arXiv subjects

Max W. Knoop

Publications and source records attributed to Max W. Knoop.

6 recordsLinked to original sources

arXiv2026

Measurements of non-linear energy transfer in canonical and drag-reduced turbulent boundary layers

Three-dimensional particle-tracking velocimetry (3D-PTV) measurements were used to compute the spectral transport of the Reynolds-stress tensor. The experimental framework is validated for a zero-pressure-gradient (ZPG) turbulent boundary layer (TBL) at a friction Reynolds number $Re_τ= 1020$, demonstrating that the dominant non-linear energy transfer mechanisms are adequately resolved to draw flow physics-based conclusions. For the streamwise Reynolds stress in the ZPG TBL, a component-wise decomposition of the non-linear transport term is considered for the first time, which reveals distinct energy transfer mechanisms associated with the spanwise and wall-normal advection. The same experimental framework was applied to a drag-reduced ($\approx 38\%$) TBL flow, achieved by imposing a steady streamwise-alternating spanwise wall velocity. This wall forcing causes a strong attenuation of non-linear energy transfer and its shift away from the wall. The energy transfer mechanisms remain qualitatively similar to those of the canonical ZPG TBL, suggesting that the existing mechanisms simply readjust to their new low-turbulent-energy state.

physics.flu-dyn↗

arXiv2026

Coherent structure modulation and recovery in drag-reduced turbulent boundary layers

Drag reduction is achieved by a steady square-wave forcing of the spanwise wall velocity, based on the experiments in Knoop et al. (Phys. Rev. Fluids, 10, 2025). Particle tracking velocimetry data are analyzed for a non-actuated reference case and actuation at forcing amplitude $A^+ = 12$ ($+$ denotes viscous scaling) for three streamwise forcing wavelengths, which correspond to sub-optimal ($Λ_x^+ = 471$), near-optimal ($Λ_x^+ = 942$), and post-optimal ($Λ_x^+ = 1884$) drag reduction conditions. Conditionally averaged fields on large-scale bursts of turbulent kinetic energy show that forcing suppresses near-wall ejections across all cases, while outer-layer sweep suppression strengthens with $Λ_x^+$. Post-optimal forcing exhibits streamwise-periodic attenuation and recovery of turbulence. The recovery phenomenon is caused by an enhancement of very small scales, significantly smaller than those typically energetic in wall turbulence, and is linked to the emergence of small-scale bursting events. While these small-scale bursts are statistically insignificant in the non-actuated and sub-optimal cases, their frequency increases by a factor of four between the near-optimal and post-optimal cases. The small-scale bursts exhibit uniform signatures and intensities, hinting at the possible universality of the recovery phenomenon. A wavelet analysis shows that, in the post-optimal case, very small scales increase progressively in the streamwise direction in regions where the wall velocity remains constant, driving a cyclic pattern of small-scale re-energization and suppression consistent with earlier statistical analysis. This turbulence modulation mechanism is scale-selective: while small-scale structures emerge periodically, large-scale motions are more effectively suppressed as the forcing wavelength increases.

physics.flu-dyn↗

arXiv2026

Turbulent boundary layers altered by passively rotating discs

Turbulent boundary layers characterised by friction Reynolds numbers in the range $Re_τ = 880 - 1460$ and flowing over flush-mounted passively rotating discs are investigated in a wind tunnel with the purpose of reducing the skin-friction drag. The test surface is composed of thirty-two rotating discs arranged in a staggered configuration and supported by bearings mounted in cylindrical cavities. As the discs are half covered by thin rigid plates, a steady rotation of the discs is sustained via the asymmetric distribution of the wall-shear stress exerted by the wall turbulence on the exposed halves of the discs. Direct force measurements reveal that the drag increases with respect to a flat-plate case because of the flow interaction with the disc housings and the covering plates. The effect of the disc motion is isolated and a 3\% drag reduction is measured with respect to the flow over stationary discs. The skin-friction identity by \cite{Elnahhas_Johnson_2022} (\emph{J. Fluid Mech.}, vol. 940, 2022), extended herein to include the disc-flow effects, is utilised for the first time to analyse experimental data. This direct slip effect, quantified by using the measured disc angular velocities in the Elnahhas-Johnson identity, is negligible. Measurements obtained by particle image velocimetry disclose that a roughness mean-flow effect occurs between adjacent discs because of the clearance gaps around the discs and that a downwash secondary flow exists near the covering plates, analogous to flows over streamwise-elongated rectangular roughness elements. This downwash velocity is streamwise modulated because of the spanwise disc motion and alters the wall-normal transport term in the Elnahhas-Johnson identity, thus reducing the drag locally.

physics.flu-dyn↗

arXiv2026

Passive transverse forcing of turbulent boundary-layer flow using sinusoidal surface grooves

A surface geometry consisting of parallel, meandering streamwise grooves has been experimentally studied as an alternative means of passive transverse forcing of turbulent boundary-layer flow. Contrary to the original expectation, the flow does not exhibit a spanwise-uniform undulation aligned with the grooves; instead, a converging-diverging flow pattern results. This flow pattern can be attributed to the spanwise periodicity of the lateral pressure gradient. The forcing effect is found to initially increase with the groove amplitude, but it saturates when the groove slope becomes too steep. The observed induced flow, referred to as a Passive Stokes Layer (PSL), can be considered as being composed of an inertial (pressure-driven) outer solution generated by the displacement effect of the non-smooth surface geometry, and a viscous inner solution to accommodate the no-slip condition at the wall. The mechanism of transverse flow generation is elucidated by an inviscid flow model that relates the forcing to the surface geometric properties, with predictions in good agreement with the experimental results. Although a reduction in the near-wall turbulence levels over the groove surfaces is observed, no direct evidence for (mean) drag reduction is evident from the data. Instead, an estimate of the frictional drag potential is based on establishing a tentative relation to an equivalent spatial Stokes layer (SSL) induced by active wall forcing. This theoretical comparison indicates that the induced passive forcing is sufficient to act on the (active) spanwise forcing mechanism, but produces at most a few per cent of frictional drag reduction. Any potential savings are likely offset by pressure drag and other losses, so that, similar to active forcing, its potential for net drag reduction in practical applications is limited.

physics.flu-dyn↗

arXiv2025

Response of a turbulent boundary layer to steady, square-wave-type transverse wall-forcing

This study investigates the spatial evolution of a zero pressure gradient turbulent boundary layer (TBL) imposed by a square-wave (SqW) of steady spanwise wall-forcing, which varies along the streamwise direction ($x$). The SqW wall-forcing is imposed experimentally via a series of streamwise periodic belts running in opposite spanwise directions, following the methodology of Knoop et al. (Exp. Fluids, vol 65, 2024), with the streamwise extent increased to beyond $\sim 11$ times the boundary layer thickness ($δ_o$) in the present study. This unique setup is leveraged to investigate the influence of viscous-scaled wavelength of SqW wall-forcing on the turbulent drag reduction (DR) efficacy for $λ^+_x = $ 471 (sub-optimal), 942 (near-optimal), and 1884 (post-optimal conditions), at fixed viscous-scaled wall-forcing amplitude, $A^+ = 12$, and friction Reynolds number, $Re_τ= 960$. The TBL's response to this wall-forcing is elucidated by drawing inspiration from established knowledge on traditionally studied sinusoidal forcing (SinW), based on analysis of the streamwise-phase variation of the Stokes strain rate (SSR). The analysis reveals the SqW forcing to be characterized by a combination of two markedly different SSR regimes whose influence on the overlying turbulence is found to depend on the forcing waveform: sub-phase-I of local and strong impulses of SSR downstream of the half- ($λ_x$/2) and full-phase ($λ_x$) locations, associated with a reversal in spanwise forcing directions, leading to significant turbulence attenuation, and sub-phase-II of near-zero SSR over the remainder of forcing phase that enables turbulence recovery (when wall-forcing magnitudes and direction remain constant).

physics.flu-dyn↗

arXiv2024

Experimental assessment of square wave spatial spanwise forcing of a turbulent boundary layer

We present an experimental realisation of spatial spanwise forcing in a turbulent boundary layer flow, aimed at reducing the frictional drag. The forcing is achieved by a series of spanwise running belts, running in alternating spanwise direction, thereby generating a steady spatial square-wave forcing. SPIV in the streamwise-wall-normal plane is used to investigate the impact of actuation on the flow in terms of turbulence statistics, drag performance characteristics, and spanwise velocity profiles, for a non-dimensional wavelength of $λ_x^+ = 397$. We confirm that a significant flow control effect can be realised with this type of forcing. The scalar fields of the higher-order turbulence statistics show a strong attenuation of stresses and production of turbulence kinetic energy over the first belt already, followed by a more gradual decrease to a steady-state energy response over the second belt. The streamwise velocity in the near-wall region is reduced, indicative of a drag-reduced flow state. The profiles of the higher-order turbulence statistics are attenuated up to a wall-normal height of $y^+ \approx 100$, with a maximum streamwise stress reduction of 45% and a reduction of integral turbulence kinetic energy production of 39%, for a non-dimensional actuation amplitude of $A^+ = 12.7$. An extension of the classical laminar Stokes layer theory is introduced, to describe the non-sinusoidal boundary condition that corresponds to the current case. The spanwise velocity profiles show good agreement with this extended theoretical model. The drag reduction was estimated from a linear fit in the viscous sublayer in the range $2 \leq y^+\leq 5$. The results are found to be in good qualitative agreement with the numerical implementations of Viotti et al. (2009), matching the drag reduction trend with $A^+$, and reaching a maximum of 20%.

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