Energetic Scales Research Articles

Detection of Energetic Low Dimensional Subspaces in Spatio-Temporal Space in Turbulent Pipe Flow

AbstractLow dimensional subspaces are extracted out of highly complex turbulent pipe flow at $$Re_{\tau }=181$$ R e τ = 181 using a Characteristic Dynamic Mode Decomposition (CDMD). Having lower degrees of freedom, the subspaces provide a more clear basis to detect events which meet our understanding of large-scale coherent structures. To this end, a temporal sequence of state vectors from direct numerical simulations are rotated in space-time such that persistent dynamical modes on a hyper-surface are found travelling along its normal in space-time, which serves as the new time-like coordinate. The main flow features are captured with a minimal number of modes on a moving frame of reference whose velocity matches that of the most energetic scale. Reconstruction of the candidate modes in physical space gives the low rank model of the flow. The structures living in this subspace have long lifetimes, posses wide range of length-scales and travel at group velocities close to that of the moving frame of reference. The modes within this subspace are highly aligned, but are separated from the remaining modes by larger angles. We are able to capture the essential features of the flow like the spectral energy distribution and Reynolds stresses with a subspace consisting of about 10 modes. The remaining modes are collected in two further subspaces, which distinguish themselves by their axial length scale and degree of isotropy.

Effects of Pressure and Characteristic Scales on the Structural and Statistical Features of Methane/Air Turbulent Premixed Flames

In this study, the highly nonlinear and multi-scale flame-turbulence interactions prevalent in turbulent premixed flames are examined by using direct numerical simulation (DNS) datasets to understand the effects of increase in pressure and changes in the characteristic scale ratios at high pressure. Such flames are characterized by length-scale ratio (ratio of integral length scale and laminar thermal flame thickness) and velocity-scale ratio (ratio of turbulence intensity and laminar flame speed). A canonical test configuration corresponding to an initially laminar methane/air lean premixed flame interacting with decaying isotropic turbulence is considered. We consider five cases with the initial Karlovitz number of 18, 37, 126, and 260 to examine the effects of an increase in pressure from 1 to 10 atm with fixed turbulence characteristics and at a fixed Karlovitz number, and the changes to characteristic scale ratios at the pressure of 10 atm. The increase in pressure for fixed turbulence characteristics leads to enhanced flame broadening and wrinkling due to an increase in the range of energetic scales of motion. This further manifests into affecting the spatial and state-space variation of thermo-chemical quantities, single point statistics, and the relationship of heat-release rate to the flame curvature and tangential strain rate. Although these results can be inferred in terms of an increase in Karlovitz number, the effect of an increase in pressure at a fixed Karlovitz number shows differences in the spatial and state-space variations of thermo-chemical quantities and the relationship of the heat release rate with the curvature and tangential strain rate. This is due to a higher turbulent kinetic energy associated with the wide range of scales of motion at atmospheric pressure. In particular, the magnitude of the correlation of the heat release rate with the curvature and the tangential strain rate tend to decrease and increase, respectively, with an increase in pressure. Furthermore, the statistics of the flame-turbulence interactions at high pressure also show sensitivity to the changes in the characteristic length- and velocity-scale ratios. The results from this study highlight the need to accurately account for the effects of pressure and characteristic scales for improved modeling of such flames.

Assessing turbulence and mixing parameterizations in the gray-zone of multiscale simulations over mountainous terrain during the METEX21 field experiment

Multiscale numerical weather prediction models transition from mesoscale, where turbulence is fully parameterized, to microscale, where the majority of highly energetic scales of turbulence are resolved. The turbulence gray-zone is situated between these two regimes and multiscale models must downscale through these resolutions. Here, we compare three multiscale simulations which vary by the parameterization used for turbulence and mixing within the gray-zone. The three parameterizations analyzed are the Mellor-Yamada Nakanishi and Niino (MYNN) Level 2.5 planetary boundary layer scheme, the TKE-1.5 large eddy simulation (LES) closure scheme, and a recently developed three-dimensional planetary boundary layer scheme based on the Mellor-Yamada model. The simulation domain includes complex (i.e., mountainous) terrain in Nevada that was instrumented with meteorological towers, profiling and scanning lidars, a tethered balloon, and a surface flux tower. Simulations are compared to each other and to observations, with assessment of model skill at predicting wind speed, wind direction and TKE, and qualitative evaluations of transport and dispersion of smoke from controlled releases. This analysis demonstrates that microscale predictions of transport and dispersion can be significantly influenced by the choice of turbulence and mixing parameterization in the terra incognita, particularly over regions of complex terrain and with strong local forcing. This influence may not be apparent in the analysis of model skill, and motivates future field campaigns involving controlled tracer releases and corresponding modeling studies of the turbulence gray-zone.

Strain gradient plasticity with nonlinear evolutionary energetic higher order stresses

This paper explores the effect of evolutionary-type nonlinear energetic higher order stress inside the strain gradient plasticity framework that allows nonlinearity in dissipation. Based on the fundamental principles of thermodynamics, a multi-term Chaboche-type model has been formulated to describe the evolution of energetic moment stresses that depend on strain gradient and effective plastic strain. The derived evolutionary relation shows a coupling between energetic and dissipative length scales. The energetic part of the higher order stress, related to the GND formation, saturates as effective plastic strain increases during plastic flow. Higher order stress update equation and material tangent are derived using implicit time discretization. The proposed nonlinear energetic moment stress model confirms its applicability compared to experimentally observed responses. Our study demonstrates the importance of incorporating a nonlinear kinematic hardening rule to accurately represent the Bauschinger effect in samples with a thickness of less than 1μm. The cyclic bending experiment with a single slip sample shows that the nonlinear kinematic hardening rule can effectively capture nonlinearity in the experimental observation. Compressed shear layer simulation reveals that consideration of thickness-dependent relaxation coefficient accurately models the experimental observations. Thus, it makes further relevant consideration of a more advanced kinematic hardening rule through the proposed approach.

The Time Scale of Shallow Convective Self-Aggregation in Large-Eddy Simulations Is Sensitive to Numerics.

Numerical simulations of the tropical mesoscales often exhibit a self-reinforcing feedback between cumulus convection and shallow circulations, which leads to the self-aggregation of clouds into large clusters. We investigate whether this basic feedback can be adequately captured by large-eddy simulations (LESs). To do so, we simulate the non-precipitating, cumulus-topped boundary layer of the canonical "BOMEX" case over a range of numerical settings in two models. Since the energetic convective scales underpinning the self-aggregation are only slightly larger than typical LES grid spacings, aggregation timescales do not converge even at rather high resolutions (<100m). Therefore, high resolutions or improved sub-filter scale models may be required to faithfully represent certain forms of trade-wind mesoscale cloud patterns and self-aggregating deep convection in large-eddy and cloud-resolving models, and to understand their significance relative to other processes that organize the tropical mesoscales.

Concluding remarks: Sustainable nitrogen activation - are we there yet?

The activation of dinitrogen as a fundamental step in reactions to produce nitrogen compounds, including ammonia and nitrates, has a cornerstone role in chemistry. Bringing together research from disparate fields where this can be achieved sustainably, this Faraday Discussion seeks to build connections between approaches that can stimulate further advances. In this paper we set out to provide an overview of these different approaches and their commonalities. We explore experimental aspects including the positive role of increasing nitrogen pressure in some fields, as well as offering perspectives on when 15N2 experiments might, and might not, be necessary. Deconstructing the nitrogen reduction reaction, we attempt to provide a common framework of energetic scales within which all of the different approaches and their components can be understood. On sustainability, we argue that although green ammonia produced from a green-H2-fed Haber-Bosch process seems to fit the bill, there remain many real-world contexts in which other, sustainable, approaches to this vital reaction are urgently needed.

A data-driven optimal disturbance procedure for free-stream turbulence induced transition

The investigation of free-stream turbulence induced transition by means of simple and effective numerical methods traditionally represents a major challenge in the aerodynamic field. In this work, a data-driven algorithm aimed at obtaining optimal forcing and response concerning free-stream turbulence induced boundary layer transition is introduced. The method, referred to as Data-driven Optimal Disturbance (DOD) in the following, relies on dynamic mode decomposition to compute the linear matrix responsible for disturbance evolution in the streamwise direction and opens the possibility for optimal disturbance analysis in an equation-free manner. The procedure has been applied to high-fidelity large-eddy simulation (LES) results concerning zero pressure gradient flows. Four different combinations of turbulence intensity Tu and integral length scale Lg have been adopted as boundary conditions to investigate the sensitivity of the transition route to the free-stream turbulence properties. Overall, DOD applied within the transitional region identifies highly energetic turbulent scales embedded in the free-stream as the optimal forcing inducing the formation of streaky structures within the boundary layer. Furthermore, streaky structures characterized by the same spanwise wavelength observed in the LES results are identified by DOD as the boundary layer response to the optimal forcing. Finally, the amplification of disturbances provided by DOD along the streamwise direction clearly resembles the well-established transient growth. Thus, DOD appears a useful tool to analyze the free-stream turbulence induced transition of boundary layers by a simple equation-free algorithm merely based on data analytics.

Effects of thermal stratification and turbulent intensity on auto-ignition and combustion mode transition

Hydrogen engines with zero-carbon emissions have recently drawn attention while they often suffer from pre-ignition and knocking issues. It is generally understood that knocking intensity is closely associated with auto-ignition development modes, which are affected by multiple variables and their interactions. In this work, the role of thermal stratification and turbulent intensity in auto-ignition development modes were numerically investigated, addressing combustion mode transition. Representative end-gas auto-ignition conditions were employed for hydrogen/air mixtures. Meanwhile, the support vector machine (SVM) algorithm was first applied in the predictions of detonation development. The results show that thermal stratification plays a decisive role in auto-ignition development modes, and supersonic auto-ignition deflagration, direct detonation, and subsonic auto-ignition deflagration can be sequentially observed with the increase of temperature gradient. However, affected by multiple hotspot interactions and pressure wave disturbance, deflagration to detonation transition arising from secondary hotspot auto-ignition becomes prevalent. It is noted that, unlike direct detonation that evolves at the entire circumferential directions, deflagration to detonation transition develops only along certain directions with intermediate temperature gradient, and such gradient steepness is much higher than previous results based on simplified models. When turbulence fluctuation is introduced, the distribution of thermal stratification is modified significantly and the local temperature field is broken into multiple smaller regions filled with mixed temperature gradients. Consequently, deflagration to detonation transition is promoted both temporally and spatially, especially at high turbulence intensity. Besides, the SVM classifier is trained using the above results of numerical simulations for detonation predictions. A diagram consisting of the most energetic length scale and temperature fluctuation is proposed, which shows good performance in predicting detonation occurrence. The present study demonstrates that thermal stratification and turbulent intensity can significantly affect the transition behavior of auto-ignition development mode, and machine learning approaches have the potential to achieve good predictions for detonation occurrence in multiple physical fields.

Experimental Analysis of the Wake Meandering of a Floating Wind Turbine under Imposed Surge Motion

With the development of floating wind farms, the understanding of the far wake becomes of utmost importance because it cannot only be based on the experience acquired on fixed offshore turbine as the range of motion of the floater due to met-ocean conditions is in the same order of magnitude compared to the energetic turbulent scales of the atmosphere and to the characteristic scales of the wake. The objective of this wind-tunnel experiment is to analyse the behaviour of the wake center of a floating turbine subject to imposed surge motion. The experiment is carried out in the LHEEA wind tunnel where a 1/500 scale wind turbine model is immersed in a realistic offshore atmospheric-boundary layer. The model is actuated in surge by a linear motor able to reproduced idealised second order surge motion of a floating platform (mainly due to the waves) with a realistic amplitude and range of frequencies. Stereoscopic particle image velocimetry measurements are performed at two planes normal to the free-stream at distances of 4.6 and 8.1 diameters downstream of the turbine. Instantaneous velocity fields acquired at 14.1 Hz are individually analysed by convolution to find the location of the wake center. Results show that the wake center spreading is largely influenced by the downstream distance and only slightly affected by the surge motion. However, when analysing the wake position time series by a power spectral density, the signature of the surge motion becomes very clear for both downstream distances. These findings tell that the far wake (at least up to 8.1 diameters downstream) of a floating wind turbine has a “memory” of the motion in its frequency content. When extrapolating to a floating wind farm, this result suggests that a turbine inside a floating wind farm will be immersed in a flow including a significant dynamic signature in the range of its own motion.

Large‐eddy simulation of very stable boundary layers. Part I: Modeling methodology

AbstractThe large‐eddy simulation of very stable boundary layers (SBLs) remains challenging due to the large anisotropy of turbulent motions resulting from buoyancy suppression effects, and to the general reduction of its energetic scales. Here, we develop a novel large‐eddy simulation model setup to enable the modeling of the very SBL, avoiding the use of the Monin–Obukhov similarity theory at its lower boundary condition, as it breaks down in these conditions in agreement with previous studies. The new approach requires very fine grids in the vertical direction, in the order of a few centimeters. A series of Ekman‐layer‐type boundary layers under weak‐wind conditions ( and 2 ms), and strong surface cooling rates (1 and 3 Khr) at high latitude is studied using isotropic grids of 0.05 and 0.10 m resolution. The low‐order statistics show some sensitivity to the grid resolution; for example, both the SBL height and the low‐level jet position decrease with increasing grid resolution. In general, some differences are spotted regarding the shape of the wind speed and temperature vertical profiles, compared with weakly to moderately stratified conditions, suggesting that the structure and characteristics of the SBL evolve with increasing stratification. Moreover, the wind turning is significant from the surface, where the surface wind angle relative to the geostrophic wind is about 50. Lastly, two regimes within very stable conditions can be qualitatively identified primarily based on the gradient Richardson number () profiles: In the less stable regime, increases almost linearly with height and a quasi‐steady state is achieved; however, in the most stable regime, sharply increases near the surface and remains constant throughout the SBL while increasing with time up to . Thus, a quasi‐steady state is not achieved; and although turbulence does not collapse, it remains weak.

Wave‐Enhanced Tracer Dispersion

AbstractRecent oceanic datasets indicate high gravity wave‐to‐balance energy ratio at submesoscales. Idealized investigations exploring such wave‐dominated regimes have found that waves can break up coherent vortices and generate energetic small scale flow structures, indicating that the turbulence phenomenology is very different in wave‐dominated regimes when compared to the quasi‐geostrophic regime. Motivated by these recent investigations revealing significant differences in the flow dynamics in quasi‐geostrophic and wave‐dominated regimes and multiple oceanic observations pointing out enhanced tracer stirring at submesoscales, in this paper we compare and contrast passive tracer dispersion by barotropic flows in quasi‐geostrophic and wave‐dominated turbulent regimes using the reduced model explored by Thomas and Yamada (2019), https://doi.org/10.1017/jfm.2019.465. On comparing passive tracer dispersion by barotropic flows in the two different regimes, we find that wave‐dominated turbulent flows stir and mix tracer fields much more rapidly than quasi‐geostrophic turbulent flows that consist of well‐defined coherent vortices. The presence of energetic small‐scale features in wave‐dominated flows increases small‐scale turbulent diffusivity and results in steeper tracer variance spectrum in wave‐dominated flows compared to the quasi‐geostrophic flows. Our findings point out that gravity waves can play an indirect role in enhancing tracer dispersion: waves modify the flow, generating energetic small‐scale structures, that makes stirring of tracers more efficient. Despite our study being idealized, we speculate the qualitative phenomenology of waves indirectly enhancing tracer dispersion to be of significance at submesoscales in the world's oceans.

Kinetic energy cascade in stably stratified open-channel flows

In this paper, the kinetic energy cascade in stably stratified open-channel flows is investigated. A mathematical framework to incorporate vertical scales into the conventional kinetic energy spectrum and its budget is introduced. This framework defines kinetic energy density in horizontal spectral and vertical scale space. The energy cascade is studied by analysing the evolution of kinetic energy density. It is shown that energetic streamwise scales ($\lambda _x$) become larger with increasing vertical scale. For the strongest stratification, for which the turbulence becomes intermittent, the energetic streamwise scales are suppressed, and energy density resides in $\lambda _x$ of the size of the domain. It is shown that, in an unstratified case, vertical scales of the size comparable to the height of the logarithmic layer connect viscous regions to the outer layer. By contrast, in stratified cases, such a connection is not observed. Moreover, it is shown that nonlinear transfer for streamwise scales is dominated by in-plane triad interactions and inter-plane transfer is more active in transferring energy density among small vertical scales of the size comparable to the height of viscous sublayer. The vertical scales of size comparable to the height of the viscous sublayer and buffer layer are the most active scales in the viscous term and the production term in the energy density budget, respectively.

A micromechanics-based constitutive model for nanocrystalline shape memory alloys incorporating grain size effects

A micromechanics-based model is developed to capture the grain-size dependent superelasticity of nanocrystalline shape memory alloys (SMAs). Grain-size effects are incorporated in the proposed model through definition of dissipative length scale and energetic length scale parameters. In this paper, nanocrystalline SMAs are considered as two-phase composites consisting of the grain-core phase and the grain-boundary phase. Based on the Gibbs free energy including the spatial gradient of the martensite volume fraction, a new transformation function determining the evolution law for transformation strain is derived. Using micromechanical averaging techniques, the grain-size-dependent superelastic behavior of nanocrystalline SMAs can be described. The internal length scales are calibrated using experimental results from published literature. In addition, model validation is performed by comparing the model predictions with the corresponding experimental data on nanostructured NiTi polycrystalline SMA. Finally, effects of the internal length scales on the critical stresses for forward and reverse transformations, the hysteresis loop area (transformation dissipation energy), and the strain hardening are investigated.

SPH Viscous Flow Around a Circular Cylinder: Impact of Viscous Formulation and Background Pressure

Two-dimensional dynamics of the wake in transitional flow around a circular cylinder is studied using weakly compressible smoothed particle hydrodynamics scheme up to 10 cylinder diameters downstream at a Reynolds number of 4000. The main objectives of this study are to evaluate the capability of SPH-LES and artificial viscosity in capturing flow activity as well as to test the performance of these formulations and background pressure coupling against the so-called tensile instability and to understand the effect of this instability in terms of mean integral quantities, first-order statistics and frequency spectra. It is observed that the effect of viscous formulation on flow dynamics becomes significant between four-and-seven diameters downstream of the cylinder. Background pressure coupling shifts the onset of transition about two diameters upstream by creating stiffer density field; however, it results in more energetic smaller scale activity.

The Influence of Magnetic Turbulence on the Energetic Particle Transport Upstream of Shock Waves

Energetic particles are ubiquitous in the interplanetary space and their transport properties are strongly influenced by the interaction with magnetic field fluctuations. Numerical experiments have shown that transport in both the parallel and perpendicular directions with respect to the background magnetic field is deeply affected by magnetic turbulence spectral properties. Recently, making use of a numerical model with three dimensional isotropic turbulence, the influence of turbulence intermittency and magnetic fluctuations on the energetic particle transport was investigated in the solar wind context. Stimulated by this previous theoretical work, here we analyze the parallel transport of supra-thermal particles upstream of interplanetary shock waves by using in situ particle flux measurements; the aim was to relate particle transport properties to the degree of intermittency of the magnetic field fluctuations and to their relative amplitude at the energetic particle resonant scale measured in the same regions. We selected five quasi-perpendicular and five quasi-parallel shock crossings by the ACE satellite. The analysis clearly shows a tendency to find parallel superdiffusive transport at quasi-perpendicular shocks, with a significantly higher level of the energetic particle fluxes than those observed in the quasi-parallel shocks. Furthermore, the occurrence of anomalous parallel transport is only weakly related to the presence of magnetic field intermittency.

Lagrangian pair dispersion in upper-ocean turbulence in the presence of mixed-layer instabilities

Turbulence in the upper ocean in the submesoscale range (scales smaller than the deformation radius) plays an important role for the heat exchanges with the atmosphere and for oceanic biogeochemistry. Its dynamics should strongly depend on the seasonal cycle and the associated mixed-layer instabilities. The latter are particularly relevant in winter and are responsible for the formation of energetic small scales that extend over the whole depth of the mixed layer. The knowledge of the transport properties of oceanic flows at depth, which is essential to understand the coupling between surface and interior dynamics, however, is still limited. By means of numerical simulations, we explore the Lagrangian dispersion properties of turbulent flows in a quasi-geostrophic model system allowing for both thermocline and mixed-layer instabilities. The results indicate that, when mixed-layer instabilities are present, the dispersion regime is local from the surface down to depths comparable with that of the interface with the thermocline, while in their absence dispersion quickly becomes nonlocal with depth. We then identify the origin of such behavior in the existence of fine-scale energetic structures due to mixed-layer instabilities. We further discuss the effect of vertical shear on the Lagrangian particle spreading and address the correlation between the dispersion properties at the surface and at depth, which is relevant to assess the possibility of inferring the dynamical features of deeper flows from the more accessible surface ones.

Sea Surface Salinity Seasonal Variability in the Tropics from Satellites, Gridded In Situ Products and Mooring Observations

Satellite observations of sea surface salinity (SSS) have been validated in a number of instances using different forms of in situ data, including Argo floats, moorings and gridded in situ products. Since one of the most energetic time scales of variability of SSS is seasonal, it is important to know if satellites and gridded in situ products are observing the seasonal variability correctly. In this study we validate the seasonal SSS from satellite and gridded in situ products using observations from moorings in the global tropical moored buoy array. We utilize six different satellite products, and two different gridded in situ products. For each product we have computed seasonal harmonics, including amplitude, phase and fraction of variance (R2). These quantities are mapped for each product and for the moorings. We also do comparisons of amplitude, phase and R2 between moorings and all the satellite and gridded in situ products. Taking the mooring observations as ground truth, we find general good agreement between them and the satellite and gridded in situ products, with near zero bias in phase and amplitude and small root mean square differences. Tables are presented with these quantities for each product quantifying the degree of agreement.

Spectral-scaling-based extension to the attached eddy model of wall turbulence

Two-dimensional (2-D) spectra of the streamwise velocity component, measured at friction Reynolds numbers ranging from 2400 to 26000, are used to refine a model for the logarithmic region of turbulent boundary layers. Here, we focus on the attached eddy model (AEM). The conventional AEM assumes the boundary layer to be populated with hierarchies of self-similar wall-attached ($Type\,A$) eddies alone. While $Type\,A$ eddies represent the dominant energetic large-scale motions at high Reynolds numbers, the scales that are not represented by such eddies are observed to carry a significant proportion of the total kinetic energy. Therefore, in the present study, we propose an extended AEM that incorporates two additional representative eddies. These eddies, named $Type\,C_A$ and $Type\,SS$, represent the self-similar but wall-incoherent low-Reynolds number features, and the non-self-similar wall-coherent superstructures, respectively. The extended AEM is shown to better predict a greater range of energetic length scales and capture the low- and high-Reynolds number scaling trends in the 2-D spectra of all three velocity components. A discussion on spectral self-similarity and the associated $k^{-1}$ scaling law is also presented.

Linearized torsional problem of plastic thin wires

This paper develops an elegant plastic flow rule which relies on linearized constitutive relations governing the dissipative microscopic plastic stress responses in material bodies, and presents size-effects in torsional deformation of elasto-plastic thin wire using the derived flow equation. The obtained flow rule is based on strain gradient plasticity model, and is used to formulate an initial-boundary value problem describing the torsion problem of thin wire. Graphical illustration of the finite element solution of the problem shows that the accumulated plastic strain increases along radial axis of the wire’s cross section. Finally, it is observed that the effect of energetic length scale is significantly pronounced than that of the dissipative length scale during torsional deformation of the wire.

Near wall coherence in wall-bounded flows and implications for flow control

Opposition-control of the energetic cycle of near wall streaks in wall-bounded turbulence, using numerical approaches, has shown promise for drag reduction. For practical implementation, real-time opposition control is only realizable if there is a degree of coherence between the turbulent velocities passing a sensor and the target point within the flow; for practicality, a sensor (and actuator) should be wall-based to avoid parasitic drag. As such, we here inspect the feasibility of real-time control of the near wall cycle, by considering the coherence between a measurable wall-quantity, being the wall-shear stress fluctuations, and the streamwise and wall-normal velocity fluctuations in a turbulent boundary layer. Synchronized spatial and temporal velocity data from two direct numerical simulations and a fine large eddy simulation at Reτ≈590 and 2000 are employed. This study shows that the spectral energy of the streamwise velocity fluctuations that is stochastically incoherent with wall signals is independent of Reynolds number in the near wall region (up to the viscous-scaled wall-normal height z+≈20). Consequently, the streamwise energy-fraction that is stochastically wall-coherent grows with Reynolds number due to the increasing range of energetic large scales. This thus implies that a wall-based control system has the ability to manipulate a larger portion of the total turbulence energy at off-wall locations, at higher Reynolds numbers, while the efficacy of predicting/targeting the small scales of the near wall cycle remains indifferent with varying Reynolds number. Coherence values of 0.55 and 0.4 were found between the streamwise and wall-normal velocity fluctuations at the near wall peak in the energy spectrogram, respectively, and the streamwise fluctuating friction velocity. These coherence values, which are considerably lower than 1 (maximum possible coherence) suggest that a closed-loop drag reduction scheme targeting near wall cycle streaks alone (based on sensed friction velocity fluctuations) will be of limited success in practice.