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.

We present an experimental investigation of the mutual synchronization between hydrodynamic and thermoacoustic oscillations in a turbulent lean-premixed bluff‐body flame. By fixing the equivalence ratio ($\varphi =0.65$) and Reynolds number ($\mathrm{Re}=5.4\times {10}^3$) and systematically varying the combustor length, we sweep the acoustic chamber eigenfrequency through the hydrodynamic vortex-shedding frequency. As the combustor length increases, the system evolves from a pure hydrodynamic vortex-shedding mode, through a thermoacoustically self-excited combustor mode, to a hybrid quasiperiodic state in which both modes coexist, and finally to a 1:2 mutually synchronized state in which both modes lock together, amplifying both the heat release rate (HRR) and pressure oscillations. Temporal analyses–Hilbert‐transform metrics, recurrence quantification, and Pearson correlation–reveal the route from desynchronization to phase and generalized synchronization, the latter coinciding with a significant amplification of the HRR and pressure amplitudes. Spatiotemporal analyses—local frequency and HRR amplitude maps, Rayleigh index fields, phase-locking distributions, and modal decomposition of ${\mathrm{CH}}^{*}$ chemiluminescence images—reveal the bluff‐body recirculation zone as the dominant energy-injection site for thermoacoustic instability. Finally, two flame blow-off pathways are identified: (i) isolated pinch-off events that cause global extinction when $\varphi$ drops below the lean flammability limit and (ii) coupled pinch-off/wall-quenching events driven by high-amplitude thermoacoustic forcing. These findings clarify the interplay between hydrodynamic and thermoacoustic modes, guiding control strategies for next-generation low-emission combustors.

Two cylinder geometries, circular and square, were subjected to four distinct inflows to investigate the effects of freestream turbulence (FST) on their wake development. The wake flow fields were measured using planar particle image velocimetry with a large field of view, covering a contiguous area up to 20 cylinder diameters ($D$) downstream of the wake-generating body. The experiments were conducted at a Reynolds number of ${\mathrm{Re}}_D=33000$. The turbulent inflows were generated using an active grid, which produced freestream turbulence intensities ranging from 1.1% to 13.8%. The integral scales of the turbulence varied between $4.32D$ and $7.86D$. The findings demonstrate that FST facilitates the recovery of the wake velocity deficit and promotes an earlier trend towards self-similarity in the velocity profile. Moreover, a reduction in the coherence of the shed vortices is observed in the wake as FST increases, resulting in a lower average number of coherent shed vortices and a transfer of energy from the proper orthogonal decomposition modes associated with vortex shedding to modes associated with the background turbulence. These observations explicitly demonstrate that the enhanced mixing due to elevated freestream turbulence facilitates faster wake recovery, loss of coherence of the shed vortices, approach to self-similarity of velocity statistics, and significant alterations in the instantaneous wake flow field.

While recent approaches, such as the macroscopic forcing method (MFM) or Green's function-based approaches, can be used to compute Reynolds-averaged Navier-Stokes closure operators using forced direct numerical simulations, MFM can also be used to directly compute moments of the effective nonlocal and anisotropic eddy diffusivities. The low-order spatial and temporal moments contain limited information about the eddy diffusivity but are often sufficient for quantification and modeling of nonlocal and anisotropic effects. However, when using MFM to compute eddy diffusivity moments, the statistical convergence can be slow for higher-order moments. In this work, we demonstrate that using the same direct numerical simulation (DNS) for all forced MFM simulations improves statistical convergence of the eddy diffusivity moments. We present its implementation in conjunction with a decomposition method that handles the MFM forcing semianalytically and allows for consistent boundary condition treatment, which we develop for both scalar and momentum transport. We demonstrate that for a two-dimensional Rayleigh-Taylor instability case study, using the same DNS for all forced MFM simulations results in convergence with $\mathcal{O}\left(100\right)$ simulations rather than $\mathcal{O}\left(1000\right)$ simulations. We then demonstrate the impacts of improved convergence on the quantification of the eddy diffusivity.

We study the transient energy growth of linearly stable diffusive convection with and without a bounded Couette flow. In contrast to the one-component thermal (Rayleigh-Bénard) convection, diffusive convection can generate a nontrivial transient growth even in the absence of shear. This growth is characterized by (quasi)periodic oscillations, and the largest transient growth occurs at the peak of the first oscillation. Driven by the synchronous action of temperature and salinity fields, this growth results from resonance between the symmetric oscillatory modes, and also benefits from the catalytic enhancement by stationary modes of specific growth rates. In the presence of shear, the transient growth of longitudinal rolls is always the largest and three nonmodal instability regimes are identified with increasing density gradient. Unless the density gradient is very high, the lift-up mechanism is always the fundamental mechanism to drive the amplification of disturbances while double diffusion tends to enhance it by two means. Specifically, in regime I double diffusion can extend the duration of the lift-up mechanism and thus moderately enhance the nonmodal instability. In regime II where the transient growth of the mixed convection is the largest, double diffusion can effectively increase the working efficiency of the lift-up mechanism by feeding the perturbed vertical velocity. In regime III where the density gradient is sufficiently high, the high-frequency oscillation resulting from double diffusion can directly cause non-negligible transient growth but the duration of the lift-up mechanism is decreased.