arXiv subjects

Ivan Marusic

Publications and source records attributed to Ivan Marusic.

At least 19 recordsLinked to original sources

arXiv2026

Reynolds-number evolution of wall-pressure statistics beneath canonical turbulent boundary layers

This study investigates the Reynolds-number (Re_\tau) evolution of wall-pressure statistics beneath zero-pressure-gradient TBLs, and links their logarithmic variation to the increasingly energetic large-scale motions in the logarithmic region. The wall-pressure skewness is found to become more negative with increasing Re_\tau, owing to increasing contributions from large-scale wall-pressure fluctuations (that are negatively skewed) and their nonlinear interaction with the statistically invariant inner-scale fluctuations (that are positively skewed). The analysis draws on new, well-resolved simultaneous measurements of wall pressure and streamwise velocity spanning 5000 < Re_\tau < 11300 in the Melbourne tunnel, atmospheric surface-layer measurements at Re_\tau = O(10^6) and a published simulation dataset at Re_\tau = O(10^3). Particular attention is paid to the principal experimental limitations affecting wall-pressure statistics: spatial resolution, Helmholtz resonance, facility noise and statistical convergence. Helmholtz resonance is shown to contaminate inner-scale wall-pressure contributions even after conventional corrections, and reliable estimation of skewness is found to require acquisition durations of O(10^5) eddy-turnover times or longer. The inner-scaled wall pressure spectrum is Reynolds-number invariant over the small-scale regime, in contrast to turbulent channel and pipe flows, whereas at intermediate and large scales it grows substantially with Re_\tau, consistent with these internal flows. Linear and quadratic velocity--wall-pressure coherence link these intermediate- and large-scale contributions to two dynamically distinct coherent structures: the self-similar attached-eddy hierarchy and turbulent superstructures, respectively. These analyses establish the connection between the inertial region and the log variation of wall-pressure variance and skewness with Re_\tau

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arXiv2026

Wall-scaled eddies and embedded shear layers in high-Reynolds-number moderate adverse-pressure-gradient boundary layers

This study compares high-Reynolds-number turbulent boundary layers under zero and low-to-moderate adverse pressure gradients, showing similar scaling and energy contributions from the wall-scaled attached-eddy hierarchy and superstructures in both flows. The main differences occur in the outer/wake region, where APG-induced energisation is linked to an outer-scaled, embedded-shear-layer-type organisation that progressively penetrates the logarithmic region as the pressure-gradient strength increases. The analysis uses two complementary datasets for ZPG and APG boundary layers at matched friction Reynolds numbers of approximately 10,000, with minimal upstream pressure-gradient history: a new two-point hot-wire dataset and a previously published two-dimensional particle image velocimetry dataset. In the hot-wire experiment, one probe is fixed near the wall while the second traverses the full boundary layer, allowing estimation of the linear coherence spectrum. The results confirm the geometric self-similarity of the wall-scaled eddy hierarchy that remains coherent with the wall. Using the linear coherence spectrum as a spectral filter shows that most of the additional APG-induced energy is incoherent with the wall and is linearly superimposed on the wall-coherent component of the streamwise variance. This wall-incoherent contribution explains the departure of the variance profile from the inverse logarithmic law observed in canonical high-Reynolds-number boundary layers. Conditional averaging of the particle image velocimetry data identifies the structures responsible for this energy amplification. The results link enhanced outer-region Reynolds stresses, an outer inflection point in the mean velocity profile, and an ejection-sweep organisation of Reynolds shear stress, all characteristic of shear-layer dynamics.

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arXiv2026

On the wake region of high-Reynolds-number turbulent boundary layers subject to adverse pressure gradients

The effect of a moderate adverse pressure gradient (APG) on the structure of a high-Reynolds-number turbulent boundary layer (TBL) was investigated experimentally using complementary multi-point measurements. Unlike many previous studies, the present work focuses on the wake region and aims to characterise the turbulent motions that are energised by local APG conditions. Simultaneous two-point hot-wire measurements of the streamwise velocity were used to estimate the linear coherence spectrum (LCS), quantifying the wall-normal coherence between a wake-region reference point and the rest of the TBL. LCS-based decomposition of the spectral energy and variance showed that motions coherent with the wake reference account for a significant part of the APG-induced increase at large time scales, but not all of the enhanced energy. The remaining increase is associated with relatively smaller-scale motions that are not correlated with the selected wake location. High-spatial-resolution snapshot PIV measurements were then used to examine this broader range of energetic motions, which are associated with spanwise vortices in the wake region. Spanwise vorticity statistics were evaluated over 0.2 < z/{\delta} < 0.4, where the largest APG-induced change in spectral energy was observed. Under APG, both the mean and variance of spanwise vorticity increased significantly in this region, while swirling-strength distributions confirmed a relative increase in both the population and magnitude of spanwise vortices. Finally, dynamically significant clockwise rotating spanwise vortices were identified using different swirling-strength thresholds. Higher thresholds produced conditionally averaged velocity fields that best captured the key wake-region dynamics, motivating their use for vortex-based conditional averaging in future analyses.

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arXiv2026

High-Reynolds-number turbulent boundary layers under adverse pressure gradients. Part 2. A composite mean velocity profile

A robust composite mean velocity profile is developed for turbulent boundary layers (TBLs) subjected to adverse pressure gradients (APGs), extending the composite formulation for generic pressure-gradient TBLs proposed by \citeauthor{nickels} (\textit{J.\ Fluid Mech.}, vol.\ 521, 2004). Several modifications are introduced to capture key features of APG flows. A new parameter accounts for pressure-gradient history effects in the wake region, a velocity-overshoot function is incorporated in the inner region, and the wake function is reformulated using an independent, physically motivated definition of boundary-layer thickness. A compilation of APG TBL datasets from the literature, including the new dataset presented in Part~1, is used to assess and refine the formulation. The resulting composite profile contains three physically meaningful parameters that capture pressure-gradient effects on the mean velocity profile, determined through nonlinear curve fitting. These parameters provide a framework for identifying `well-behaved' APG TBLs and quantifying the strength of pressure-gradient history effects. The profile also enables reliable estimation of the friction velocity and boundary-layer thickness in well-behaved APG TBLs, providing a practical tool for scaling analyses when these quantities are not directly measurable. Its analytical form yields improved estimates of mean velocity gradients, facilitating evaluation of the indicator function and identification of inflection points. Finally, the formulation predicts both the coefficients and spatial extent of the logarithmic region of the mean streamwise velocity profile, enabling assessment of its universality in high-Reynolds-number APG TBLs. This shows that the von K'arm'an coefficient approaches an invariant value of $\kappa \approx 0.39$ at sufficiently high Reynolds numbers, independent of pressure-gradient effects.

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arXiv2025

High-Reynolds-number turbulent boundary layers under adverse pressure gradients. Part 1. Decoupling local and upstream pressure gradient effects

This study presents a controlled examination of the universality of the von Karman and additive coefficients in the logarithmic law of the mean streamwise velocity profile for high-Reynolds-number turbulent boundary layers under low-to-moderate adverse pressure gradients. The experiments use a method for prescribing pressure gradients along Melbourne's high-Reynolds-number boundary layer wind tunnel, combined with direct friction velocity measurements from oil-film interferometry. This allows systematic variation of upstream pressure-gradient history while maintaining locally matched Reynolds number and Clauser parameter at the measurement location. The configuration therefore separates the effects of Reynolds number, local adverse pressure gradient, and pressure-gradient history on turbulence statistics and energy spectra across the boundary layer. Owing to the high Reynolds number and moderate pressure-gradient conditions, the overlap region is sufficiently extended to assess the logarithmic law. The von Karman coefficient remains invariant within experimental uncertainty, whereas the additive coefficient varies systematically with both local pressure gradient and pressure-gradient history. Local adverse pressure gradients energize both large- and small-scale motions in the wake region around 0.4 delta, while pressure-gradient history also affects large-scale motions down to about 0.25 delta, just above the overlap region. In contrast to lower-Reynolds-number studies, neither effect extends into the inner region. These measurements provide a high-fidelity dataset for improving physical understanding and developing composite mean velocity profile formulations for adverse-pressure-gradient turbulent boundary layers.

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arXiv2025

Defining the mean turbulent boundary layer thickness based on streamwise velocity skewness

A new statistical definition for the mean turbulent boundary layer thickness is introduced, based on identification of the point where the streamwise velocity skewness changes sign, from negative to positive, in the outermost region of the boundary layer. Importantly, this definition is independent of arbitrary thresholds, and broadly applicable, including to past single-point measurements. Further, this definition is motivated by the phenomenology of streamwise velocity fluctuations near the turbulent/non-turbulent interface, whose local characteristics are shown to be universal for turbulent boundary layers under low freestream turbulence conditions (i.e., with or without pressure gradients, surface roughness, etc.) through large-scale experiments, simulations and coherent structure-based modelling. The new approach yields a turbulent boundary layer thickness that is consistent with previous definitions, such as those based on Reynolds shear stress or `composite' mean velocity profiles, and which can be used practically e.g., to calculate integral thicknesses. Two methods are proposed for estimating the turbulent boundary layer thickness using this definition: one based on simple linear interpolation and the other on fitting a generalised Fourier model to the outer skewness profile. The robustness and limitations of these methods are demonstrated through analysis of several published experimental and numerical datasets, which cover a range of canonical and non-canonical turbulent boundary layers. These datasets also vary in key characteristics such as wall-normal resolution and measurement noise, particularly in the critical turbulent/non-turbulent interface region.

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arXiv2024

Turbulent/non-turbulent interface in high Reynolds number pressure gradient boundary layers

We report two-dimensional particle image velocimetry experiments in high Reynolds number turbulent boundary layers imposed with a moderately strong streamwise pressure gradient. The unique aspect of these data are the highly resolved measurements across the outer region of a physically thick boundary layer, enabling accurate detection of turbulent/non-turbulent interfaces (TNTI). The present dataset is used to detect the TNTI of an adverse pressure gradient turbulent boundary layer and compare its characteristics with that for a zero-pressure gradient boundary layer, at a nominally similar friction Reynolds number. It is found that the TNTI exists across a broader range of wall-normal distance in presence of an adverse pressure gradient, as compared to the zero-pressure gradient case. Implications on conditionally averaged turbulence statistics are discussed based on detection of the TNTI.

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arXiv2024

A method for evaluating relations of turbulent normal-stresses by experimental data over a wide range of Reynolds numbers

Recently, Nagib et al (2024} utilized indicator functions of profiles of the streamwise normal stress to reveal the ranges of validity, in wall distance and Reynolds number, for each of two proposed models in DNS of channel and pipe flows. A method more suited to experimental data is proposed here, as establishing accurate indicator functions is a challenge. The new method is outlined and used with the two leading models that propose either a logarithmic or power trend, for the normal stresses of turbulence in a fitting region of wall-bounded flows. The method, which is simple and robust, is used to evaluate each model over a wide range of Reynolds numbers by applying it to two of the prominent experimental data sets in zero-pressure-gradient boundary layers (ZPG) and pipe flows. A somewhat larger exponent for the power trend equal to 0.28, instead of 0.25, is found to slightly extend its range of validity. Correcting for outer intermittency in ZPG data also extends validity of the power trend to around half the boundary layer thickness. Projecting near-wall peak normal-stress values using both models based on data from locations in the fitting region, yields nearly identical results up to the highest Re available from these two experiments.Neither model directly represents the inner peak values and differ by as much as 30%. However, the two relations provide projected values at Re=10M with a relative difference of approximately 6.2%; distinguishing between these values would require measurement accuracy well beyond our capabilities. Current results and those of Monkewitz and Nagib (2023) on the mean flow, suggest that considerations of nonlinear growth of eddies from the wall and accounting for some viscous effects, are important for modeling wall-bounded flows. Such effects also apply to potential refinements of the logarithmic trend along ideas advanced by Deshpande et al. (2021).

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arXiv2024

A note on the amplitude modulation phenomenon in non-canonical wall-bounded flows

The amplitude modulation phenomena, defined originally by Mathis et al. (J. Fluid Mech., 628, 311-337; 2009), corresponds to a unique non-linear interaction between Reynolds number ($Re_{\tau}$) dependent large-scale motions and $Re_{\tau}$-invariant inner-scale motions observed in canonical wall-bounded flows. While similar non-linear interactions have been quantified previously in non-canonical wall-bounded flows, linking them solely to amplitude modulation is questionable due to the fact that each non-canonical effect is associated with distinct variations in the energies of both the large and inner scaled motions. This study revisits analysis of non-linear triadic interactions, with consideration to various non-canonical effects, by analyzing published hot-wire datasets acquired in the large Melbourne wind tunnel. It is found that triadic interactions, across the entire turbulence scale hierarchy, may become statistically significant with increasing intensity of non-canonical effects such as wall roughness, pressure gradients, and spanwise or wall-normal forcing (when compared relative to their respective canonical baseline cases at matched $Re_{\tau}$). This stands in contrast to previous observations made in canonical flows, where only the interaction between inner scales and inertia-dominated large scales was considered dynamically significant for increasing $Re_{\tau}$. The implications of these findings are discussed for near-wall flow prediction models in non-canonical flows, which should take into account \emph{all} non-linear interactions coexisting in wall-bounded flows.

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arXiv2024

Active and inactive contributions to the wall pressure and wall-shear stress in turbulent boundary layers

A phenomenological description is presented to explain the intermediate and low-frequency/large-scale contributions to the wall-shear-stress (${\tau}_w$) and wall-pressure (${p}_w$) spectra of canonical turbulent boundary layers, which are well known to increase with Reynolds number. The explanation is based on the concept of active and inactive motions (Townsend, J. Fluid Mech., vol. 11, 1961) associated with the attached-eddy hypothesis. Unique data sets of simultaneously acquired ${\tau}_w$, ${p}_w$ and velocity fluctuation time series in the log region are considered, across friction-Reynolds-number ($Re_{\tau}$) range of $\mathcal{O}$($10^3$) $\lesssim$ $Re_{\tau}$ $\lesssim$ $\mathcal{O}$($10^6$). A recently proposed energy-decomposition methodology (Deshpande et al., J. Fluid Mech., vol. 914, 2021) is implemented to reveal the active and inactive contributions to the ${\tau}_w$- and $p_w$-spectra. Empirical evidence is provided in support of Bradshaw's (J. Fluid Mech., vol. 30, 1967) hypothesis that the inactive motions are responsible for the non-local wall-ward transport of the large-scale inertia-dominated energy, which is produced in the log region by active motions. This explains the large-scale signatures in the ${\tau}_w$-spectrum, which grow with $Re_{\tau}$ despite the statistically weak signature of large-scale turbulence production, in the near-wall region. For wall pressure, active and inactive motions respectively contribute to the intermediate and large scales of the $p_w$-spectrum. Both these contributions are found to increase with increasing $Re_{\tau}$ owing to the broadening and energization of the wall-scaled (attached) eddy hierarchy. This potentially explains the rapid $Re_{\tau}$-growth of the $p_w$-spectra relative to ${\tau}_w$, given the dependence of the latter only on the inactive contributions.

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arXiv2024

Characteristics of active and inactive motions in high-Reynolds-number turbulent boundary layers

Wall-scaled (attached) eddies play a significant role in the overall drag experienced in high-Reynolds-number turbulent boundary layers (TBLs). This study aims to delve into the underlying mechanisms driving this phenomenon by dissecting the active and inactive components of these attached eddies, as initially proposed by Townsend (1976). Employing a recently introduced energy-decomposition scheme, we analyze TBL datasets covering a wide range of Reynolds numbers ($Re_{\tau}$ $\sim$ $\mathcal{O}$(10$^{3}$)--$\mathcal{O}$(10$^{6}$)). This analysis provides empirical evidence of the distinct contributions of these components to drag generation, and reveals that while active motions are responsible solely for generating Reynolds shear stresses, inactive motions are crucial for transporting streamwise momentum from the logarithmic region to the wall, thus corroborating earlier hypotheses in the literature.

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arXiv2023

Pressure drag reduction via imposition of spanwise wall oscillations on a rough wall

The present study tests the efficacy of the well-known viscous drag reduction strategy of imposing spanwise wall oscillations to reduce pressure drag contributions in a transitional- and fully-rough turbulent wall flow. This is achieved by conducting a series of direct numerical simulations of a turbulent flow over two-dimensional (spanwise aligned) semi-cylindrical rods, placed periodically along the streamwise direction with varying streamwise spacing. Surface oscillations, imposed at fixed viscous-scaled actuation parameters optimum for smooth wall drag reduction, are found to yield substantial drag reduction (>25%) for all the rough wall cases, maintained at matched roughness Reynolds numbers. While the total drag reduction is due to a drop in both viscous and pressure drag in the case of transitionally-rough flow (i.e. with large inter-rod spacing), it is solely associated with pressure drag reduction for the fully-rough cases (i.e. with small inter-rod spacings), with the latter being reported for the first time. The study finds that pressure drag reduction in all cases is caused by the attenuation of the vortex shedding activity in the roughness wake, in response to wall-oscillation frequencies that are of the same order as the vortex shedding frequencies. Contrary to speculations in the literature, this study confirms that the mechanism behind pressure drag reduction, achieved via imposition of spanwise oscillations, is independent from the viscous drag reduction. This mechanism is responsible for weakening of the Reynolds stresses and increase in base pressure in the roughness wake, explaining the pressure drag reduction observed by past studies, across varying roughness heights and geometries.

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arXiv2023

Experimental study of a turbulent boundary layer with a rough-to-smooth change in surface conditions at high Reynolds numbers

This study presents an experimental dataset documenting the evolution of a turbulent boundary layer downstream of a rough-to-smooth surface transition. To investigate the effect of upstream flow conditions, two groups of experiments are conducted. For the \emph{Group-Re} cases, a nominally constant viscous-scaled equivalent sand grain roughness $k_{s0}^+\approx160$ is maintained on the rough surface, while the friction Reynolds number $Re_{\tau 0}$ ranges from 7100 to 21000. For the \emph{Group-ks} cases, $Re_{\tau 0}\approx14000$ is maintained while $k_{s0}^+$ ranges from 111 to 228. The wall-shear stress on the downstream smooth surface is measured directly using oil-film interferometry to redress previously reported uncertainties in the skin-friction coefficient recovery trends. In the early development following the roughness transition, the flow in the internal layer is not in equilibrium with the wall-shear stress. This conflicts with the common practise of modelling the mean velocity profile as two log laws below and above the internal layer height, as first proposed by Elliott (\textit{Trans. Am. Geophys. Union}, vol. 39, 1958, pp 1048--1054). As a solution to this, the current data are used to model the recovering mean velocity semi-empirically by blending the corresponding rough-wall and smooth-wall profiles. The over-energised large-scale motions leave a strong footprint in the near-wall region of the energy spectrum, the frequency and magnitude of which exhibit dependence on $Re_{\tau 0}$ and $k_{s0}^+$ respectively. The energy distribution in near-wall small scales is mostly unaffected by the presence of the outer flow with rough-wall characteristics, which can be used as a surrogate measure to extract the local friction velocity.

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arXiv2023

Recovery of the wall-shear stress to equilibrium flow conditions after a rough-to-smooth step-change in turbulent boundary layers

This paper examines recovery of the wall-shear stress of a turbulent boundary layer that has undergone a sudden transition from a rough to a smooth surface. Early works of Antonia and Luxton questioned the reliability of standard smooth-wall methods to measure wall-shear stress in such conditions, and subsequent studies show significant disagreement depending on the approach used to determine the wall-shear stress downstream. Here we address this by utilising a collection of experimental databases at Re_\tau \approx 4100 that have access to both `direct' and `indirect' measures of the wall-shear stress to understand the recovery to equilibrium conditions to the new surface. Our results reveal that the viscous region (z^+\lesssim 4) recovers almost immediately to an equilibrium state with the new wall conditions, however, the buffer region and beyond takes several boundary layer thicknesses before recovering to equilibrium conditions, which is longer than previously thought. A unique direct numerical simulation database of a wall-bounded flow with a rough-to-smooth wall transition is employed to confirm these findings. In doing so, we present evidence that any estimate of the wall-shear stress from the mean velocity profile in the buffer region or further away from the wall tends to underestimate its magnitude in the near vicinity of the rough-to-smooth transition, and this is likely to be partly responsible for the large scatter of recovery lengths to equilibrium conditions reported in the literature. Our results also reveal that the smaller energetic scales in the near-wall region recover to an equilibrium state associated with the new wall conditions within one boundary layer thickness downstream of the transition, while the larger energetic scales exhibit an over-energised state for several boundary layer thicknesses downstream of the transition.

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arXiv2023

Quantifying inner-outer interactions in non-canonical wall-bounded flows

We investigate the underlying physics behind the change in amplitude modulation coefficient in non-canonical wall-bounded flows in the framework of the inner-outer interaction model (IOIM) (Baars et al., Phys. Rev. Fluids 1 (5), 054406). The IOIM captures the amplitude modulation effect, and here we focus on extending the model to non-canonical flows. An analytical relationship between the amplitude modulation coefficient and IOIM parameters is derived, which is shown to capture the increasing trend of the amplitude modulation coefficient with an increasing Reynolds number in a smooth-wall dataset. This relationship is then applied to classify and interpret the non-canonical turbulent boundary layer results reported in previous works. We further present the case study of a turbulent boundary layer after a rough-to-smooth change. Both single-probe and two-probe hotwire measurements are performed to acquire streamwise velocity time series in the recovering flow on the downstream smooth wall. An increased coherence between the large-scale motions and the small-scale envelope in the near-wall region is attributed to the stronger footprints of the over-energetic large-scale motions in the outer layer, whereas the near-wall cycle and its amplitude sensitivity to the superposed structures are similar to that of a canonical smooth-wall flow. These results indicate that the rough-wall structures above the internal layer interact with the near-wall cycle in a similar manner as the increasingly energetic structures in a high-Reynolds number smooth-wall boundary layer.

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arXiv2023

Reynolds-number effects on the outer region of adverse-pressure-gradient turbulent boundary layers

We study the Reynolds-number effects on the outer region of moderate adverse-pressure-gradient (APG) turbulent boundary layers (TBLs) and find that their small scale energy reduces with increasing friction Reynolds-number ($Re_{\tau}$). The trend is based on analyzing APG TBL data across 600 $\lesssim$ $Re_{\tau}$ $\lesssim$ 7000, and contrasts with the negligible variation in small scale energy noted for canonical wall flows. The datasets considered include those from a well-resolved numerical simulation (Pozuelo et al. 2022), which provides access to an APG TBL maintained at near-equilibrium conditions across 1000 $\lesssim$ $Re_{\tau}$ $\lesssim$ 2000, with a well-defined flow history, and a new high-$Re_{\tau}$ ($\sim$ 7000) experimental study from the large Melbourne wind tunnel, with its long test section modified to permit development of an APG TBL from a 'canonical' upstream condition. The decrease in small scale energy with $Re_{\tau}$ is revealed via decomposing the streamwise normal stresses into small and large scale contributions, based on a sharp spectral cut-off. The origin for this trend is traced back to the production of turbulent kinetic energy in an APG TBL, the small scale contribution to which is also found to decrease with $Re_{\tau}$ in the outer region. The conclusion is reaffirmed by investigating attenuation of streamwise normal stresses due to changing spatial-resolutions of the numerical grid/hotwire sensors, which reduces with increasing $Re_{\tau}$ and is found to be negligible at $Re_{\tau}$ $\sim$ 7000 in this study. The results emphasize that new scaling arguments and spatial-resolution correction schemes should be tested rigorously across a broad $Re_{\tau}$ range, particularly for the outer region of pressure gradient TBLs.

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arXiv2023

Identifying regions of importance in wall-bounded turbulence through explainable deep learning

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 for the first time 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 completely new 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.

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arXiv2022

On the relationship between manipulated inter-scale phase and energy-efficient turbulent drag reduction

We investigate the role of inter-scale interactions in the high-Reynolds number skin-friction drag reduction strategy reported by Marusic et al. (Nat. Commun., vol. 12, 2021). The strategy involves imposing relatively low-frequency streamwise travelling waves of spanwise velocity at the wall to actuate the drag generating outer-scales. This approach has proven to be more energy-efficient than the conventional method of directly targeting the drag producing inner-scales, which typically requires actuation at higher frequencies. Notably, it is observed that actuating the outer-scales at low frequencies leads to a substantial attenuation of the major drag producing inner-scales, suggesting that the actuations affect the non-linear inner-outer coupling inherently existing in wall-bounded flows. In the present study, we find that increased drag reduction, through imposition of spanwise wall oscillations, is always associated with an increased coupling between the inner and outer scales. This enhanced coupling emerges through manipulation of the phase relationships between these triadically linked scales, with the actuation forcing the entire range of energy-containing scales, from the inner (viscous) to the outer (inertial) scales, to be more in-phase. We also find that a similar enhancement of this non-linear coupling, via manipulation of the inter-scale phase relationships, occurs with increasing Reynolds number for canonical turbulent boundary layers. This indicates improved efficacy of the energy-efficient drag reduction strategy at very high Reynolds numbers, where the energised outer-scales are known to more strongly superimpose and modulate the inner-scales. Leveraging the inter-scale interactions, therefore, offers a plausible mechanism for achieving energy-efficient drag reduction at high Reynolds numbers.

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