In the interest of reducing wave loads on offshore structures, this study explores the mitigation of wave loading on a bottom-standing cylinder by surrounding it with a floating annular viscoelastic plate. A matched eigenfunction expansion method is developed within the framework of linear potential flow theory to analyze the hydrodynamic interactions among the incident waves, the central cylinder, and the surrounding viscoelastic plate. The model accounts for both elastic flexural stiffness and viscous damping of the plate, which are tunable engineering properties. Parametric analyses are performed to evaluate the effects of plate rigidity and viscous damping on hydrodynamic responses, including hydrodynamic forces, wave runup, and wave energy dissipation. The results demonstrate that the viscoelastic plate can significantly reduce both linear and second-order wave loads on the central cylinder, provided that its elastic and viscous properties are appropriately engineered. Notably, an optimal range of viscous damping is present that maximizes wave energy dissipation. The study provides useful guidance for the design of floating barriers for offshore structure protection and proposes a tunable, passive wave load mitigation approach.

A direct numerical simulation of turbulent channel flow at ${\mathrm{Re}}_{\tau }\approx 16000$ has been performed, providing a channel-flow DNS in a Reynolds-number regime where inertial-layer behavior can be examined directly. Theoretical predictions associated with the inertial layer are assessed through the corresponding wall-normal derivative forms, allowing the wall-normal locations at which these asymptotic behaviors emerge to be identified quantitatively. The wall-normal Reynolds normal stress exhibits the clearest agreement with theory, allowing a candidate inertial-layer region to be identified directly. The dissipation-rate scaling is independently found to be consistent with the same wall-normal interval. These results provide direct evidence that inertial-layer behavior becomes observable at ${\mathrm{Re}}_{\tau }\approx 16000$. The mean velocity exhibits two logarithmic-region candidates: one near the Reynolds-stress peak and another near the upper edge of the inner layer. The Reynolds normal stresses and dissipation rate also exhibit trends broadly consistent with their corresponding asymptotic predictions. However, the wall-normal locations at which these predictions are realized differ among the turbulence quantities. The present results suggest that inertial-layer behavior emerges progressively with increasing Reynolds number and that the degree of realization remains quantity dependent.

Inviscid bubble dynamics in a viscous fluid, moving with velocity $V$ far from the bubble, is considered. The Cauchy problem of recovering the bubble evolution from its initial shape is completely solved without surface tension. This dynamical system is well-posed (after a Tikhonov regularization) and possesses an extensive list of unsteady nonsingular closed-form solutions due to integrability. A new rational class of solutions is obtained and added to the logarithmic class found earlier [Phys. Rev. E 89, 061003(R) (2014)]. The only attractor of the system selects the observable bubble shape and velocity $U=2V$ from the continuum of possible solutions. The attractor is asymptotically stable. Numerical results essential for illustrating and understanding the most salient geometric aspects of the bubble dynamics are presented.

Astrophysical dynamos feature various spatial structures and dynamical regimes, ranging from hemispherical magnetic fields to the random reversals of the geodynamo. The Tayler-Spruit dynamo, recently confirmed in direct numerical simulations, has been invoked to explain angular momentum transport in stellar radiative zones and magnetar formation in a proto-neutron star spun up by fallback accretion. Whether this dynamo mechanism can lead to different dynamical regimes remains an open question. Using three-dimensional direct numerical simulations, we model the dynamics of a stably stratified spherical Couette flow, with the outer sphere rotating faster than the inner one. While the generation of strong stationary and hemispherical dynamos has been observed in our previous studies, we report the existence of reversals and complex temporal dynamics. We observe that the dynamics is strongly correlated with the equatorial symmetry breaking of the flow. Focusing on a fiducial dynamo simulation, we propose an interpretation of its dynamics that consists of the coupling of two large-scale magnetic modes with opposite equatorial symmetries by the flow symmetry breaking. While this interpretation captures the simplest observed dynamics, the nonlinear interaction between a higher number of magnetic modes is certainly required to describe more complex regimes. The wide diversity of dynamical regimes generated by the Tayler-Spruit dynamo may have interesting implications for the geometry of the neutron star magnetic fields, and therefore neutron star emissions.

Dynamic mode decomposition (DMD) is a widely used technique for analyzing flow dynamics, particularly with experimental data. Traditionally, in experimental applications, the method frequently relies on time-resolved particle image velocimetry (PIV) data to construct an embedding to track incremental changes in the flow state. In this study, we propose an extension of DMD to enable the extraction of DMD modes from standard (non-time-resolved) PIV data. Standard PIV data typically consist of paired snapshots of particle positions taken with a small time delay, used to compute instantaneous velocity fields. However, the time delay between successive pairs is often too large to effectively capture the evolution of the velocity field. To address this limitation, we associate particle-position data with flow dynamics by introducing a gap-based DMD (gDMD) formulation. In this approach, the local distribution of seed particles is mapped to directional gap fields, which are then used as observables for extracting velocity-associated DMD modes. The method is showcased using two direct numerical simulation databases: a confined two-dimensional cylinder wake and the fluidic pinball configuration, together with PIV data of a rectangular jet. In the numerical case, artificial PIV data were generated by seeding the flow with passive tracers. Our results indicate that dominant DMD modes can be accurately predicted even with significant time delays between successive snapshot pairs—an interval that would typically hinder the application of standard DMD. This approach broadens the applicability of DMD, providing a robust tool for analyzing flow dynamics with non-time-resolved PIV data.

The aeroacoustic design of porous trailing-edge inserts for wind turbine noise attenuation requires knowledge of the penetration depth of pressure fluctuations into the porous material. Computationally efficient modeling of the attenuation of unsteady pressure and velocity fluctuations within porous materials will enable improved trailing-edge noise attenuation while minimizing aerodynamic performance loss. Steady models fail to capture the frequency dependence of the attenuation of these fluctuations through the material, while high-fidelity unsteady scale-resolved porous medium models are computationally too expensive for the early-stage design phase. In this study, high-fidelity simulations of a porous material sample subjected to low-amplitude modal inflows are used to evaluate the accuracy of the unsteady Darcy model, which is proposed to fill the gap between high-fidelity unsteady simulations and the steady models for porous medium flows. Two important regimes are identified when considering the local conversion of pressure fluctuations into velocity fluctuations, separated in the frequency domain by a critical frequency. For the investigated porous material and flow conditions, the Strouhal number separating these regimes lies between $0.6$ and $1.3$, based on the inflow velocity and porous skeleton strut diameter. Above this critical number, pressure and velocity fluctuation attenuation closely follow the unsteady Darcy model. Below this critical number, the local response of the flow features a strong spatial variation throughout the porous sample. In future research, the underlying mechanism affecting the presence of these spatial variations in the low frequencies will be investigated.

This study presents band-ensemble spectral proper orthogonal decomposition (bSPOD). The approach is inspired by frequency smoothing, a method used to reduce estimator variance in power spectral density estimates, and is here extended to SPOD. The algorithm estimates SPOD modes from consecutive Fourier coefficients obtained from a single Fourier transform of the full-time record and thus avoids time segmentation. In this study, bSPOD is applied to artificial test data and to a particle image velocimetry data set of a broadband-tonal cavity flow. Compared to the more commonly used Welch-based SPOD formulation, bSPOD reduces spectral leakage, permits increased frequency resolution, and retains frequency information of tonal components at comparable computational cost. These features enable reduced estimator variance while maintaining low bias for tonal components, making bSPOD particularly effective for broadband-tonal flows.

Horizontal convection (HC) serves as a canonical model for geophysical and industrial flows driven by differential heating along a surface. While the classical Oberbeck-Boussinesq (OB) approximation is well established, the impact of a nonlinear equation of state, specifically the density extremum of water near $4{}^{\circ }\mathrm{C}$, remains underexplored. Here, we investigate this effect using two-dimensional numerical simulations over the Rayleigh-number range ${10}^6\le \mathrm{Ra}\le 5\times {10}^{10}$. We examine four configurations, contrasting extremum (EXT) and monotonic (MON) buoyancy boundary conditions with linear (LE) and nonlinear (NE) equations of state. Our results reveal that, owing to strong cabbeling, the EXT-NE case develops mixing plumes that drive a strong bicellular circulation. At $\mathrm{Pr}=1$, as $\mathrm{Re}$ increases, this bicellular state becomes unstable and transitions to a single-roll circulation. This reorganization manifests as transitional anomalies in the Reynolds-number ($\mathrm{Re}$) scaling, while the emergence of full-depth plumes alters the heat-transport mechanism. Consequently, in contrast to the classical Rossby scaling ($\mathrm{Nu}\sim {\mathrm{Ra}}^{1/5}$) observed in the reference cases, the EXT-NE case exhibits enhanced heat-transport scaling ranging from $\mathrm{Nu}\sim {\mathrm{Ra}}^{1/4}$ to $\mathrm{Nu}\sim {\mathrm{Ra}}^{1/3}$. To interpret this behavior, we examine the total energy budget and identify an additional potential-energy transfer term, ${\mathrm{\Phi }}_{i2}$, arising from the nonlinear equation of state. The scaling argument suggests that the magnitude of this contribution is controlled by the characteristic plume height ($\widehat{z}$). Specifically, when the plumes penetrate the entire cavity depth ($\widehat{z}\sim H$), as observed in the EXT-NE case, the global kinetic-energy dissipation is no longer described by the standard OB-HC energy closure alone. The resulting model captures the main trends of the numerical data and provides a possible energy-budget interpretation of the enhanced transport observed in this two-dimensional configuration.

Unstable periodic orbits and steady states are believed to form the backbone of spatiotemporal chaos and turbulence, yet their computation in thermally driven flows remains scarce for transitional regimes. In this work, we compute and characterize a steady state and three families of periodic orbits in two-dimensional Rayleigh-Bénard flow at $Pr=1$, near the transition to chaos. We find that in its route to chaos, the flow hops between several sets of orbits after becoming quasiperiodic. We use Floquet analysis to study the stability of the orbits obtained and characterize their bifurcations, showing how the appearance of primary and secondary frequencies, as well as phase-locking mechanisms, are all related to the dynamics of the orbits. We study in detail how the flow shadows the orbits found, and we determine in which regimes each orbit is dynamically relevant or not. Our analysis also reveals two important insights: (1) all symmetries are broken before the onset of chaos, and (2) this onset does not alter the behavior of the heat transport.

Pressure-driven flow is numerically investigated in curved channels at low aspect ratio, where centrifugal forces act along the largest dimension. The dynamics is studied numerically, as a function of the characteristic Dean number, $\mathrm{De}=\mathrm{Re}\sqrt{\delta }$, by varying independently the Reynolds number $\mathrm{Re}$ and the curvature ratio $\delta$, the ratio between the hydraulic diameter and the radius of curvature. A wide range of dimensionless numbers is considered; $\mathrm{De}\lesssim 200$ and $0.005\le \delta \le 0.15$. For $\mathrm{De}\lesssim 100$, the flow remains steady, whereas at larger Dean numbers, the flow is stable for several turns before transient structures develop. While investigating the flow features in the stable regime, only one pair of counterrotating vortices is observed. At small $\mathrm{De}$ and large $\delta$, the peak of the streamwise velocity and the center of the vortices are located near the inner channel wall. They both shift toward the outer wall as $\mathrm{De}$ is increased and/or $\delta$ is decreased, a feature that is expected to affect the transport of particles in curved channels. A scaling law for the secondary flow is formulated from dimensional analysis, rather than relying on empirical correlations. The friction coefficient of the flow as well as the development angle are also rationalized in terms of both $\mathrm{Re}$ and $\delta$.

We experimentally investigate drag modulation by finite-size particles in viscoelastic Taylor-Couette turbulence. Three spheroidal particle shapes, namely oblate, spherical, and prolate particles, are considered. By combining global torque measurements with particle-distribution measurements, we identify two distinct particle-polymer-turbulence coupling regimes. At lower Reynolds number, the flow is particle dominated: polymer elasticity only weakly modifies the carrier turbulence, while finite-size particles introduce additional particle-related stresses and locally enhance the particle-polymer interaction. In this regime, the particle-induced drag penalty increases monotonically with polymer concentration. At higher Reynolds number, the flow becomes polymer dominated: stronger elasticity suppresses turbulent fluctuations and weakens the ability of particles to enhance angular momentum transport, leading to a nonmonotonic dependence of the particle-induced drag penalty on polymer concentration. Particle shape further modulates this particle-polymer-turbulence coupling. Spherical particles generate larger torque than oblate and prolate particles, and this shape dependence is amplified in the viscoelastic fluid, suggesting that polymer elasticity enhances the sensitivity of the global drag to shape-dependent local disturbances. Particle-distribution measurements provide the spatial signature of the two regimes: polymers have little influence at low Reynolds number, whereas at high Reynolds number they reduce the near-wall accumulation of spherical particles and make the axial distribution more strongly organized by Taylor vortices. These results reveal the regime-dependent coupling mechanisms in complex multiphase turbulence, where dispersed particles, polymer elasticity, turbulence, and secondary flows act as a coupled dynamical system to determine the particles and momentum transport.

A real-space measure of the scale-by-scale distribution of turbulent kinetic energy was introduced in [P. A. Davidson, Turbulence: An Introduction for Scientists and Engineers (Oxford University Press, Oxford, 2004)], called the signature function. However, this signature function has two weaknesses. First, although measurements suggest that it is positive in fully developed turbulence, non-negative results cannot be guaranteed. Second, its definition involves derivatives, and so its calculation from experimental data is sensitive to noise. Here, we develop a refinement of the original signature function. This version improves on the original in that it can be shown to be strictly positive in isotropic turbulence. Moreover, it is obtained from experimental data through a process of integration, rather than differentiation, and so is less sensitive to noise. We apply this diagnostic to grid turbulence. Here the signature function is shown to recover many of the expected features of a scale-by-scale energy density. For example, it falls off below ten Kolmogorov scales and also for scales that exceed the integral scale. Moreover, it exhibits a 2/3 law in the inertial subrange, coupled to a bottleneck at the top of the dissipation range. We also apply the signature function to the near-wall region of smooth and rough-wall boundary layers. Although the diagnostic is not guaranteed to stay positive in such a shear layer, in practice it is observed to remain positive. As with grid turbulence, the signature function captures the expected features of a scale-by-scale energy distribution. In particular, it confirms that the energy of the large eddies near the wall scales on the square of the shear velocity.

The effect of free-stream turbulence on the dynamics of laminar separation bubble (LSB) over a circular cylinder is investigated via experiments at three turbulence intensities: $T_u=0.06\%, 0.51\%$, and $0.76\%$. Sectional drag and lift force coefficients are calculated from pressure measurements along the circumference of the cylinder at its midspan. A new definition is proposed to identify the onset and end of the critical regime, based on the local minimum in root-mean square of the drag coefficient ($C_d^{\prime }$). The drag crisis shifts to a lower $\text{Re}$ with increase in $T_u$, resulting in an increase in the mean drag coefficient (${\overline{C}}_d$) at the onset of the critical regime with $T_u$. A scaled parameter, $\beta$, is proposed for comparing the critical regimes across different $T_u$. A methodology is devised to identify various flow states and their respective probability at each $\beta$. Based on the number of states observed, the critical regime is divided into subregimes. In the first subregime, the flow intermittently switches between four states, irrespective of $T_u$. For $T_u=0.06\%$, the appearance and disappearance of LSB is found to be synchronized with the formation and shedding of the vortex from the same side. The nondimensional vortex shedding frequency in this subregime is relatively low ($\text{St}=0.12$). Upon increase in $\beta$, an asymmetric, one-bubble state becomes stable. For $T_u=0.51\%$, this asymmetry is intermittent and limited to a smaller subregime, while it nearly vanishes for $T_u=0.76\%$. At the end of the critical regime, the flow is in a stable two-bubble state for all $T_u$.

How well turbulence mixes a scalar $\theta$ is ultimately governed by the scalar dissipation rate $\chi ={2D\left|\mathbf{\nabla }\theta \right|}^2$, where $D$ is the scalar diffusivity, making scalar gradients central to turbulent mixing. We study the structure and amplification of these gradients for the canonical problem of passive scalar driven by a uniform mean gradient in stationary isotropic turbulence, using well-resolved direct numerical simulations at grid resolutions up to ${8192}^3$. The Taylor-scale Reynolds number ${\mathrm{Re}}_{\lambda }$ spans $140\text{–}1000$, and the Schmidt number $\mathrm{Sc}\equiv \nu /D$ spans $1\text{–}512$, where $\nu$ is the kinematic viscosity. We analyze joint statistical correlations of velocity and scalar gradients that underlie scalar-gradient amplification. Unconditional statistics reaffirm earlier observations that production of scalar dissipation is dominated by nonlinear amplification of scalar gradients by strain rate. Scalar gradients preferentially align with the most compressive strain eigenvector and remain orthogonal to vorticity, with both trends virtually independent of ${\mathrm{Re}}_{\lambda }$ and $\mathrm{Sc}$. Conditional statistics reveal that this organization becomes dramatically enhanced in regions of intense scalar dissipation: Scalar gradient becomes near-perfectly aligned with the most compressive strain eigendirection and orthogonal to the other strain eigendirections and to vorticity. This geometry, also supported by visualizations, suggests that intense scalar dissipation is organized in sheetlike structures formed in shear layers between vortex tubes, where intense strain also generally resides. However, the effective strain acting along intense scalar gradients is comparatively much weaker, indicating intense scalar dissipation arises primarily from optimal alignments rather than intense strain alone. Molecular diffusion arrests intense scalar-gradient events primarily by redistributing scalar-gradient variance away from intense structures. The contribution from imposed mean gradient is negligible but still imprints anisotropy directly onto smallest scales via the strain field. The conditional statistics broadly exhibit progressively weaker $\mathrm{Sc}$ dependence as ${\mathrm{Re}}_{\lambda }$ increases, demonstrating convergence towards an asymptotic state governing the local structure and dynamics of intense scalar dissipation.

The channel flow of a liquid metal driven by a rapidly varying applied magnetic field is analyzed. The flow configuration, physical properties, and parameters correspond to a duct within a liquid-metal blanket of a nuclear fusion reactor under off-normal plasma conditions, such as plasma disruptions. The problem is solved numerically using a one-dimensional flow approximation. The longitudinal magnetic field, decaying at a typical rate on the order of 100 T/s, induces eddy currents that interact with a steady wall-normal magnetic field, generating the Lorentz force that drives the flow. Standing Alfvén waves are identified as the key mechanism controlling the liquid metal's response. These waves manifest as large-amplitude, gradually decaying oscillations of velocity, the induced magnetic field, and eddy currents. A parametric study predicts a severe response developing within the first few milliseconds of the event, with maximum flow velocities reaching several meters per second and Lorentz forces exceeding ${10}^9{\text{N/m}}^3$. Power-law approximations for the dependencies of the response characteristics on the flow parameters are developed. Finally, the effects of fluid compressibility and pressure waves are analyzed and found not to lead to a major modification of the flow evolution.

We investigate gas injection into axisymmetric water-saturated porous channels with Gaussian and parabolic profiles as idealized models of underground gas storage in dome-shaped anticlines. Exploiting the slenderness of each channel, we derive an evolution equation for the gas-liquid interface using a composite asymptotic approximation that accommodates large channel slopes and has a simplified small-slope form describing spreading in weakly curved channels. In the high gas-mobility limit, in contrast with flat planar channels, buoyancy influences the dynamics through different mechanisms in each geometry. For gas injected steadily into a Gaussian channel, buoyancy can continually affect the flow due to the attenuation of the gas velocity caused by axisymmetry. In parabolic channels, the increasing channel slope ensures that buoyancy eventually influences the flow at a timescale depending on injection rate and fluid properties. Asymptotic analysis of the parabolic-channel flow reveals five temporal regimes, each with multiple spatial regions and a distinct spreading rate, reflecting the evolving spatiotemporal competition between injection and buoyancy. Initially, a thin film of gas spreads along the upper boundary; the channel slope and elongation of the film then generate a hydrostatic pressure gradient, which strengthens until buoyancy arrests the upper contact line and thickens the film. Beneath the film, liquid then drains until the interface flattens under buoyancy. Analytical solutions of reduced-order models capture interface evolution and contact-line motion through each regime and are validated against full numerical simulations. These results have implications for subsurface hydrogen and ${\mathrm{CO}}_2$ storage, where a horizontal interface that advances vertically enhances both safety and storage efficiency.

The flow-induced vibration of a D-section cylinder is investigated at $\text{Re}=100$ using two-dimensional laminar flow simulations, with the cylinder restricted to transverse motion. The orientation angle is fixed at $\alpha ={60}^{\circ }$, and three mass ratios, $m^{*}=5$, 10, and 20, are considered over a range of reduced velocities. The analysis combines nonlinear numerical simulations with linear stability analysis using a reduced model identified by the eigensystem realization algorithm, structural energy share analysis, instantaneous phase analysis, and dynamic mode decomposition (DMD). At low reduced velocities, the lift and displacement remain frequency synchronized, but the lift response reaches its maximum before the displacement response. The linear stability and structural energy share results associate this offset with a change in the structural participation of the flow-related and structural modes. At higher reduced velocities, a finite transitional interval is observed in which the dominant structural and lift frequencies no longer coincide. Within this interval, the displacement amplitude decreases after the main lock-in response and subsequently shows a local recovery, while the instantaneous phase difference between lift and displacement does not remain close to either $0^{\circ }$ or $\pm {180}^{\circ }$. Representative DMD results show a corresponding shift of the dominant wake-frequency component toward a higher frequency. At still higher reduced velocities, the response approaches a low-amplitude state with the lift and displacement close to antiphase. The transitional interval becomes broader as the mass ratio increases, after which the system approaches a low-amplitude state with the lift and displacement close to antiphase. These results characterize the finite transitional response and clarify its evolution toward the low-amplitude state within the investigated range of reduced velocity.

Sand-laden cavitating flows involve the evolution of solid particles, discrete bubbles, and macroscopic cavity structures across a wide range of temporal and spatial scales, posing a formidable challenge for accurate simulation. To simulate the complicated multiphase flow, a multiscale gas-liquid-solid modeling method in OpenFOAM has been developed in this work. The dynamics of particles and bubbles are resolved in the Lagrangian framework, whereas the cavity volume is captured in the Eulerian framework, while a two-way coupling algorithm is established to bridge these scales. The new solver is validated using available experimental data. Analyses of pure-water and sand-laden unsteady cavitating flows with three particle sizes over a Clark-Y hydrofoil indicate that particles promote cavitation and increase the cavity shedding frequency. The reduction in particle velocity near the wall increases the local fluid velocity, thereby reducing the adverse pressure gradient and weakening the reentrant jet along the hydrofoil suction surface. The particle streamwise velocity distributions for all three particle sizes exhibit a Gamma distribution, with larger particles concentrating the streamwise velocity distribution. Particles promote the generation of discrete bubbles in the cloud cavitation, and increase the overall bubble size. Although the presence of particles does not modify the theoretical −10/3 power law in the large bubble regime, it increases the Hinze scale by weakening the turbulent dissipation rate and thereby suppresses the continuous breakup cascade from large to small bubbles. As a result, the power law of small bubbles deviates more strongly from the theoretical −4/3 scaling. These findings provide new insight into the instability mechanism of sand-laden cavitating flows.

We study hydrodynamic spin coupling in a two-rotor corral using direct numerical simulation of the two-dimensional incompressible Navier-Stokes equations. An active rotor is driven at angular velocity $\mathrm{\Omega }$, and a nearby torque-free passive rotor selects an angular velocity $\omega$ through hydrodynamic torque balance. The signed gear ratio $\mathrm{\Gamma }=\omega /\mathrm{\Omega }$ distinguishes corotation from counterrotation, with Reynolds number $\mathrm{Re}=\left|\mathrm{\Omega }\right|r^2/\nu$. Motivated by a recent quasi-two-dimensional experiment [Smith et al., Phys. Rev. Lett. 136, 024001 (2026)], we use a distributed Lagrange multiplier/fictitious domain method to compute planar phase diagrams of $\mathrm{\Gamma }(G,\mathrm{Re})$ at corral sizes $C=3$, 4.5, and 6. The planar model recovers the benchmark gap route at $\mathrm{Re}=20$: An intermediate counterrotation band, a wide-gap transition to corotation, gear-ratio magnitudes of order ${10}^{-2}$, and the observed sequence of vortex attachment, detachment, and merger. It also produces a reentrant-like gap structure with a small-gap corotation region whose relation to the experimental close-range geometric state remains unresolved. The main discrepancy is the high-$\mathrm{Re}$ boundary. At the experimental midgap transect $G\approx 0.3$, the planar gear ratio approaches zero from the counterrotating side but does not cross through $\mathrm{Re}=400$; at the narrower gap $G=0.22$, by contrast, the planar terminal spin reverses near $\mathrm{Re}=44$ while a gap-facing arc of counterrotating traction persists. The computed traction-based arc exhibits less contraction and deflection than the pathline-defined experimental shear zone; because these are different observables, the comparison identifies distinct diagnostic signatures without assigning the discrepancy to a unique mechanism. The planar model captures the broad gap-route structure and supports Reynolds-driven spin reversal, but places the boundary at smaller gaps over the sampled range. Finite-depth secondary motion, end-wall stresses, and apparatus geometry are candidate contributors to the remaining mismatch.

The addition of a small amount of polymers to turbulence drastically alters the energy transfer across different scales and leads to the emergence of an elastic scaling range. How polymers alter the intermittency in the elastic range remains elusive. We here present an experimental study on the elastic range intermittency by probing the velocity structure functions up to the 12th order. We show that the scaling of the longitudinal velocity structure functions exhibits a bifractal-like behavior: intermittency-free at low orders ($n\le 4, n$ being the order of the velocity structure function), and monofractal with a Hölder scaling $h=0.53$ and dimension $D=2.22$ at higher orders ($4<n\le 12$). We find that the Hölder dimension is close to the fractal dimension of the sheet-like flow structures ($D_f\approx 2.20$), pointing to a connection between the elastic range intermittency and the coherent flow structures in bulk polymeric turbulence. The scaling exponents of the transverse velocity structure functions deviate from those of longitudinal velocity structure functions at high orders ($n\ge 4$). This behavior might be related to the low Reynolds number in the present study and persistent anisotropy in the flow. These results highlight the importance of sheet-like structures in polymeric turbulence and offer new insights into polymer-turbulence interaction.