Unsteady load alleviation is crucial for engineering applications such as tidal turbines. Herein, we present an experimental study into the load alleviation capacities of constant-section airfoils with flexible trailing-edges. The trailing-edge studied here consists of two independent flexible skins, enabling large skin deformations and enhanced load alleviation compared to conventional flexible trailing-edge designs. We test high-amplitude plunging kinematics (up to peak-to-peak amplitude of one chord length) at reduced frequency $k=0.2$ and Reynolds numbers $\mathrm{Re}=\mathcal{O}\left({10}^4\right)$. To quantify the role of airfoil flexibility, we introduce two Cauchy numbers (${\mathrm{Ca}}_u$ and ${\mathrm{Ca}}_v$), which normalize the freestream and plunging velocities, respectively. We demonstrate that both the trailing-edge deflection and the resulting lift alleviation scale with these Cauchy numbers provide a fundamental framework for understanding flexible airfoil dynamics. Furthermore, we propose semi-empirical models for unsteady lift alleviation, which agree with our measurements. These findings lay the groundwork for fully predictive low-order models, advancing the design of passively morphing airfoils for efficient load control in unsteady flow environments.

Cerebrospinal fluid (CSF) flow is modelled in human perivascular spaces (PVSs) that surround brain penetrating arteries. It is proposed that the outer PVS boundary oscillates due to brain pulsations, and the arterial wall motion is driven by a blood pressure wave. Lubrication theory is employed to derive a mathematical model for the CSF flow, which is then solved numerically. A parametric analysis is undertaken to investigate the effect of the brain pulsations, which shows that pulsations magnify the net axial CSF flows created by the arterial wall motion. The findings suggest that net axial CSF flows are almost entirely positive (deeper into the brain), with arterial wall motion highly dependent on PVS-penetrating artery configurations. Given the glymphatic hypothesis, the findings support the clinical practice of treating dilated PVSs as indicators of an increased likelihood of neurodegenerative conditions, such as dementia.

This paper is associated with a poster winner of a 2024 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2024.GFM.P2692828.

This paper is associated with a poster winner of a 2024 American Physical Society's Division of Fluid Dynamics (DFD) Milton Van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2024.GFM.P2676604.

This paper is associated with a poster winner of a 2024 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2024.GFM.P2685195

This paper is associated with a video winner of a 2024 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2024.GFM.V2560348.

This paper is associated with a video winner of a 2024 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2024.GFM.V2561866

This paper is associated with a video winner of a 2024 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2024.GFM.V2694489.

This paper is associated with a video winner of a 2024 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2024.GFM.V2684816.

This paper is associated with a video winner of a 2024 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2024.GFM.V2685343

This paper is associated with a video winner of a 2024 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2024.GFM.V2634768

This paper is associated with a poster winner of a 2024 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2024.GFM.P2652209

This paper is associated with a poster winner of a 2024 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2024.GFM.P2685516

The mechanism of generation of a localized solitary azimuthal vortex in an axial liquid metal flow is found by numerical simulations. Initially, two counter-rotating magnetic field inducers create two vortices by electromagnetic forces in the cylindrical channel with an axial through flow of liquid metal. Beyond a certain threshold of azimuthal forcing, the second vortex is completely suppressed by the first counter-rotating vortex. The threshold value is reached when the Reynolds numbers for rotating and axial flows become equal. The solitary vortex has clear-cut boundaries. After the switch-off the driving forces, the solitary vortex is frozen in the axial flow when transferred by it.

We investigate the effect of a four-dimensional Fourier transform on the formulation of the Navier-Stokes equation in Fourier space and the way the energy is transferred between Fourier components. Since time in a sampled high-intensity turbulence must be considered a stochastic variable in the energy exchange between scales, we refer to these dynamic triad interactions as modal interactions, rather than the commonly referred to triad interactions in the classical three-dimensional analysis. The inclusion of time as a parameter broadens the phase match condition from the classical one, $\mathrm{\Delta }\mathit{k}·\mathit{r}=[\mathit{k}-({\mathit{k}}_1+{\mathit{k}}_2)]·\mathit{r}$, to the more general formulation that also includes temporal frequencies: $\mathrm{\Delta }\mathit{k}·\mathit{r}-\mathrm{\Delta }\omega t=[\mathit{k}-({\mathit{k}}_1+{\mathit{k}}_2)]·\mathit{r}-[\omega -({\omega }_1+{\omega }_2)]t$. This renders possible the occurrence of “delayed” and “advanced” interactions. The observation that mismatches in the wavevector triadic interactions may be compensated by a corresponding mismatch in the frequencies supports the empirically deduced delayed interactions reported in Josserand et al. [J. Stat. Phys. 167, 596 (2017)]. These results explain the occurrence and inherent time development of the so-called Richardson cascade and also how finite temporal overlap of wave components can result in significant nonlocal interactions and consequently nonequilibrium turbulence, e.g., fractal grid generated turbulence. The consequences of including time as a parameter in practical experiments or simulations in terms of limited resolution, domain size, etc., are treated in the companion paper (Part II) of the present work.

We investigate how momentum and kinetic energy is transferred between Fourier components (the so-called triad interactions) in measured turbulent flow fields, i.e., in practical, discretely sampled signals with limited temporal and spatial domains. We empirically observe that the finite resolution in experimental investigations causes a decoupling between time and space, which broadens the phase match condition to include both spatial and temporal frequencies as predicted in part I. It is also empirically observed that the Fourier components may interact with a finite time delay and within a broadened frequency window (finite overlap widths) in both time and space, as compared to the usual integrals over infinite ranges where Fourier components interact by overlapping Dirac δ-functions. Furthermore, it is empirically observed how the finite temporal and spatial measurement domains of velocity records can have a significant effect on the efficiency of the triad interactions and thereby on the shape and development of measured velocity power spectra. These finite spatial/temporal domains thus influence the measured spatial and temporal development of turbulence, the possibility for nonlocal interactions and hence also nonequilibrium turbulence, e.g., fractal grid generated turbulence.

In this work, we report a comprehensive study of turbulent compressible convection through two-dimensional (2D) and three-dimensional (3D) numerical simulations spanning a wide range of Prandtl numbers (${10}^{-2}\le \mathrm{Pr}\le {10}^2$) and Rayleigh numbers (Ra $={10}^7, {10}^8, {10}^9$). The total temperature exhibits adiabatic cooling in the bulk, with minimal variation across Pr. For Pr $<1$ and $>1$, the Nusselt number scales as ${\mathrm{Ra}}^{0.22}{\mathrm{Pr}}^{0.04}$ and ${\mathrm{Ra}}^{0.28}{\mathrm{Pr}}^{0.02}$ in 2D, and as ${\mathrm{Ra}}^{0.27}{\mathrm{Pr}}^{0.16}$ and ${\mathrm{Ra}}^{0.27}{\mathrm{Pr}}^{0.03}$ in 3D. The corresponding variations for the Reynolds number are ${\mathrm{Ra}}^{0.51}{\mathrm{Pr}}^{-0.78}$ and ${\mathrm{Ra}}^{0.60}{\mathrm{Pr}}^{-0.99}$ in 2D, and ${\mathrm{Ra}}^{0.45}{\mathrm{Pr}}^{-0.64}$ and ${\mathrm{Ra}}^{0.51}{\mathrm{Pr}}^{-0.91}$ in 3D. Top-bottom asymmetry persists in both the thermal and viscous boundary layers, with thicker top layers. As Pr increases, thermal boundary layers become thinner while viscous boundary layers thicken, with distinct scaling near the top and bottom boundaries.

Visualization and scaling of charged droplet transport in gas jet crossflows at near- and sub-atmospheric pressures are presented to describe the physics of droplet-gas interactions and predict when gas jets can redirect droplet trajectories. Laser scattering of electrospray and schlieren photography of gas jet expansion are employed to assess charged droplet-gas interactions in variable pressure environments. Experimental results reveal that the greatest gas influence on droplet trajectories occurs at intermediate pressures ($P/P_{\mathrm{atm}}=2.1\times {10}^{-2}$), when gas jets achieve supersonic velocities and exert substantial drag before rarefaction effects become significant. A fundamental understanding of the underlying physics is gained through a scaling analysis for an individual charged droplet's transport that introduces a dimensionless parameter, representing the ratio of gas drag to the maximum of the electric or inertial force, to predict droplet deflection in a gas crossflow. This dimensionless parameter that can be predicted analytically using the experimentally controlled inputs is shown to effectively capture the behavior without the need for complex and computationally expensive multiphysics simulations. Comparisons with experimental results and computational fluid dynamics and electrostatic simulations validate the scaling framework while identifying limitations of continuum models at high Knudsen numbers. These results delineate distinct regimes of droplet transport and provide a predictive foundation for droplet control strategies by gas jets for numerous engineering applications.

Particle-laden turbulence involves highly complex interactions between the dynamics of the dispersed particle phase and that of the continuous turbulent phase. Particles with different physical properties, such as shape, density, and size, are particularly interesting as these can be sensitive to or influence different specific aspects of the flow. In this contribution we focus on the coupling between the angular dynamics of particles and turbulent vorticity in turbulence. To this end, we detail the development and demonstrate the capabilities of a special experimental setup where the angular dynamics of particles can be both measured (via optical image processing techniques) and imposed (via the application of external rotating magnetic fields). We further discuss how particles of different densities and magnetic properties can be manufactured, with specific interest toward light particles as these can be transformed into vorticity probes and localized forcing acting on small-scale vortex filaments. The ordinary optical method for particle tracking velocimetry is here extended to accurately measure the angular velocity of particles with sizes significantly smaller than the Taylor microscale, typically an order of magnitude larger than the Kolmogorov scale of the turbulence in which they are suspended. Remarkably, the optical method employed in this study enables accurate measurement of the full three-dimensional angular velocity vector of particles using only two-dimensional image sequences, thereby requiring only one camera. The present contribution discusses in detail how the different design choices are entangled with each other and which considerations are relevant when designing such an experimental setup. Beyond advancing the study of particle dynamics in turbulence, this approach opens up possibilities for actively studying how to modulate turbulence through externally applied magnetic fields.