached structures on the two-point correlation and premultiplied two-dimensional spectra by analyzing direct numerical simulation data of the turbulent boundary layer.

Wall-attached temperature structures in supersonic turbulent boundary layers

It is well known that low- and high-speed velocity streaks are statistically asymmetric. However, it is unclear how different the low- and high-temperature structures (T-structures) are even though they are strongly coupled with the streamwise velocity. Therefore, this paper identifies three-dimensional wall-attached temperature structures in supersonic turbulent boundary layers over cooled and heated walls (coming from direct numerical simulations) and separates them into positive and negative families. Wall-attached T-structures are self-similar; especially, the length and width of the positive family are linear functions of the height. The superposed temperature variance in both positive and negative families exhibits a logarithmic decay with the wall distance, while the superposed intensity of the wall-normal heat flux in the negative family shows a logarithmic growth. The modified strong Reynolds analogy proposed by Huang, Coleman, and Bradshaw [“Compressible turbulent channel flows: DNS results and modelling,” J. Fluid Mech. 305, 185–218 (1995)] is still valid in the negative family. The relative position between T-structures of opposite signs depends on the wall temperature and that in the cooled-wall case differs significantly from the relative position between low- and high-speed streaks, especially those tall ones. In the cooled-wall case, although positive temperature fluctuations below and above the maximum of the mean temperature can cluster to large-scale wall-attached structures, they are very likely dynamically unrelated.

Parabolic resolvent modes for streaky structures in transitional and turbulent boundary layers

Resolvent analysis is a powerful tool in fluid mechanics, both for laminar and turbulent flows. Depending on application, computational cost is still a limiting factor. We develop a parabolic method for the calculation of low-frequency resolvent modes, associated with streaky structures, which can enable more than an order of magnitude speed up compared to usual global calculations. The method is applied to both laminar and turbulent boundary layers, unveiling physical mechanisms such as those associated with streak growth due to free-stream turbulence, in the laminar case, and the double peak in the frequency spectrum of velocity fluctuations, in a turbulent boundary layer.

Outer-layer coherent structures from the turbulent/non-turbulent interface perspective at moderate Reynolds number

This study reports the observation of outer-layer coherent structures in turbulent boundary layer from the turbulent/non-turbulent interface perspective at moderate Reynolds number. The observation relies on time-resolved particle image velocimetry measurements with a large field-of-view. The local turbulent kinetic energy is used to detect the turbulent/non-turbulent interface. In the reference frame of turbulent/non-turbulent interface, raw velocity is decomposed into three components: time average of raw velocity, conditionally averaging components and turbulent fluctuations. The triple velocity decomposition eliminates the bias of Reynolds decomposition fluctuations in the intermittent region. The conditional statistics based on the turbulent/non-turbulent interface is considered to discuss the turbulence characteristics. The basic statistics of mean raw velocity, Reynolds stresses, and swirling strength are observed in conditional statistics. And the results are compared with the results based on the traditional wall surface reference frame. Quadrant analysis is introduced to extract ejections & sweeps and reflect the statistical characteristics of the outer-layer structure. The contribution of ejections and sweeps to the Reynolds shear stresses exhibits significantly different characteristics. Then, the configuration of the turbulent fluctuations and instantaneous structures is presented relied on the uniform momentum zones in the instantaneous frames. The spatial characteristics of coherent structures are reflected by two-point correlation of the streamwise turbulent fluctuations. In addition, the spatial scale of the outer-layer structures is revealed from the turbulent/non-turbulent interface perspective.

Effects of submerged synthetic jet on the coherent structures in turbulent boundary layer

Effects of submerged synthetic jet on the coherent structures in turbulent boundary layer

Effect of compressibility on the small-scale structures in hypersonic turbulent boundary layer

The effects of the wall temperature and local compressibility on the small-scale structures, local flow topology, and enstrophy production in the hypersonic turbulent boundary layer are numerically investigated. The colder wall temperature significantly enhances the unstable topologies and non-focal topologies near the wall, mainly due to stronger compressibility and more sheet-like structures. The eigenvalue decomposition of the strain rate tensor is introduced to investigate the mechanism of the enstrophy production and small-scale structures. It is shown that in the near wall region, the enstrophy production is mainly governed by the intermediate eigenvalue of strain-rate tensor through flow topologies unstable node/saddle/saddle (UN/S/S), stable focus/stretching (SFS), unstable focus/stretching, and unstable node/unstable node/unstable node, while the enstrophy destruction is primarily contributed by the intermediate eigenvalue through flow topologies stable node/saddle/saddle, stable focus/compressing (SFC), and stable node/stable node/stable node. Moreover, in the far wall region, the third eigenvalue in flow topology SFS and the intermediate eigenvalue in UN/S/S make major contributions to the enstrophy production, while the first eigenvalue in flow topologies unstable focus/compressing and SFC, and the intermediate eigenvalue in SFC mainly lead to the enstrophy destruction.