A number of approximations have been proposed to estimate basic hydrodynamic quantities, in particular, the frequency of a limit cycle. One of these, real zero imaginary frequency (RZIF), calls for linearizing the governing equations about the mean flow and estimating the frequency as the imaginary part of the leading eigenvalue. A further reduction, the self-consistent model (SCM), approximates the mean flow as well, as resulting only from the nonlinear interaction of the leading eigenmode with itself. Both RZIF and SCM have proven dramatically successful for the archetypal case of the wake of a circular cylinder. Here, the SCM is applied to thermosolutal convection, for which a supercritical Hopf bifurcation gives rise to branches of standing waves and traveling waves. The SCM is solved by means of a full Newton method coupling the approximate mean flow and leading eigenmode. Although the RZIF property is verified for the traveling waves, the SCM reproduces the nonlinear frequency only very near the onset of the bifurcation and for another isolated parameter value. Thus, the nonlinear interaction arising from the leading mode is insufficient to reproduce the nonlinear mean field and frequency.

Particle-laden pipe flows exhibit a gradual laminar-turbulent transition, beyond a critical volume fraction ($\varphi$). While classical transition behavior is characterized by the presence of turbulent puffs, this intermittent nature is absent for particle-induced transition. For small pipe-to-particle diameter ratios ($D/d$) even dilute systems exhibit this particle-induced transition behavior. In this study we use neutrally buoyant particles with a $D/d$ of 5.7, which represents a “sweet spot,” allowing the use of particle image velocimetry to study this particular phenomenon. The average velocity profile gradually changes from a parabola (laminar flow) to a blunted velocity profile for increasing Reynolds number. The instantaneous velocity profiles fluctuate around this profile. These velocity fluctuations, described by $u_x-rms$ and $u_r-rms$, gradually increase for increasing Reynolds number, as do the Reynolds stresses. For low ${\text{Re}}_s$, the velocity fluctuations increase proportional to the bulk velocity, which can be explained by a simple model based on the finite size of the particles. The velocity fields show the presence of elongated streamwise structures. The largest length scales are found in the transition region, where average integral length scales up to $5D$ are found. The structures decrease in length when the flow has fully transitioned to a turbulent state.

Streaks in the buffer layer of wall-bounded turbulence are tracked in time to study their life cycle. Spatially and temporally resolved direct numerical simulation data are used to analyze the strong wall-parallel movements conditioned to low-speed streamwise flow. The analysis of the streaks shows that there is a clear distinction between wall-attached and detached streaks, and that the wall-attached streaks can be further categorized into streaks that are contained in the buffer layer and the ones that reach the outer region. The results reveal that streaks are born in the buffer layer, coalescing with each other to create larger streaks that are still attached to the wall. Once the streak becomes large enough, it starts to meander due to the large streamwise-to-wall-normal aspect ratio, and consequently the elongation in the streamwise direction, which makes it more difficult for the streak to be oriented strictly in the streamwise direction. While the continuous interaction of the streaks allows the superstructure to span extremely long temporal and length scales, individual streak components are relatively small and short-lived. Tall-attached streaks eventually split into wall-attached and wall-detached components. These wall-detached streaks have a strong wall-normal velocity away from the wall, similar to ejections or bursts observed in the literature. Conditionally averaging the flow fields to these split events show that the detached streak has not only a larger wall-normal velocity compared to the wall-attached counterpart, it also has a larger (less negative) streamwise velocity, similar to the velocity field at the tip of a vortex cluster.

The accurate measurement of flows and aerodynamic characteristics around a bluff body has been a challenging task due to the existence of interference between the wake and mechanical model supports in wind-tunnel experiments. The present study focuses on a freestream-aligned circular cylinder with an extremely low fineness ratio (the ratio of the axial length to diameter) ranging from 0.30 to 0.50, which has never been investigated without interference from a mechanical model support. We employed a magnetic suspension and balance system to eliminate interference from the model support and measured the drag and velocity fields in the diameter-based Reynolds number between $2.0\times {10}^4$ and $7.7\times {10}^4$. As the fineness ratio decreases below 1.50, the size of the recirculation bubble increases and the velocity distribution on the central axis inside the bubble gradually converges to that of the circular disk. Furthermore, large-eddy simulations were performed in the Reynolds number of $4.0\times {10}^4$, whose drag coefficient agrees well with experiments. Based on those results, it was found that the drag coefficient monotonically converges to that of the circular disk without local maximum. This study revealed that in the low-fineness-ratio regime (0.10–0.50), a critical geometry, at which the drag coefficient shows a local maximum, does not exist in the circular cylinder. Subsequently, unsteady flow analyses were performed, where two characteristic frequencies, i.e., $\mathrm{St}=0.05$ and 0.155, were identified from power spectral densities of the drag coefficient and the pitching moment coefficient. The associated flow structures are then extracted by a phase-averaging procedure, where the phase-averaged flows with $\mathrm{St}=0.05$ represent the recirculation bubble pumping while the phase-averaged flows with $\mathrm{St}=0.155$ show nonaxisymmetric structures inside the recirculation bubble.

A tropical cyclone (TC) over ocean functions as a heat engine fueled by ocean moisture. By contrast, its decay past landfall is thought to be akin to a dry vortex spinning-down due to friction with the land, an intrinsically nonthermodynamic process. We study the evolution of TCs past landfall using computational simulations where we explicitly account for thermodynamics. Doing so allows us to uncover that past landfall the TC's dynamical heart—the warm core—does not simply wither away. Instead, thermodynamic processes modulated by the moisture stored in the TC invariably engender a cold core that grows underneath and at the expense of the warm core. Our findings underscore the key role of moist thermodynamics in the postlandfall evolution of TCs. Additionally, they have direct implications on the prevailing weather forecasting methods which invoke the birth of a cold core as a telltale signature of an extratropical transition.

The ambient conditions surrounding liquid droplets determine their growth or shrinkage. However, the precise fate of a liquid droplet expelled from a respiratory puff as dictated by its surroundings and the puff itself has not yet been fully quantified. From the view of airborne disease transmission, such as SARS-CoV-2, knowledge of such dependencies is critical. Here, we employ direct numerical simulations (DNS) of a turbulent respiratory vapor puff and account for the mass and temperature exchange with respiratory droplets and aerosols. In particular, we investigate how droplets respond to different ambient temperatures and relative humidity ($\mathrm{RH}$) by tracking their Lagrangian statistics. We reveal and quantify that in cold and humid environments, as there the respiratory puff is supersaturated, expelled droplets can first experience significant growth, and only later followed by shrinkage, in contrast to the monotonic shrinkage of droplets as expected from the classical view by Wells in 1934. Indeed, cold and humid environments diminish the ability of air to hold water vapor, thus causing the respiratory vapor puff to supersaturate. Consequently, the supersaturated vapor field drives the growth of droplets that are caught and transported within the humid puff. To analytically predict the likelihood for droplet growth, we propose a model for the axial RH based on the assumption of a quasistationary jet. Our model correctly predicts supersaturated RH conditions and is in good quantitative agreement with our DNS. Our results culminate in a temperature-RH map that can be employed as an indicator for droplet growth or shrinkage.

Microscopic organisms must frequently swim through complex biofluids, including bacterial biofilms and the mucus lining of the upper respiratory tract. Recently, there has been great interest in understanding how the non-Newtonian behavior of the fluids, in particular fluid elasticity, can enable methods of self-propulsion that otherwise would not work in a Newtonian fluid. We present such a swimmer that consists of two spheres of unequal size that rotate in opposite directions. The swimmer is force- and torque-free and placed in an elastic fluid. Using a combination of analytical theory and numerical simulations, we show that this model swimmer, which has zero propulsion in a Newtonian fluid under Stokes flow, swims in the direction of the larger of the two spheres in an elastic fluid. We show that the speed of swimming increases nearly linearly with the Deborah number De or primary normal stress coefficient ${\mathrm{\Psi }}_1$, which is an appropriate measure of the elasticity of the fluid and for $\text{De}\le 1$ is also nearly linear in the concentration of polymer in the fluid. The dependence of the swim speed on the relative size of the two spheres is nonmonotonic, exhibiting a maximum at a size ratio of about 0.75. By analyzing the forces acting on the swimmer and the surrounding flow field, we find that propulsion is driven by thrust due to pressure applied along the swimmer. This thrust originates from flow advection driven by hoop stresses surrounding the faster-spinning smaller sphere. We compare our predictions to experimental measurements of swimming speeds for the bacterium E. coli, which swims via a rotating flagellar bundle and counterrotating body, and find that the speeds predicted by our analysis are remarkably close to the speed increase E. coli experiences in viscoelastic fluids. Finally, we conclude our work by showing how our analysis can be extended to different swimmer configurations and gaits, as long as the propulsion is driven by swirl alone.

Turbulent signals are intermittent with large instantaneous fluctuations. Such large fluctuations lead to small Kolmogorov scales that are hard to resolve in numerical simulations [P. K. Yeung, K. R. Sreenivasan, and S. B. Pope, Effects of finite spatial and temporal resolution in direct numerical simulations of incompressible isotropic turbulence, Phys. Rev. Fluids 3, 064603 (2018)]. The present paper follows the above basic logic, but instead of dissipation events in isotropic turbulence, we study wall-shear stress events in plane channel flow. Wall-shear stress fluctuations are increasingly more intermittent as the Reynolds number increases. Hence, one has to employ higher grid resolutions as the Reynolds number increases in order to resolve a given percentage of wall-shear stress events. The objective of this paper is to quantify effects of the grid resolutions on the rare and high intensity wall-shear stress events. We find that the standard grid resolution resolves about 99% of the wall-shear stress events at ${\text{Re}}_{\tau }=180$. A slightly higher grid resolution has to be employed in order to resolve 99% of the wall-shear stress events at higher Reynolds numbers, and if the standard grid resolution is used for, e.g., a ${\text{Re}}_{\tau }=10000$ channel flow, one resolves about 90%–95% wall-shear stress events.

A free surface, placed in a strong viscous flow (such that viscous forces overwhelm surface tension), often develops ends with very sharp tips. In Courrech du Pont and Eggers [Proc. Natl. Acad. U. S. A. 117, 32238 (2020)] we have shown that the axisymmetric shape of the ends, nondimensionalized by the tip curvature, is governed by a universal similarity solution. The shape of the similarity solution is close to a cone, but whose slope varies with the square root of the logarithmic distance from the tip. Here we develop the calculation of the tip similarity solution to next order, using which we demonstrate matching to previous slender-body analyses, which fail near the tip. This allows us to resolve the long-standing problem, first raised by G. I. Taylor, of finding the global solution of a bubble in a strong hyperbolic flow. We also calculate the tip curvature quantitatively, beyond the scaling behavior of the leading-order solution. Our results are shown to agree in detail with full numerical simulations of the Stokes equation.

Particle-resolved direct numerical simulations of monodisperse settling suspensions of cubes and spheres are performed for Galileo numbers $\text{Ga}=70$ and $\text{Ga}=160$, and solid volume fractions in the range $0.01⩽\varphi ⩽0.2$. The solid-to-fluid density ratio $m={\rho }_s/{\rho }_f$ is taken to be fixed at 2, representing liquid-solid suspensions. Strong columnar clustering is observed for $\text{Ga}=160$ and $\varphi =0.01$ in a sphere suspension, whereas similar vertical structures are not present as prominently in a cube suspension. We find that in all cases, cube suspensions tend to be more homogeneous compared to sphere suspensions, as indicated by both their microstructure and momentum transfer properties. The enhanced homogeneity is associated with the pronounced angular velocities of cubes and the resulting orientation- and rotation-induced lift forces, which promote transverse motions and the likelihood of escaping from clusters. Higher rotation rates of cubes thus play a major role in the transfer of momentum from the gravity to the transverse direction, demonstrated by the lower anisotropy of particle velocity fluctuations in cube suspensions. In more dilute cases, cubes induce significantly stronger pseudoturbulence in the flow, especially in the transverse direction. The drag of dynamic cube suspensions is found to be generally similar to static beds of cubes, the reason for which is speculated to be relevant to their motion freedom and the more homogeneous microstructure.

Air film stability underneath a drop is crucial for drop contact dynamics upon impact. An unstable film leads to the drop contacting the surface and subsequent spreading or splashing. Apart from previously reported film and kink contact modes, here we present the experimental evidence for a dimple failure mode of an air film, driven by a thin film instability when a drop impacts onto an atomically smooth surface. The dimple failure occurs beyond the inertial-capillary timescale and is initiated when the dimple inverts at the drop's central axis. For the same impact Weber number, the dimple failure observed in low-viscosity drops is absent at a higher viscosity, due to damping of capillary waves.

Flow and transport in coupled channel-matrix systems are ubiquitous to many environmental and engineering applications such as flows in fractured porous media over canopies and in membrane filtration units. The multiscale nature of such systems, where the horizontal length scale is often orders of magnitude larger than the vertical one, allows one to employ vertically averaged descriptions of the system. As a result, two-dimensional transport in the channel and the matrix can be upscaled to a coupled system of transient one-dimensional advection-dispersion equations, where matrix and channel properties can be analytically related to macroscopic transport observables. In this work, we first develop a semianalytical solution based on integral transforms that can be employed to predict macroscopic transport in channel-matrix shear flows in a computationally efficient manner. Then we demonstrate that under appropriate dynamic conditions, the coupled system at the macroscale can be further simplified to a single upscaled one-dimensional advection-dispersion equation, which admits an analytical closed-form solution, thus enabling real-time macroscale concentration estimates in relevant applications.

Dispersions of bubbles with a compound interface in liquids are ubiquitous in nature and various industrial processes, such as marine oil transport and froth flotation, hence understanding surface phenomena effect on bubble formation in liquids remains as a canonical topic in fundamental multiphase flows. Here, we experimentally investigate the formation of an oil-coated bubble at submerged coaxial orifices in quiescent liquids. The air bubble is initially injected inside a confined oil domain and then exits into the surrounding water under buoyancy, forming an oil-coated bubble. Compared with the bubble formation in a single-phase liquid, the bubble size is significantly modified due to the presence of the oil phase. We develop a force balance model to predict the oil-coated bubble size, considering the orifice geometry as well as the compound air/oil/water interface, which agrees well with the experimental results. We further discuss the dependencies of the bubble size on the Bond number, size ratio of the coaxial orifices, and the interfacial tension ratio of oil-water and oil-air interfaces. Our study could contribute to further understandings on the dynamics of bubble formation with a compound interface.

Gamma ($\gamma$) instability theory, originally proposed in 2003, continues to provide the most promising explanation of salt-fingering engendered thermohaline staircases that are ubiquitously present in both the global ocean and lakes. Our purpose herein is to extend $\gamma$ instability theory to salt-fingering systems in which the vertical gradients of temperature and salinity are not constant. Our goal is to explain why the characteristic “step size” in a salt-fingering staircase is larger in regions characterized by weak gradients. Through application of an appropriately modified linear stability analysis, we first demonstrate that the most quickly growing mode of instability is unaltered by the inhomogeneity of the background stratification in most cases. We then perform numerical simulations based upon the mean field equations to show that staircases tend to form and thereafter merge much more quickly in the low gradient regions than the high gradient regions. After explaining this difference of timescale within the framework of our model, we argue that the differences in background gradients of physical properties may arise naturally in a quasiequilibrium staircase environment. We further invoke observations from the Tyrrhenian Sea to support a quasiequilibrium staircase hypothesis.

A liquid hanging from a liquid-filled tube can spread spontaneously on rough hydrophilic surfaces while it cannot on smooth hydrophilic surfaces, a difference resulting from the competition between the capillary suction pressures provided by the tube and by the surface roughness. In order to pattern liquids on solid surfaces utilizing such wetting characteristics, we investigate the dynamics of a spontaneous liquid spreading from a tube onto a nanostructured superhydrophilic microlane surrounded by a superhydrophobic background. We find distinct regimes of liquid film propagation dynamics to arise depending on the lane width and the liquid column height in the tube. We theoretically analyze the spreading rates of films, which change power laws in the course of spreading, and corroborate the theory with experiments. The spontaneous liquid patterning process reported in this work can provide a viable venue for such applications as electronic circuit printing and biochip fabrication.

This work reports an experimental investigation of a liquid-solid fluidized bed involving inertial particles at a large Reynolds number. Owing to optical techniques and index matching, the statistics of the velocity fluctuations of both the particles and the liquid are measured for a wide range of the particle volume fraction ${\alpha }_p$. The dynamics of the fluctuations suggests that the flow possesses the following three properties: (1) The liquid volume involves a wake region in which vertical fluctuations are negative and an interstitial region where they are positive. (2) The statistics of the horizontal fluctuations are similar to vertical ones, except that they are symmetric. (3) Local instant particle fluctuations are proportional to liquid ones. Assuming these properties are true allows us to derive a model for the probability density functions (PDFs) of the two components of the velocity fluctuations of the two phases. This model involves a single reference PDF that is independent of ${\alpha }_p$ and one weighting parameter for each phase. The weighting parameter of the liquid phase is an affine function of ${\alpha }_p$, which characterizes the volume of the wakes relative to that of the interstices. That of the particle phase depends on the preferential concentration of the particles, which tend to avoid the wakes at low ${\alpha }_p$. This model accurately describes the experimental PDFs up to the third-order moment and reproduces all their peculiar features: the skewness of the vertical fluctuations which reverses at a given volume fraction, the presence of exponential tails corresponding to rare intense events, and the symmetry between low and large volume fractions.

The force experienced by an object moving in a granular medium is a necessary input to describe locomotion problems in such a context. Towards this objective, resistive force theory (RFT) has been developed for granular flows inspired by previous developments in the case of viscous flows. In viscous fluids, a reciprocal motion does not lead to a net propulsion due to the kinematics reversibility of viscous flows that is included in the RFT. We show that, in a granular medium, a reciprocal motion allows for propulsion. We investigate the specific mechanisms underlying this propulsion and discuss how they differ from that of viscous flows. Understanding these phenomena permit both the accurate description of locomotion in sand and the refinement of the RFT for granular materials. These achievements provide opportunities towards the development of robots that are able to progress inside granular media and are suitable for controlling industrial processes.

Small conical-shaped jets may emanate from a liquid bath a short while after a small drop has hit a liquid pool. Here we perform Particle Image Velocimetry (PIV) measurements of the liquid flow inside upward jets after drop impact and show that fluid elements inside the jets may decelerate up to 5–20 times the gravitational acceleration. The measurements show that both the shape of the jet and the velocity profile are self-similar. A theoretical model including surface tension, fluid inertia and gravity correctly predicts the self-similar velocity profile and shape of the jet, allowing us to provide the first quantitative explanation of the shape and dynamics of the emanating jets.

Iceberg meltwater is a critical freshwater flux from the cryosphere to the oceans. Global climate simulations therefore require simple and accurate parametrizations of iceberg melting. Iceberg shape is an important but often neglected aspect of iceberg melting. Icebergs have an enormous range of shapes and sizes, and distinct processes dominate basal and side melting. We show how different iceberg aspect ratios and relative ambient water velocities affect melting using a combined experimental and numerical study. The experimental results show significant variations in melting between different iceberg faces, as well as within each iceberg face. These findings are reproduced and explained with multiphysics numerical simulations. At high relative ambient velocities melting is largest on the side facing the flow, and mixing during vortex generation causes local increases in basal melt rates of over 50%. Double-diffusive buoyancy effects become significant when the relative ambient velocity is low. Existing melting parametrizations do not reproduce our findings. We propose several corrections to capture the influence of aspect ratio on iceberg melting.

Red blood cells (RBCs)—erythrocytes—suspended in plasma tend to aggregate and form rouleaux. During aggregation the first stage consists in the formation of RBC doublets [S. M. Bertoluzzo, A. Bollini, M. Rasia, and A. Raynal, Blood Cells Mol. Dis. 25, 339 (1999)]. While aggregates are normally dissociated by moderate flow stresses, under some pathological conditions the aggregation becomes irreversible, which leads to high blood viscosity and vessel occlusion. We perform here two-dimensional (2D) simulations to study the doublet dynamics under shear flow in different conditions and its impact on rheology. A few illustrative results obtained here in 3D agree with 2D results. We sum up our results on the dynamics of doublet in a rich phase diagram in the parameter space (flow strength, adhesion energy) showing four different types of doublet configurations and dynamics. We find that membrane tank-treading plays an important role in doublet disaggregation, in agreement with experiments on RBCs. A remarkable feature found here is that when a single cell performs tumbling (by increasing vesicle internal viscosity) the doublet formed due to adhesion (even very weak) remains stable even under a very strong shear rate. It is seen in this regime that an increase of shear rate induces an adaptation of the doublet conformation allowing the aggregate to resist cell-cell detachment. We show that the normalized effective viscosity of doublet suspension increases significantly with the adhesion energy, a fact which should affect blood perfusion in microcirculation.