A transformation that relates a compressible wall-bounded turbulent flow with nonuniform fluid properties to an equivalent incompressible flow with uniform fluid properties is derived and validated. The transformation accounts for both variable-property and intrinsic compressibility effects, the latter being the key improvement over the current state of the art. The importance of intrinsic compressibility effects contradicts the renowned Morkovin's hypothesis.

The coupling between ion transport and fluid flow near ion-selective surfaces plays a crucial role in various electrohydrodynamic applications. Above a critical voltage threshold, electroconvective vortices emerge inside the liquid electrolyte and enhance ion transport. Applying a magnetic field modifies the ion mobility and electroconvection by inducing a Lorentz force. To investigate this phenomenon, we numerically study the electroconvection under a perpendicular magnetic field by incorporating the Lorentz force into the coupled Poisson-Nernst-Planck-Stokes equation. The magnetic field induces a cross-flow similar to a pressure-driven Poiseuille flow and completely suppresses the electroconvection when the applied voltage is slightly above the critical threshold. At a high voltage, the crossflow reduces the fluctuation of ion flux passing through the ion-selective surfaces and induces net ion flux along the flow direction. The analysis of the spatial spectra of flow kinetic energy and electric energy reveals that the magnetic field reduces the size of the flow structures.

We present and analyze a theoretical model for the dynamics and interactions of “capillary surfers,” which are millimetric objects that self-propel while floating at the interface of a vibrating fluid bath. In our companion paper [I. Ho et al., Phys. Rev. Fluids 8, L112001 (2023)], we reported the results of an experimental investigation of the surfer system, which showed that surfer pairs may lock into one of seven bound states, and that larger collectives of surfers self-organize into coherent flocking states. Our theoretical model for the surfers' positional and orientational dynamics approximates a surfer as a pair of vertically oscillating point sources of weakly viscous gravity-capillary waves. We derive an analytical solution for the associated interfacial deformation and thus the hydrodynamic force exerted by one surfer on another. Our model recovers the bound states found in experiments and exhibits good agreement with experimental data. Moreover, we conduct a linear stability analysis of bound state solutions and compute numerically the associated eigenvalues. We find that the spacings of the bound states are quantized on the capillary wavelength, with stable branches of equilibria separated by unstable ones. Generally, our work shows that self-propelling objects coupled by capillary waves constitute a promising platform for studying active matter systems in which both inertial and viscous effects are relevant.

We generalize the “filtering spectrum” to probe scales along different directions by spatial coarse-graining. This multidimensional filtering spectrum quantifies the spectral content of flows that are not necessarily homogeneous. From multidimensional spectral information, we propose a simple metric for shape anisotropy at various scales. The method is applied to simulations of two-dimensional (2D) and 3D Rayleigh-Taylor (RT) turbulence, which is inhomogeneous and anisotropic. We show that 3D RT has clear shape anisotropy at large scales with approximately 4:3 vertical to horizontal aspect ratio but tends toward isotropy at small scales as expected. In sharp contrast, we find that RT in 2D simulations, which are still the main modeling framework for many applications, is isotropic at large scales and its shape anisotropy increases at smaller scales where structures tend to be horizontally elongated. While this may be surprising, it is consistent with recent results that large-scale isotropy in 2D RT is due to the generation of a large-scale overturning circulation via an upscale cascade, while small-scale anisotropy is due to the stable stratification resultant from such overturning and the inefficient mixing in 2D.

We present an experimental study of capillary surfers, a new fluid-mediated active system that bridges the gap between dissipation- and inertia-dominated regimes. Surfers are wave-driven particles that self-propel and interact on a fluid interface via an extended field of surface waves. A surfer's speed and interaction with its environment can be tuned broadly through the particle, fluid, and vibration parameters. The wave nature of interactions among surfers allows for multistability of interaction modes and promises a number of novel collective behaviors.

Particles in inertialess flows of shear thinning fluids are a model representation for several systems in biology, ecology, and microfluidics. In this paper, we analyze the motion of a spheroid in a pressure-driven flow of a shear thinning fluid. The shear thinning rheology is characterized by the Carreau model. We use a combination of perturbative techniques and the reciprocal theorem to delineate the kinematics of prolate and oblate spheroids. There are two perturbative strategies adopted, one near the zero shear Newtonian plateau and the other near the infinite shear Newtonian plateau. In both limits, we find that a reduction in effective viscosity decreases the spheroid's rotational time period in pressure-driven flows. The extent to which shear thinning alters the kinematics is a function of the particle shape. For a prolate particle, the effect of shear thinning is most prominent when the spheroid projector is aligned in the direction of the velocity gradient, while for an oblate particle the effect is most prominent when the projector is aligned along the flow direction. Last, we compare the tumbling behavior of spheroids in pressure-driven flow to those in simple shear flow. While the time period decreases monotonically with Carreau number for pressure-driven flows, the trend is nonmonotonic for shear flows where time period first increases at low Carreau number and then decreases at high Carreau numbers. Shear thinning does not resolve the degeneracy of Jefferey's orbits.

Counterintuitively, fresh water attains a maximum density at a temperature above its freezing point. As a result, it exhibits a phenomenon known as weak cabbeling. If a system is in the weak cabbeling regime, then the mean density of the system is not equal to the density evaluated at the mean temperature. The dynamics of freshwater gravity currents are known to be influenced by weak cabbeling, but research on this influence has been restricted to two-dimensional systems with stress-free (free-slip) boundaries. We extend this work by simulating pairs of three-dimensional systems in the weak cabbeling regime with no-slip conditions imposed on the vertical boundaries. In each pair, we have a floating and sinking current: The former has a cold current intruding into a system at the temperature of maximum density, and the latter has the reverse. We define currents that form such a pair to be conjugate. The initial shape and size of conjugate currents are the same, so we would expect the distribution of the intruding fluid to evolve identically under the change of coordinates $(y,z)\to (L_y-y,L_z-z)$, where $L_y$ is the domain width and $L_z$ is the domain height. This symmetry is broken two dimensions when a nonlinear equation of state is assumed; we will show that this result extends to three dimensions. We will report on differences among the lobe-cleft instability, the shear instability, the mixing, and the bed-stresses of three-dimensional conjugate currents. Curiously, we observe that differences in the lobe-cleft instability manifest only after secondary instabilities develop. We also identify and discuss structures created by the lobe-cleft instability that, to our knowledge, have been under-reported in the literature.

Unsteady wall-pressure fluctuations are of great interest to gain insight into the structures and physical mechanisms of the turbulence flows that generate the pressure fields. Wall-pressure fluctuations are investigated in high Reynolds number cavitating flows in a wide range of cavitation regimes, with the aim of providing a quantitative understanding of cavitation-induced wall-pressure fluctuations and their scaling behaviors. The experiment is conducted at a high-speed water tunnel with a backward-facing wedge test model, and a simultaneous sampling technique is adopted to synchronize the transient cavity behaviors by high-speed imaging and cavitation-induced wall-pressure fluctuations using four flush-mounted unsteady pressure transducers beneath attached cavities. The results show that with decreasing $\sigma$, transient cavity length oscillations increase with cavity regimes changing from a stable inception cavity and an intermittent sheet cavity to an unsteady quasiperiodic cloud cavity, while the time-averaged cavity structures under different cavity regimes present self-similarity. The evolution of mean cavity metrics (i.e., $L_{\mathrm{c}}, L_{\mathrm{tc}}, t_{\mathrm{c}}$, and $\theta$) is examined. Inspired by this geometrical self-similarity, statistics (i.e., root mean square pressure level, probability density function, pressure spectra, convective velocity) of wall-pressure fluctuations both inside and outside the attached cavitation are examined. Specifically, the root mean square value of wall-pressure fluctuations approaches its maximum near the cavity closure, and its amplitude is independent of the cavitation number. The probability density function (PDF) shape presents non-Gaussian and asymmetric behaviors. Generally, the PDF shape is positively skewed at the cavity leading edge, approaching Gaussian behaviors near cavity closure and slightly negatively skewed outside the cavity. Spectral analysis indicates that the scaling regions obtained by fast Fourier transform are usually classified as (1) low-frequency range; (2) mid-frequency range, spectra typically show the $f^{-2}$ behavior; (3) transition range, with a $f^{-7/3}$ relation; and (4) high-frequency range, with a $f^{-3.2}$ relation. Remarkably, the Reynolds number effects significantly enhance the non-Gaussian and asymmetric behaviors of wall-pressure fluctuation PDFs. Our study can help to improve both cavitation modeling and hydraulic designs.

Many biological materials such as cervical mucus and collagen gel possess a fibrous microstructure. This microstructure affects the emergent mechanical properties of the material and hence the functional behavior of the system. We consider the canonical problem of stretching a thin sheet of transversely isotropic viscous fluid as a simplified version of the spinnbarkeit test for cervical mucus. We propose a solution to the model constructed by Green and Friedman by manipulating the model to a form amenable to arbitrary Lagrangian-Eulerian (ALE) techniques. The system of equations, reduced by exploiting the slender nature of the sheet, is solved numerically, and we discover that the bulk properties of the sheet are controlled by an effective viscosity dependent on the evolving angle of the fibers. In addition, we confirm a previous conjecture by demonstrating that the center line of the sheet need not be flat, and perform a short timescale analysis to capture the full behavior of the center line.

Before a droplet can contact a surface during impact, it must first displace the air beneath it. Over a wide range of impact velocities, the droplet first squeezes the air into a thin film, enhancing its resistance to drainage; this slows the progress of the liquid toward the surface. Indeed, below a critical impact velocity, the air film remains intact, and the droplet rebounds off of the air film without making contact. For impact velocities exceeding this critical impact velocity, the droplet always makes contact. The initiation of contact formation requires a topological transition, whereby the initially connected gas domain is ruptured and a liquid capillary bridge forms, binding the droplet to the surface. Here we probe this transition in detail around the critical impact velocity using calibrated total internal reflection microscopy to monitor the air film thickness and profile at high speed during the impact process. Two air film rupture modalities are observed: nucleated contacts, which are isolated and do not correspond to the global minimum air film thickness, and spontaneous contacts, which occur always on a ring centered upon the impact axis where the air film reaches its global minimum. Our measurements show that for impact velocities exceeding the critical velocity for contact initiation, the air film ruptures at a nearly identical height $h_{min}\approx 20$ nm, for two fluids: silicone oil and a water-glycerol mixture. The height and time duration of the air film prior to contact are presented for over 180 droplet impact experiments. Impact events of water solution droplets show statistics for contact nucleation different from those for the silicone oil; this suggests that another mechanism may dominate contact nucleation during impact of the solution. Nevertheless, a critical impact velocity above which contact always occurs is identifiable for both liquids.

We report experiments of fingering asymmetry in Rayleigh-Taylor (RT) mixing at an extremely large viscosity ratio $(M\approx 5\times {10}^5)$ and Rayleigh numbers $[\mathrm{Ra}\sim {10}^5–(3\times {10}^6)]$. Our experiments confirm the asymmetric growth of RT instabilities across an upward-moving interface with strong downward fingering. As the Ra increases, the downward fingers reach the bottom boundary faster, resulting in a lower dispersion at the early time. However, this dynamic is not persistent since the system undergoes vigorous mixing after the elongated fingers reach the bottom boundary. A one-dimensional dispersion model is developed to simulate the RT mixing, which predicts the upward-moving front and mixing across the interface.

Fully compressible turbulent convection beyond the Oberbeck-Boussinesq limit and anelastic regime is studied in three-dimensional numerical simulations. Superadiabaticity $\epsilon$ and dissipation number $D$, which measures the strength of stratification of adiabatic equilibria, cause two limits of compressible convection—nearly top-down-symmetric, strongly superadiabatic convection and highly top-down-asymmetric, strongly stratified convection. The highest turbulent Mach numbers $M_t$ follow for a symmetric blend of these two limits, which we term the fully compressible case. Particularly, the strongly stratified convection case leads to a fluctuation-reduced top layer in the convection zone, a strongly reduced global heat transfer, and differing boundary layer dynamics between top and bottom. We detect this asymmetry for growing dissipation number $D$ also in the phase plane, which is spanned by the turbulent Mach number $M_t$ and the dilatation parameter $\delta$, which relates the dilatational velocity fluctuations to the solenoidal ones. A detailed analysis of the different transport currents in the fully compressible energy budget relates the low-$D$ convection cases to the standard definition of the dimensionless Nusselt number in the Oberbeck-Boussinesq limit.

Coupled laboratory-numerical experiments of Rayleigh-Bénard convection in liquid gallium subject to a vertical magnetic field are presented. The experiments are carried out in two cylindrical containers with diameter-to-height aspect ratio $\mathrm{\Gamma }=1.0$ and 2.0 at varying thermal forcing (Rayleigh numbers ${10}^5\lesssim \text{Ra}\lesssim {10}^8$) and magnetic field strength (Chandrasekhar numbers $0\lesssim \text{Ch}\lesssim 3\times {10}^5$). Laboratory measurements and numerical simulations confirm that magnetoconvection in our finite cylindrical tanks onsets via nondrifting wall-attached modes, in good agreement with asymptotic predictions for a semi-infinite domain. With increasing supercriticality, the experimental and numerical thermal measurements and the numerical velocity data reveal transitions between wall mode states with different azimuthal mode numbers and between wall-dominated convection to wall and interior multimodality. These transitions are also reflected in the heat transfer data, which combined with previous studies connect onset to supercritical turbulent behaviors in liquid metal magnetoconvection over a large parameter space. The gross heat transfer behaviors between magnetoconvection and rotating convection in liquid metals are compared and discussed.

The prediction of the drop size distribution (DSD) resulting from liquid atomization is key to the optimization of multiphase flows from gas-turbine propulsion through agriculture to healthcare. Obtaining high-fidelity data of liquid atomization, either experimentally or numerically, is expensive, which makes the exploration of the design space difficult. First, to tackle these challenges, we propose a framework to predict the DSD of a liquid spray based on data as a function of the spray angle, the Reynolds number, and the Weber number. Second, to guide the design of liquid atomizers, the model accurately predicts the volume of fluid contained in drops of specific sizes while providing uncertainty estimation. To do so, we propose a Gaussian process regression (GPR) model, which infers the DSD and its uncertainty form the knowledge of its integrals and of its first moment, i.e., the mean drop diameter. Third, we deploy multiple GPR models to estimate these quantities at arbitrary points of the design space from data obtained from a large number of numerical simulations of a flat fan spray. The kernel used for reconstructing the DSD incorporates prior physical knowledge, which enables the prediction of sharply peaked and heavy-tailed distributions. Fourth, we compare our method with a benchmark approach, which estimates the DSD by interpolating the frequency polygon of the binned drops with a GPR. We show that our integral approach is significantly more accurate, especially in the tail of the distribution (i.e., large, rare drops), and it reduces the bias of the density estimator by up to 10 times. Finally, we discuss physical aspects of the model's predictions and interpret them against experimental results from the literature. This work opens opportunities for modeling drop size distribution in multiphase flows from data.

In this paper, we investigate the dynamics of a wind turbine wake for three different ground surface roughness lengths, i.e., $k_0=0.001$, 0.01, 0.1 m. The computational domain is very long [until $215D$ ($D$ is the rotor diameter) wind turbine downwind], with the attempt to include the entire recovery process of a wind turbine wake. The streamwise variations of velocity deficit and turbulence intensity are analyzed. The focus of this paper is how flow structures of different scales vary as they pass through a wind turbine and travel to further downwind locations. Three different trends depending on scales are observed: (1) energy is added to motions of small scales ($<1D$) immediately in wind turbine's downwind, (2) energy for motions of scales in the range of $1D$ to $3.2D$ is first extracted by the wind turbine and then increased by the wake to a level higher than the inflow, and (3) energy for motions of scales greater than $3.4D$ is first extracted by the wind turbine, and then monotonically increase to the inflow level without a maximum. Finally, the energy density in scale space and its evolution in the streamwise direction are examined, showing the range of scales affected by a wind turbine and its wake.

In this computational paper, we model acoustic dynamics in space and time from synthetic sensor data. The tasks are (i) to predict and extrapolate the spatiotemporal dynamics and (ii) to reconstruct the acoustic state from partial observations. To achieve this, we develop acoustic neural networks. These are networks that learn from sensor data, while being constrained by prior knowledge on acoustic and wave physics. The prior knowledge is constrained as a soft constraint, which informs the training, and as a hard constraint (Galerkin neural networks), which constrains parts of the network's architecture as an inductive bias. First, we show that standard feedforward neural networks are unable to extrapolate in time, even in the simplest case of periodic oscillations. This motivates the constraints on the prior knowledge. Second, we constrain the prior knowledge on acoustics in increasingly effective ways by (i) employing periodic activations (periodically activated neural networks), (ii) informing the training of the networks with a penalty term that favors solutions that fulfill the governing equations (soft constrained), (iii) constraining the architecture in a physically motivated solution space (hard constrained), and (iv) a combination of these. Third, we apply the networks on two test cases for two tasks in nonlinear regimes, from periodic to chaotic oscillations. The first test case is a twin experiment, in which the data are produced by a prototypical time-delayed model. In the second test case, the data are generated by a higher-fidelity model with mean-flow effects and a kinematic model for the flame source. We find that (i) constraining the physics in the architecture improves interpolation while requiring smaller network sizes, (ii) extrapolation in time is achieved by periodic activations, and (iii) velocity can be reconstructed accurately from only pressure measurements with a combination of physics-based hard and soft constraints. In acoustics and thermoacoustics, this works opens possibilities for physics-constrained data-driven modeling. Beyond acoustics, this work opens strategies for constraining the physics in the architecture, rather than the training.

The microflow behavior of liquid-liquid dispersions is experimentally investigated in the presence of miscible fluid additives. Original microfluidic methods are developed to characterize the dynamic response of mobile droplets to a local change of interfacial tension with the external phase using sequential injections and stratified flows. Various oil-alcohol combinations are examined to unravel out-of-equilibrium fluid interactions at short timescales and clarify the role of flow rates and fluid properties on individual droplet deformations. Functional relationships are developed to characterize the initial droplet strain as well as rates of elongation during immersion and submersion stages in hydrodynamic focusing junctions. It is shown, in particular, that the droplet deformation process is highly nonlinear with the initial droplet size and that droplet growth coefficients remain constant for fluid additives having ultralow interfacial tension. Overall, this study shows the possibility to manipulate the morphology of strongly elongated droplets to enhance oil interfacial area in miscible organic solvents using microchannels.

Internal waves are ubiquitous in the ocean and play an essential role in the transport of energy and mixing. Their peculiar reflection enables the concentration of energy on a limit cycle. With wave beams viewed as rays, this reflection on an inclined slope shrinks its width and generically brings closer two initially different trajectories eventually reaching a limit cycle called an attractor. Following previous studies, a ray-tracing algorithm is used to track the convergence of wave beams onto such a structure in a 3D axisymmetric domain. This information is used to design experiments using a truncated conical shaped tank in order to form an inertia-gravity waves attractor in a 3D axisymmetric geometry. By increasing the amplitude of the forcing, an evolution of the attractor characteristics can be observed. The occurrence of waves at frequencies lower than the forcing frequency ${\omega }_0$ suggests triadic resonant instability in a rotating or in a stratified case. Experiments performed in a stratification-only or a rotation-only case indicate two distinct behaviors. The existence of easily excited standing waves, resonant modes of the tank, at frequencies lower than the forcing one enables sharp triadic resonance instability for internal gravity waves, which is not possible for inertial waves. The effect of the symmetry axis is also investigated by adding a cylinder of sufficient diameter at the center of the domain for the wave to reflect on and thereby avoid the interaction on the singularity. Without it, the large amplitude of the waves on the axis triggers nonlinear effects and mixing, denying the access to the wave turbulence regime.

We propose a model to obtain the subgrid-scale velocity in the context of large-eddy simulation (LES) of particle-laden turbulent flows, to recover accurate particle statistics. In our wavelet enrichment model, the subgrid-scale velocity is discretized with a divergence-free wavelet vector basis, and the coefficients of the expansion are obtained by minimizing the squared error of the linearized subfilter Navier-Stokes equations (SFNSE). The compact support of the wavelet basis is exploited to achieve continuously varying subgrid-scale velocity statistics across the domain. The performance of our wavelet enrichment model is evaluated in single-phase and particle-laden flow simulations, comparing the results with the results of direct numerical simulations (DNS). The simulations show that the model can generate inhomogeneous and anisotropic velocity statistics, accurate strain-rotation relations, and a good approximation of the kinetic energy spectrum of the corresponding DNS. Furthermore, the model significantly improves the prediction of the particle-pair dispersion, the clustering of the particles, and the turbulence modulation by particles in two-way coupled simulations. The proposed model recovers the most important interactions between fluid turbulence and the behavior of the particles, while maintaining the computational cost on the order of an LES.

This study discusses the necessity of anisotropic subgrid-scale (SGS) stress in large-eddy simulations (LESs) of turbulent shear flows using a coarse grid resolution. We decompose the SGS stress into two parts to observe the role of SGS stress in turbulent shear flows in addition to the energy transfer between grid-scale (GS or resolved scale) and SGS. One is the isotropic eddy-viscosity term, which contributes to energy transfer, and the other is the residual anisotropic term, which is separated from the energy transfer. We investigate the budget equation for GS Reynolds stress in turbulent channel flows accompanied by the SGS stress decomposition. In addition, we examine the medium and coarse filter length cases; the conventional eddy-viscosity models can fairly predict the mean velocity profile for the medium filter case and fails for the coarse filter case. The budget for GS turbulent kinetic energy shows that the anisotropic SGS stress has a negligible contribution to energy transfer. In contrast, the anisotropic stress has a large and nondissipative contribution to the streamwise and spanwise components of GS Reynolds stress when the filter size is large. Even for the medium-size filter case, the anisotropic stress contributes positively to the budget for the spanwise GS Reynolds stress. Spectral analysis of the budget reveals that the positive contribution is prominent at a scale consistent with the spacing of streaks in the near-wall region. Therefore, we infer that anisotropic stress contributes to the generation mechanism of coherent structures. Predicting the positive contribution of the anisotropic stress to the budget is key to further improving SGS models.