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Despite its great scientific and technological importance, wall-bounded turbulence is an unresolved problem in classical physics that requires new perspectives to be tackled. One of the key strategies has been to study interactions among the energy-containing coherent structures in the flow. Such interactions are explored in this study using an explainable deep-learning method. The instantaneous velocity field obtained from a turbulent channel flow simulation is used to predict the velocity field in time through a U-net architecture. Based on the predicted flow, we assess the importance of each structure for this prediction using the game-theoretic algorithm of SHapley Additive exPlanations (SHAP). This work provides results in agreement with previous observations in the literature and extends them by revealing that the most important structures in the flow are not necessarily the ones with the highest contribution to the Reynolds shear stress. We also apply the method to an experimental database, where we can identify structures based on their importance score. This framework has the potential to shed light on numerous fundamental phenomena of wall-bounded turbulence, including novel strategies for flow control.

The turbulent boundary layer developing under a turbulence-laden free stream is numerically investigated using the temporal boundary layer framework. This study focuses on the interaction between the fully turbulent boundary layer and decaying free-stream turbulence. Previous experiments and simulations of this physical problem have considered a spatially evolving boundary layer beset by free-stream turbulence. The state of the boundary layer at any given downstream position in fact reflects the accumulated history of the co-evolution of boundary layer and free-stream turbulence. The central aim of the present work is to isolate the effect of local free-stream disturbances existing at the same time as the ‘downstream’ boundary layer. The temporal framework used here helps expose when and how disturbances directly above the boundary layer actively impart change upon it. The bulk of our simulations were completed by seeding the free stream above boundary layers that were ‘pre-grown’ to a desired thickness with homogeneous isotropic turbulence from a precursor simulation. Moreover, this strategy allowed us to test various combinations of the turbulence intensity and large-eddy length scale of the free-stream turbulence with respect to the corresponding scales of the boundary layer. The relative large-eddy turnover time scale between the free-stream turbulence and the boundary layer emerges as an important parameter in predicting if the free-stream turbulence and boundary layer interaction will be ‘strong’ or ‘weak’ before the free-stream turbulence eventually fades to a negligible level. If the large-eddy turnover time scale of the free-stream turbulence is much smaller than that of the boundary layer, the interaction will be ‘weak’, as the free-stream disturbances will markedly decay before the boundary layer is able be altered significantly as a result of the free-stream disturbances. For a ‘strong’ interaction, the injected free-stream turbulence causes increased sp

Streamwise velocity and wall-shear stress are acquired simultaneously with a hot-wire and an array of azimuthal/spanwise-spaced skin friction sensors in large-scale pipe and boundary layer flow facilities at high Reynolds numbers. These allow for a correlation analysis on a per-scale basis between the velocity and reference skin friction signals to reveal which velocity-based turbulent motions are stochastically coherent with turbulent skin friction. In the logarithmic region, the wall-attached structures in both the pipe and boundary layers show evidence of self-similarity, and the range of scales over which the self-similarity is observed decreases with an increasing azimuthal/spanwise offset between the velocity and the reference skin friction signals. The present empirical observations support the existence of a self-similar range of wall-attached turbulence, which in turn are used to extend the model of Baars et al. (J. Fluid Mech., vol. 823, p. R2) to include the azimuthal/spanwise trends. Furthermore, the region where the self-similarity is observed correspond with the wall height where the mean momentum equation formally admits a self-similar invariant form, and simultaneously where the mean and variance profiles of the streamwise velocity exhibit logarithmic dependence. The experimental observations suggest that the self-similar wall-attached structures follow an aspect ratio of in the streamwise, spanwise and wall-normal directions, respectively.

The sensitivity of measured turbulent stresses to uncertainties in the probe geometry and calibration procedure is investigated for a cross-wire probe in a turbulent boundary layer using direct numerical simulation data. The errors investigated are guided by experiments, and to replicate the full experimental procedure, the cross-wire calibration procedure is simulated to generate a voltage-to-velocity mapping function, which is then utilised to calculate the measured velocity from simulated cross-wire voltages. We show that wire misalignment can lead to an incorrect mean wall-normal velocity and Reynolds shear stress in the near-wall region due to the presence of shear. Furthermore, we find that misalignment in the wire orientation cannot be fully accounted for through the calibration procedure, presumably due to increased sensitivity to an out-of-plane velocity component. This has strong implications if using a generic commercial cross-wire probe, since inclining these probes to gain access to the near-wall region can lead to a large error (up to 10%) in turbulent stresses and these errors can manifest in the log region and beyond to half the boundary layer thickness. For uncertainties introduced during the calibration procedure, the Reynolds shear stress is observed to exhibit an elevated sensitivity compared with other turbulent stresses. This is consistent with empirical observations where the repeatability in the Reynolds shear stress is found to be the poorest.

The spatial averaging effects due to a cross-wire probe on the measured turbulence statistics in a wall-bounded flow are investigated using a combined approach of direct numerical simulation data, theoretical methods and experiments. In particular, the wire length (l), spacing ( ) and angle ( ) of a cross-wire probe configured to measure the streamwise and wall-normal velocities are systematically varied to isolate effects of each parameter. The measured streamwise velocity from a cross-wire probe is found to be an average of the filtered velocities sensed by the two wires. Thus, in general, an increase in the sensor dimensions when normalised by viscous units leads to an attenuated variance for the streamwise velocity ( ), resulting from a larger contribution to the spatial averaging process from poorly correlated velocities. In contrast, the variance for the wall-normal velocity ( ) can be amplified, and this is shown to be the result of an additional contributing term (compared to ) due to differences in the filtered wire-normal velocity between the two wires. This additional term leads to a spurious wall-normal velocity signal, resulting in an amplified variance recorded by the cross-wire probe. Compared to the streamwise and wall-normal velocity variances, the Reynolds shear stress ( ) perhaps surprisingly shows less variation when l, and are varied. The robustness of Reynolds shear stress to the finite sensor size is due to two effects: (i) Reynolds shear stress is devoid of energetic contributions from the near-isotropic fine scales unlike the and statistics, hence cross-wire probe dimensions are typically sufficiently small in terms of viscous unit to adequately capture the statistics for a range of l and investigated; (ii) the dependency arises due to cross terms between the filtered velocities from two wires, however, it turns out that these terms cancel one another in the case of Reynolds shear stress, but not for the and statistics. We note that this doe

The problem of the turbulent boundary layer under decaying free-stream turbulence is numerically investigated using the temporal boundary layer framework. This tool is particularly suited to the problem since the evolution of homogeneous isotropic turbulence is classically described by temporal decay. This study focuses on the interaction between the fully turbulent boundary layer and free-stream turbulence, which has so far received little attention compared to the behaviour of the transitional boundary layer subject to free-stream turbulence. The bulk of our simulations were completed by seeding the free-stream of boundary layers ‘pre-grown’ to a desired thickness with homogeneous isotropic turbulence from a precursor simulation. This strategy allowed us to test different combinations of the turbulence intensity and largeeddy lengthscale of the free-stream turbulence with respect to the velocity- and large-eddy length-scales of the boundary layer; such a parametric investigation would remain otherwise inaccessible given available computing resources. Additionally, the present strategy permits assessment of the direct effect of the locally present free-stream disturbances, as opposed to a ‘downstream’ effect from free-stream disturbances far ‘upstream’. The relative large-eddy turnover timescale between the free-stream turbulence and the boundary layer emerges as an important parameter in predicting if the free-stream turbulence and boundary layer interaction will be ‘strong’ or ‘weak’ before the free-stream turbulence eventually fades away. For a ‘strong’ interaction, the main action of the free-stream turbulence on the boundary layer is to cause increased spreading of the boundary layer away from the wall, which then permits incursions of free-stream fluid deep within it, changing the boundary layer velocity profiles in the outer part of the flow. This has the important effect of increasing the boundary layer thickness _ by flattening the intermittency profile.

Virtual fractional flow reserve (vFFR) has been evaluated as an adjunct to invasive fractional flow reserve (FFR) in the light of its operational and economic benefits. The accuracy of vFFR and the complexity of hyperemic flow simulation are still not clearly understood. This study investigates the flow-pressure relation in an idealised multiple sequential stenoses coronary artery model via numerical and experimental approaches. Pressure drop is linearly correlated with flow rate irrespective of the number of stenosis. Computational fluid dynamics results are in good agreement with the experimental data, demonstrating reasonable accuracy of vFFR. It was also found that the difference between data obtained with steady and pulsatile flows is negligible, indicating the steady flow may be used instead of pulsatile flow conditions in vFFR computation. This study adds to the current understanding of vFFR and may improve its clinical applicability as an adjunct to invasively determined FFR.

The identification of uniform momentum zones in wall-turbulence, introduced by Adrian, Meinhart & Tomkins (J. Fluid Mech., vol. 422, 2000, pp. 1–54) has been applied to turbulent channel flow, revealing a large ‘core’ region having high and uniform velocity magnitude. Examination of the core reveals that it is a region of relatively weak turbulence levels. For channel flow in the range $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}Re_{\tau } = 1000\text {--}4000$, it was found that the ‘core’ is identifiable by regions bounded by the continuous isocontour lines of the streamwise velocity at $0.95U_{CL}$ (95 % of the centreline velocity). A detailed investigation into the properties of the core has revealed it has a large-scale oscillation which is predominantly anti-symmetric with respect to the channel centreline as it moves through the channel, and there is a distinct jump in turbulence statistics as the core boundary is crossed. It is concluded that the edge of the core demarcates a shear layer of relatively intense vorticity such that the interior of the core contains weakly varying, very low-level turbulence (relative to the flow closer to the wall). Although channel flows are generally referred to as ‘fully turbulent’, these findings suggest there exists a relatively large and ‘quiescent’ core region with a boundary qualitatively similar to the turbulent/non-turbulent interface of boundary layers, jets and wakes.

The extent or existence of similarities between fully developed turbulent pipes and channels, and in zero-pressure-gradient turbulent boundary layers has come into question in recent years. This is in contrast to the traditionally accepted view that, upon appropriate normalization, all three flows can be regarded as the same in the near-wall region. In this paper, the authors aim to provide clarification of this issue through streamwise velocity measurements in these three flows with carefully matched Reynolds number and measurement resolution. Results show that mean statistics in the near-wall region collapse well. However, the premultiplied energy spectra of streamwise velocity fluctuations show marked structural differences that cannot be explained by scaling arguments. It is concluded that, while similarities exist at these Reynolds numbers, one should exercise caution when drawing comparisons between the three shear flows, even near the wall.