Representing the glaciation of mixed-phase clouds in terms of the Wegener–Bergeron–Findeisen process is a challenge for many weather and climate models, which tend to overestimate this process because cloud dynamics and microphysics are not accurately represented. As turbulence is essential for the transport of water vapor from evaporating liquid droplets to ice crystals, we developed a statistical model using established closures to assess the role of small-scale turbulence. The model successfully captures results of direct numerical simulations and we use it to assess the role of small-scale turbulence. We find that small-scale turbulence broadens the droplet-size distribution somewhat, but it does not significantly affect the glaciation time on submeter scales. However, our analysis indicates that turbulence on larger spatial scales is likely to affect ice growth. While the model must be amended to describe larger scales, the present work facilitates a path forward to understanding the role of turbulence in the Wegener–Bergeron–Findeisen process.

Buoyant or dense plumes form in porous media during various environmental applications such as groundwater contamination and subsurface carbon storage. In this study, we investigate the spatiotemporal evolution of dense plumes in porous media as a function of permeability, injection rate, and density difference between the injected and ambient fluids. A series of laboratory experiments are conducted using light attenuation technique, focusing particularly on the evolution of plume length and volume, which in turn accounts for the mixing between the plume and the ambient. Based on the measurement of the aspect ratio of the plumes, we quantify transition time that separates a fully developed late plume from an early developing plume. Further, we propose semiempirical correlations for plume length and volume, which exhibit power-law behavior on time in both the early and late time regimes. The exponents defining the plume growth rate that we obtain here are less than the values presented by several analytical and computational models in the literature, e.g., for the convective dissolution that occurs during an underground carbon sequestration process.

Recent experiments of active particles encapsulated in various soft matter materialize their exciting potential for biomedical applications such as drug delivery. They also provide a means to validate theoretical models proposed in the last decade. The active particles in these experiments can be classified as field-driven or self-propelled. Given these options, it is natural to ponder which of these types is most appropriate for drug delivery. The answer will surely depend on design specification and existing clinical practices. However, one consideration, and the focus of this study, is the energy expenditure of these potential delivery systems. This paper uses Lighthill's swimming efficiency (the ratio of power dissipation generated by a towed rigid particle to the power dissipation generated by a self-propelled swimmer) to differentiate between active particles. As a first approximation, we consider the configuration of a spherical squirmer enclosed in a nondeforming spherical droplet. Letting the squirmer-droplet system move through homogeneous fluids and porous media, we derive exact analytical expressions for the power dissipation of the confined squirmer. To obtain the swimming efficiency of the confined squirmer, we also derive analytical formulas for the drag force on a rigid sphere that is towed at the same speed as the squirmer. Our findings reveal lower energy expenditure for field-driven active particles when the bulk fluid is homogeneous. However, in porous media, the swimming efficiency shows a strong dependence on the droplet to particle size ratio. We also consider a different squirming mechanism (torque driven), and find that it does not influence the squirmer's swimming efficiency. We conclude our analysis with a discussion of the limitations of our approach to differentiate between active particles, and expand on relevant future research directions.

We present a laboratory experiment to model convection in the atmosphere driven by latent heat of condensation (“moist convection”). The system consists of a tank filled with an aqueous solution containing a color indicator that renders the fluid yellow and transparent when acidic and blue and opaque when basic. A sodium lamp positioned above the tank serves as a heat source. Initially, the solution is entirely acidic and stably stratified in temperature. A basic layer is progressively generated at the tank's bottom through water electrolysis, forming an initially stable, blue region. This layer is internally heated by absorbing the heat from the sodium lamp, modeling the latent heat of condensation in the atmosphere. Over time, instabilities develop at the interface between the yellow and blue layers. We investigate the variation of the instability wavelength and complement our observations with a linear stability analysis to elucidate the underlying mechanisms and the process of wavelength selection. Direct numerical simulations are then employed to explore the first steps of the nonlinear regime in connection with experimental observations.

In the context of turbulent dispersal of aerosol pollutants from a source within a ventilated indoor space, the present work addresses the importance of going beyond accurate prediction of the mean ensemble-averaged exposure, by evaluating the expected level of variability in individual realizations. This uncertainty quantification requires a statistical description of the inherent stochastic turbulent dispersal process and the inhomogeneous nature of the indoor flow. We leverage large datasets from turbulence-resolving Euler-Lagrange simulations of aerosol dispersal in varying indoor geometries. The datasets provide time-resolved concentrations of pollutants emitted by a source located anywhere in a room and reaching a sink (susceptible individual) that may be located anywhere else in the same room. The statistical information is used to accurately predict the mean pollutant concentration as a function of source-sink separation distance and associated variability in two different experimental measurements to demonstrate the importance of estimating the uncertainty associated with the predicted average concentration. The average pollutant concentration results are compared with the predictions of three other commonly used models (well-mixed model, near-field/far-field model, and eddy diffusivity model).

We conduct direct numerical simulations of developed turbulence in a periodic cube to investigate the formation mechanism of the power spectral density of the Lagrangian velocity. We compare the power spectral density of the Lagrangian velocity of turbulent flows with different forcing methods and Reynolds numbers. This systematic comparison demonstrates that universal behavior is observed in a narrow high-frequency regime, whereas nonuniversality originating from the forcing method broadly appears in a low-frequency regime. To reveal the formation mechanism of the spectra in terms of the hierarchy of coherent structures in turbulence, we propose a scale-decomposition method for the Lagrangian velocity, which enables us to evaluate the contribution of vortices at different scales. This scale-decomposition analysis directly demonstrates that the largest-scale flows driven by the external force can contaminate the Kolmogorov scaling of the Lagrangian velocity spectra formed by small-scale vortices in the inertial range, thus leading to the narrow Lagrangian inertial range. Furthermore, we provide evidence that this remarkable effect by the largest-scale flows is specific to the Lagrange velocity by demonstrating that the power spectral density of the Eulerian velocity is less sensitive to the forcing method.

We study numerically the dynamical evolution of two different vorticity arrays with an initially uniform magnetic field in two-dimensional incompressible magnetohydrodynamics. We concentrate particularly on the role of the strength of the background magnetic field, which is always assumed weak in the sense that its energy is much less than the kinetic energy of the vortical flows. Within the context of a weak background field, we are able to identify four distinct regimes. When the field is so weak that the back-reaction of the Lorentz force can be ignored (the kinematic regime), classical flux expulsion occurs. As the field strength is increased, the first signs of the dynamical influence of the small-scale field generated is in the disruption of vortex filaments, with flux expulsion still occurring in the vortex cores. A further increase in field strength leads to the regime of vortex disruption, in which the magnetic field is expelled, but is then of sufficient strength to disrupt or destroy the vortices. For yet stronger fields, even the large-scale field can be sufficiently strong to be dynamically active; flux expulsion is then prevented, and the field is dynamically active throughout the evolution. Furthermore, in the case of a row of vortices, we show that the orientation of the background field significantly influences the evolution, especially at higher field strengths.

A bottom Ekman layer is defined by a dynamic balance between the Coriolis force, pressure gradient force, and turbulent transport. We investigate how this balance is modified by bottom topography by analyzing Large Eddy Simulations of separating flow over a two-dimensional ridge. The focus is on two cases that include rotation: one where the exterior flow is driven across the ridge (Cross-Hill with Rotation: “CHR”), and another where the flow is driven along the ridge axis (Along-Hill with Rotation: “AHR”). In both cases, the bottom portion of the boundary layer is dominated by topographic disturbances, including a speedup over the hill and a recirculation in the wake. While these near-bottom modifications are rooted in nonrotating flow dynamics (evidenced in nonrotating simulations presented here), they are impacted by the Coriolis force, leading to a wake jet in the along-ridge flow component of CHR and a wake deficit in the along-ridge component of AHR. These features drive magnifications in the ageostrophic transport that cannot be predicted by the bottom stress. Analysis of the transport budget suggests the wake dynamics are sensitive to the strength of the horizontal divergence of the Reynold's stresses, being stronger in CHR than in AHR. This leads to a large nonlocal influence in CHR, where averaging the ageostrophic transport over a distance that is 3 times the hill's total length leads to a more than $30\%$ increase in magnitude when compared to the flat case. Averaging over the same distance in AHR shows negligible differences to the bulk transport relative to the flat case, as the wake is more confined to the topography vicinity. These results show that the influence of rotation on the speedup and recirculation play an essential role in facilitating topographically induced changes to the bulk transport, with an evident dependence on the strength of flow separation.

The goal of this paper is to propose a theoretical framework to study homogeneous and isotropic turbulence in a viscoelastic fluid, regarded as a perturbation of a Newtonian incompressible fluid, where the fluid relaxation time, or else the Weissenberg number, plays the role of small parameter. We use a Martin-Siggia-Rose framework to obtain a formal expression for the velocity correlation function of the non-Newtonian flow, and we expand this formal expression to linear order in the relaxation time. The coefficients in this expansion are correlation functions of the base Newtonian flow. We do not derive these correlations, instead we replace them by their values according to K41 theory, which could be regarded as an extreme form of renormalization. While substantial work will be necessary to validate the model against numerical and experimental data, preliminary results are encouraging.

We study a two-dimensional isotropic rotating system and obtain both theoretically and numerically a $K^{-2}$ energy spectrum under the rapidly rotating condition ($\text{Ro}\ll 1$), which was initially obtained by Zeman [Phys. Fluids 6, 3221 (1994)] and Zhou [Phys. Fluids 7, 2092 (1995)]. In rotating turbulence, the $K^{-2}$ energy spectrum was proposed under the assumption of isotropy; however, the direction selectivity of rotation breaks isotropy, making this $K^{-2}$ spectrum not easily observable. To fill the gap between theoretical assumptions and realizability, we study the turbulence of inertial waves in an artificial two-dimensional isotropic rotating turbulence system. In the limit of a small Rossby number, we asymptotically derive a nonlinear amplitude equation for inertial waves, which gives the $K^{-2}$ spectrum using a strong turbulence argument. This scaling is justified by numerical simulations of both the amplitude equation and the original system.

This study presents a theoretical model for gravity wave attenuation in a multilayered fluid system comprising fluidized mud, water, an interfacial fluid layer (typically enriched with surface-active compounds including oil), and air, which closely mimics the atmosphere-ocean configuration. A rigorous mathematical analysis initiated from the boundary value problem yields the dispersion relation, which is then solved numerically to obtain the complex-valued wave number, whose imaginary part is the spatial attenuation rate. Parametric studies are conducted to investigate how the attenuation rate responds to changes in wave frequencies, fluid and interfacial properties, and layer depths. Results obtained are compared with published experimental data in select cases, showing good agreement. In addition, the model is applied to reduced systems by setting the densities or depths of select layers to zero. For a water-mud system, maximum attenuation rates occur when the mud layer's depth is comparable to the wavelength and exceeds the boundary layer thickness by 100%–200%. Similarly, in an oil-water-mud system, maximum attenuation rates are obtained when the mud layer's depth exceeds the boundary layer thickness by 10%. Further analysis highlights the significance of air dynamics through the ratio, $\alpha$, defined as the attenuation rate in an air-oil-water-mud system relative to that in a corresponding vacuum-oil-water-mud system. Results reveal that $\alpha \gg 1$ for low-frequency waves in deep water systems, with values reaching up to ${10}^3$ in specific cases. Such high values underscore the critical role of air dynamics in predicting attenuation rates accurately. Moreover, in an air-oil-water-mud system, the maximum value of $\alpha$ and the corresponding frequency at which it occurs exhibit power-law dependencies on water layer depth ($d_2$), scaling as $d_2^{2/3}$ and $d_2^{-1/2}$, respectively. It is inferred that maximum attenuation rates are linked to strong velocity gradients in the fluid layers; they may also be understood by analyzing variations in the group velocity and the penetration depth, which is related to the rotational part of the velocity field.

The microhydrodynamics of particle suspensions in polymeric fluids has a wide range of applications in industry and biology. To discern the dynamics of particles in such systems, it is important to analyze the stress response of the suspension to applied flow fields. While such investigations have been theoretically done for suspensions of rigid spheres in weakly viscoelastic fluids, the effect of nonsphericity of particles on the stress remains relatively unexplored. The interplay between the response of the polymeric fluid and the particle orientation yields rich physics. The viscoelastic torques make the particle inhabit a preferred orientation in a given flow, resulting in time-dependent stresses. In this paper, we determine the average extra stress in a dilute suspension of rigid, non-Brownian spheroids in a second-order fluid subject to shear and extensional flows. We perform this task by examining the flow around a single spheroid in the limit of small Weissenberg number ($\text{Wi}\ll 1$) and perform an ensemble average of the stress tensor over all particle configurations. There are two contributions to the extra stress: one from the force dipole on the particles (stresslet) and another from the fluctuations in the velocity in the bulk fluid (fluid-induced particle stress), the latter of which does not arise in a zero Reynolds number Newtonian fluid. We present results for the $O\left(\varphi \text{Wi}\right)$ corrections to the long-time effective shear viscosity, normal stress coefficients, and extensional viscosities in the suspension in shear, uniaxial extensional, and planar extensional flows, where $\varphi$ is the particle volume fraction. To elucidate the effect of particle shape on the effective viscosity, we repeat this analysis for different aspect ratios ($A_R$) for prolate (needlelike) and oblate (disklike) spheroids.

In this study, we numerically investigate the impact of droplets on elastic plates using a two-phase lattice Boltzmann method, with a particular focus on how vertical surface movements influence the spreading and retraction dynamics of the droplet. The results show that, during the spreading phase, the spreading diameter is smaller on elastic surfaces compared to rigid ones due to the vertical velocity of the surface. A universal linear evolution of the drop spreading is derived for the early stage across both rigid and elastic substrates, accounting for the surface motion by rescaling time, and this relationship is in good agreement with the numerical results. In the retraction phase, unlike the nearly constant retraction speed observed on rigid surfaces, the retraction speed $V_{\mathrm{ret}}$ oscillates with the vibrations of the elastic surface, with the oscillation period remaining relatively consistent. Further analysis reveals that the variation in $V_{\mathrm{ret}}$ is not influenced by the surface's velocity but rather by its acceleration, as additional inertia is introduced during surface acceleration. Based on this understanding, a predictive model for $V_{\mathrm{ret}}$ during droplet impacts on moving surfaces is proposed, which demonstrates strong agreement with the numerical findings.

Is ice always covered by a thin layer of water? This question has been discussed for over 150 years. Here we show that the apparent contact angle of a droplet of water on ice increases steeply with decreasing ice temperature, from around 12 degrees near the melting point, to close to 160 degrees at $-{100}^{\circ }\mathrm{C}$. This indicates that ice is never completely wetted. We quantitatively model the temperature dependence of the apparent contact angle by assuming the droplet's contact line gets pinned due to the crystallization of a thin layer of ice on the cold surface. However close to the melting temperature, where the formation of the ice layer is slowest, surface energy considerations need to be included to explain the nonzero contact angle observed in experiments.

Previous studies on peristalsis, the pumping of fluid along a channel by wavelike displacements of the channel walls, have shown that the elastic properties of the channel and the peristaltic wave shape can influence the flow rate. We model a prescribed wave motion of a single boundary which pumps fluid at small Reynolds number near an elastic half space. We investigate the relationship between flow rate and elastic deformation, considering transverse and longitudinal motion of the driving peristaltic wave. The phase of the periodic solid deformation is found to depend on peristalsis being driven transversely or longitudinally. It is concluded that softness of the elastic material always reduces the net flow rate for transversely driven flows but can increase flow rate for longitudinally driven flows when in narrow confinement. In an applied example, we use measured values of cerebrospinal fluid flow parameters with our model and find agreement with in vivo velocity data, suggesting that the mechanism of perivascular pumping is a plausible driver of cerebrospinal fluid flow in the brain.

Understanding the dynamics of the turbulent velocity gradient tensor (VGT) is essential to gain insights into the Navier-Stokes equations and improve small-scale turbulence modeling. However, characterizing the VGT dynamics conditional on all its relevant invariants in a continuous fashion is extremely difficult. Hence, in this paper, we represent the Lagrangian dynamics using a network where each node represents a unique flow state in the space of the invariants of the VGT. The sign and relative magnitude ranking of the invariants resulting from a Schur decomposition of the VGT determines the discrete flow state vector. Our analysis reveals intriguing features of the resulting network dynamics, such as a grouping of the influential nodes where the eigenvalues of the VGT are real, in the proximity of the right Vieillefosse tail. We relate our complex network approach to the well-established VGT discretization based on the sign of its principal invariants, $Q$ and $R$, and its discriminant, $\mathrm{\Delta }$ into six regions representing very different physical and topological states. We study the shortest paths on the network based on the six regions to which their starting and ending nodes belong. This analysis shows that the typically clockwise path on the $Q\text{−}R$ diagram arises in a varying manner: sometimes region transitions are based on multiple pathways of more equal probability, while others are focused on specific nodes that are pivotal in these interregion dynamics. Comparisons to an enhanced Gaussian closure model show that the model captures the out-degree distribution for the nodes well. However, it uses a greater number of nodes to transition from real to complex eigenvalues and is far less efficient at generating clockwise motions that are counter to the restricted Euler dynamics.

Low Reynolds number flight frequently involves aggressive maneuvers or rotating wings at a high angle of attack. In these conditions a leading-edge vortex (LEV) forms, augmenting the force produced by the wing. To better understand how the LEV grows during its initial formation and to be able to compare across different conditions, it is important to have a normalization method that is grounded in the governing equations for vorticity. The result of an integral analysis of the vorticity equation for a general unsteady motion is a linear relationship between normalized circulation, $\frac{\mathrm{\Gamma }}{u\left(t\right)c}$, and the number of chord lengths traveled. To determine the validity of this analysis, planar particle image velocimetry measurements of the flow on three different wing motions were analyzed. Surging wing data from prior work, an impulsively started rotating wing, and a pitching wing were the three cases used in this study. For all of these cases, the relationship derived in the integral analysis accurately described how the normalized circulation grows with the number of chords traveled for a period from 0.01 to at least 1.6 chords traveled, with a modification to the distance traveled normalization for pitching wings to include the effect of angle of attack.

Recently, new models of the boundary condition for the Boltzmann equation were proposed on the basis of a kinetic model of gas-surface interactions [K. Aoki et al., Phys. Rev. E 106, 035306 (2022)]. In the present paper, the kernel representations of the models are given, and the models are applied to some basic problems of a rarefied gas between two parallel plates. To be more specific, the heat transfer between the plates with different temperatures, plane Couette flow, and plane Poiseuille flow driven by an external force are numerically investigated by using the Bhatnagar-Gross-Krook model of the Boltzmann equation and the new models of the boundary condition. The results are compared with those based on the conventional Maxwell-type boundary condition. It is shown that when the interaction of gas and solid molecules is strong, the results based on the new models tend to approach those based on the diffuse reflection. However, when the interaction is not strong, the former results deviate from those based on the Maxwell-type condition with a constant accommodation coefficient.

The identification of cells and particles based on their transport properties in microfluidic devices is crucial for numerous applications in biology and medicine. Neutrally buoyant particles transported in microfluidic channels migrate laterally toward stable locations due to inertial effects. However, the effect of the particle and flow properties on these focusing positions remain largely unknown. We conduct large scale simulations with dissipative particle dynamics, demonstrating that freely moving particles exhibit significant differences in their focusing patterns from particles that are prevented from rotation. In circular pipes, we observe drastic changes in rotating versus nonrotating focusing positions. We demonstrate that rotation-induced lateral lift force is significant, unlike previously believed, and is linearly dependent on the rotation magnitude. A simple phenomenological explanation extending existing theories is presented, that agrees well with our numerical findings. In square ducts, we report four face-centered stable positions for rotating particles, in accordance with experimental studies on a range of Reynolds numbers $50\le \text{Re}\le 200$. However, nonrotating particles stay scattered on a concentric one-dimensional annulus, revealing qualitatively different behavior with respect to the free ones. Our findings suggest new designs for microparticle and cell sorting in inertia-based microfluidics devices.

The levitating Leidenfrost (LF) state of a droplet on a heated substrate is often accompanied by fascinating behaviors such as star-shaped deformations, self-propulsion, bouncing, and trampolining. Here, we report on the intermittent trampolining events at specific drop sizes over the entire lifespan of an evaporating LF droplet. Between the trampolining events, the droplet exhibits decreased amplitude bouncing or quiescent hovering. We show that the reemergence of trampolining behavior of the droplet at specific radii is triggered by parametric resonance between the intervening vapor layer oscillation and the droplet, where the oscillations in the droplet subharmonically excite increased amplitude oscillations in the vapor. The trampolining events are observed when the ratio of the natural frequency of the vapor layer and Rayleigh frequency corresponds to the instability zones on the corresponding Mathieu's chart. This model even explains the observation of trampolining from a quiescent hovering state of the droplet. The proposed mechanism of resonance-driven trampolining of LF droplets is observed to be applicable for different liquids irrespective of the initial volume and substrate temperatures, thus indicating a universality of the behavior.