Damage produced by repeated bubble collapse to neighboring rigid objects in hydraulic systems is an important consequence of cavitation. Although bubble collapse near a single wall has received significant attention in the past, few studies exist on the dynamics of bubbles collapsing near a corner, i.e., two flat rigid surfaces intersecting at a right angle. In this work we quantify the pressure fields produced by a single bubble collapsing near two perpendicular rigid walls. Using a high-order accurate shock- and interface-capturing method to solve the three-dimensional compressible Navier-Stokes equations for gas and liquid flows, we simulate the dynamics of a single bubble collapsing at different initial stand-off distances from the two walls. In contrast to a bubble collapsing near a single wall, the collapse of bubbles within a critical stand-off distance is not symmetric about the bisecting plane due to the interaction between the bubble and the second wall. The second wall affects the pressure produced during the collapse in the following ways: (i) For bubbles initially located sufficiently close to both walls, the reentrant jet produced during collapse no longer points in the direction normal to the closest wall but at an angle toward the corner, (ii) the part of the emitted shock with the highest amplitude propagates in line with the jet, and (iii) the bubble migrates in that same direction during its collapse with a dependence on the stand-off distance, consistent with predictions made using Kelvin impulse. The location of maximum pressure along the walls is measured for the different initial stand-off distances. Using acoustic arguments, we find a semiempirical relationship to predict the initial stand-off distances for which the maximum pressure occurs in the corner. We find that when the bubble is sufficiently close to equidistant from each boundary, the maximum pressure is observed in the corner due to the water-hammer and implosion shocks reflecting off the boundaries and intersecting in the corner. We also show that when bubbles are initially attached to either wall the wall pressure produced can be significantly increased compared to bubbles detached from either wall.

The fall or rise of inertial particles plumes in an initially quiescent fluid is ubiquitous in natural and industrial processes. Disentangling the influence of the numerous parameters of these systems on the plume velocity is thus a major issue. Moreover, understanding the energy transfer between the two phases and the structure of induced flow is another very relevant question. A specific experiment has been designed to tackle these problems. A continuous plume of inertial particles released above the center of a still water tank generates a large-scale recirculation flow. The present experimental study investigates the stationary settling dynamics and induced flow properties using various particle populations with particle-to-fluid density ratios from $3.8\mathrm{to}14.3$, Archimedes numbers $4\mathrm{to}580$, and mass fractions ${10}^{-6}\mathrm{to}{10}^{-3}$, revealing an unexplored region of the parameter space. The fluid and particle velocities are measured simultaneously by two cameras, utilizing optical filtering and image postprocessing. It is found that the settling in the laboratory frame generally follows the terminal velocity predicted using the Schiller-Naumann drag. The particle velocity relative to the surrounding fluid is unaffected by the particle mass fraction and always hindered due to the kinetic energy transferred to the fluid. This transfer of energy is most effective for low Archimedes numbers. All modifications of the settling behavior due to the particle mass fraction are caused by the back-reaction of the induced flow on the particles; no direct particle-particle interactions are observed.

We report an experimental study on the enhancement of heat transfer efficiency in turbulent thermal convection via manipulation of the bulk flow, which is achieved by inserting artificial structures into the convection domain. These structures are designed to alter the bulk flow without perturbing the boundary layer. Two types of convective domains are designed and fabricated. The Type-I domain has an extruded square grid structure in the bulk and the Type-II domain can be viewed as a modification to the first one that devides the domain into parallel connected dual-channel structures. The working fluid is water at a Prandtl number of Pr = 4.3 and the Rayleigh number covers a range of $6.4\times {10}^7\le \text{Ra}\le 8.5\times {10}^9$. It is found that structuring the bulk flow can enhance the Nusselt number by a factor of up to 14% for the Type-I domain and by 30% for the Type-II domain, respectively. Local temperature and velocity field measurements reveal that the enhancement in Nusselt number results from both an increase in plume coherency and an enhanced flow strength. The later feature is in sharp contrast with the significantly reduced flow strength found in geometrical-confinement-induced heat transfer enhancement reported in previous studies. Our results thus shed new light on flow manipulation and inspire future research on the optimization of thermal control.

Most idealized studies of stratified shear instabilities assume that the shear interface and the buoyancy interface are coincident. We discuss the role of asymmetry on the evolution of shear instabilities. Using linear stability theory and direct numerical simulations, we show that asymmetric shear instabilities exhibit features of both Holmboe and Kelvin-Helmholtz (KH) instabilities, and develop a framework to determine whether the instabilities are more Holmboe-like or more KH-like. Further, the asymmetric instabilities produce asymmetric mixing that exhibits features of both overturning and scouring flows and that tends to realign the shear and buoyancy interfaces. In all but the symmetric KH simulations, we observe a collapse in the distribution of gradient Richardson number (${\text{Ri}}_g$), suggesting that asymmetry reduces the parameter dependence of KH-driven mixing events. The observed dependence of the turbulent dynamics on small-scale details of the shear and stratification has important implications for the interpretation of oceanographic data.

In homogeneous turbulent flow, a relation for the correlation between velocity gradient $m_{ij}\equiv \frac{\partial u_i}{\partial x_j}$ and pressure Hessian $h_{ij}^p\equiv \frac{{\partial }^{2}p}{\partial x_i\partial x_j}$ was found recently: $\langle \mathrm{tr}\left({\mathbf{mh}}^{\mathbf{p}}\mathbf{m}\right)\rangle =-\frac{1}{2}\langle {\left(\mathrm{tr}\left({\mathbf{m}}^2\right)\right)}^2\rangle$. We discuss the implications of this relation to the velocity gradient dynamics: together with the Poisson equation for pressure, the homogeneity relation yields an identity between $\langle {\left(\mathrm{tr}\left({\mathbf{m}}^2\right)\right)}^2\rangle$ and the integration of a two-point fourth-order correlation function of velocity gradient for isotropic flows. Our results indicate that the main contributions to $\langle \mathrm{tr}\left({\mathbf{mh}}^{\mathbf{p}}\mathbf{m}\right)\rangle$ come from scales less than roughly 20 times the Kolmogorov scale. Also, the homogeneity relation provides restrictions to the parameters in the closure models of pressure Hessian in velocity gradient dynamics. We further discuss the generalization of this homogeneity relation to turbulent shear flows, and we show numerically that this relation between $\langle \mathrm{tr}\left({\mathbf{mh}}^{\mathbf{p}}\mathbf{m}\right)\rangle$ and $\langle {\left(\mathrm{tr}\left({\mathbf{m}}^2\right)\right)}^2\rangle$ is approximately satisfied even in the presence of a shear and of a wall, as it occurs in turbulent channel flows.

Isolated supercooled water drops have been observed to move spontaneously while freezing in vacuum. This motion is caused by an increase of the evaporation rate during the early stages of freezing, which transfers momentum to the drops, similar to rocket propulsion. As in other cases of self-propulsion, symmetry breaking is necessary, and occurs when ice nucleation occurs away from the center of the drop. The self-propulsion velocity was modeled analytically for a simplified case, and numerically for two experiments. The model predicts peak velocities on the order of 1 m/s in vacuum, and a drop kinematics similar to that observed experimentally. In air, the self-propulsion velocity is expected to be much smaller but may be detectable for micron-sized drops.

We present a theoretical analysis of large-aspect-ratio turbulent vertical convection that yields two relationships between heat flux and wall shear stress, measured respectively by the Nusselt number ($\text{Nu}$) and shear Reynolds number (${\text{Re}}_{\tau }$), in terms of the Rayleigh ($\text{Ra}$) and Prandtl numbers ($\text{Pr}$): ${\text{Re}}_{\tau }^2\text{Nu}=f\left(\text{Pr}\right){\text{Pr}}^{-1}\text{Ra}$ in the high-$\text{Ra}$ limit and $\text{Nu}\approx C{\text{Pr}}^{\varepsilon }{\text{Re}}_{\tau }$ with $\varepsilon =1/3$ for $\text{Pr}\gg 1$ and $\varepsilon =1$ for $\text{Pr}\ll 1$, where $f\left(\text{Pr}\right)$ is not a power law of $\text{Pr}$ and $C$ is a constant. These relationships imply $\text{Nu}\approx {\left[C^{2}f\left(\text{Pr}\right)\right]}^{1/3}{\text{Pr}}^{-(1-2\varepsilon )/3}{\text{Ra}}^{1/3}$ and ${\text{Re}}_{\tau }\approx {[f\left(\text{Pr}\right)/C]}^{1/3}{\text{Pr}}^{-(1+\varepsilon )/3}{\text{Ra}}^{1/3}$ for high $\text{Ra}$.

Under a fully developed Poiseuille flow with nonisothermal condition, it has been widely reported that the thermocapillary effects always strengthen the droplet migration velocity as long as the temperature increases along the direction of Poiseuille flow. The insoluble surfactant, on the other hand, always retards the droplet migration. This is due to the fact that, for most of the models, the Langmuir equation of state for the surface tension is usually simplified under the assumption of low surfactant concentration. The coupling term of temperature and surfactant concentration is dropped, and the thermo-induced and surfactant-induced Marangoni forces are therefore decoupled. In the present study, we develop a thermodynamically consistent phase-field model for investigating the coupling effects of temperature and surfactant concentration on droplet migration under a fully developed Poiseuille flow. By choosing the interface free energy sophisticatedly, the surface tension of our model consists of not only the classical linear part for the thermocapillary effects but also a nonlinear coupling term of temperature and surfactant concentration that recovers the Langmuir equation of state. This coupling term allows us to investigate the case of high surfactant concentration. Through 3D numerical simulations, we find that this nonlinear coupling term introduces extra thermo-induced and surfactant-induced Marangoni forces to the droplet migration, leading to a competition between the two, especially for the case of high surfactant concentration. In particular, the initial migration velocity of a surfactant-covered droplet is always faster than that of a droplet with a clean interface. The terminal velocity, on the other hand, does not reach its steady state but instead decreases gradually as the droplet moves toward the hotter region, whereas, for the case without this term, the initial migration velocity of a surfactant-covered droplet is always lower than that of a clean interface and the terminal velocity stays steady.

A kinetic model is proposed for the nonequilibrium flow of dense gases composed of hard-sphere molecules, which significantly simplifies the collision integral of the Enskog equation using the relaxation-time approach. The model preserves the most important physical properties of high-density gas systems, including the Maxwellian at rest as the equilibrium solution and the equation of state for hard-sphere fluids; all the correct transport coefficients, namely, the shear viscosity, thermal conductivity, and bulk viscosity; and inhomogeneous density distribution in the presence of a solid boundary. The collision operator of the model contains a Shakhov model-like relaxation part and an excess part in low-order spatial derivatives of the macroscopic flow properties; this latter contribution is used to account for the effect arising from the finite size of gas molecules. The density inhomogeneity in the vicinity of a solid boundary in a confined flow is captured by a method based on the density-functional theory. Extensive benchmark tests are performed, including the normal shock structure and the Couette, Fourier, and Poiseuille flow at different reduced densities and Knudsen numbers, where the results are compared with the solutions from the Enskog equation and molecular dynamics simulations. It is shown that the proposed kinetic model provides a fairly accurate description of all these nonequilibrium dense gas flows. Finally, we apply our model to simulate forced wave propagation in a dense gas confined between two plates. The inhomogeneous density near the solid wall is found to enhance the oscillation amplitude, while the presence of bulk viscosity causes stronger attenuation of the sound wave. This shows the importance of a kinetic model to reproduce density inhomogeneity and correct transport coefficients, including bulk viscosity.

The distribution of capsules and rheological properties of suspensions in curved tubes are investigated by using an immersed-boundary lattice Boltzmann method. We mainly focus on the effective suspension viscosity and equilibrium positions of capsules as functions of Reynolds number $\left(\text{Re}\right)$, Capillary number $\left(\text{Ca}\right)$ and volume fraction of capsules $\left(\varphi \right)$. We found that at limited inertia ($\mathrm{Re}O\left(10\right)$), the effective viscosity decreases with increasing $\mathrm{Re}$, which is different from the variation trend in straight tubes. Dean's vortices play an important role. When the fluid inertia increases, the vortices are strengthened. They greatly promote the capsules' circumferential transportation by trapping the capsules into their centers and making the location of maximum azimuthal velocity close to them. The curvature effect of the torus vessel is also investigated. When the curvature $\kappa$ is large enough, e.g., $\kappa >0.2$, a scaling law for the effective viscosity as a function of a redefined $\mathrm{Re}$ is proposed. Furthermore, the distribution feature of multiple capsules in the torus vessel is revealed. Generally, for the semidilute regime, the capsules concentrate on the symmetrical plane at low $\mathrm{Re}$ but the center of Dean's vortex at high $\mathrm{Re}$. In addition, for both the dilute and semidilute regime, the scaling law connecting the effective viscosity and the average location of capsules is proposed. Our data support the scaling well. This study may be useful in the design of tubes for capsule transportation.

This work describes a numerical investigation of the impact dynamics and outcomes accompanying the impingement of a liquid drop on a liquid pool. A regime map of these outcomes as a function of the governing dimensionless factors is presented. We find that these outcomes are controlled by inertia, surface tension, and viscous forces. Hence, the phenomena are investigated over a wide range of Weber number ($0\le \mathrm{We}\le 350$) and Ohnesorge number ($0.002\le \mathrm{Oh}\le 0.020$). Based on the morphologies, these outcomes are distinguished by two regimes, namely coalescence and splashing, which can be further divided into three subregimes, namely partial coalescence, complete coalescence, and regular bubble entrapment. We quantify the phase boundaries between them and illustrate them in We-Oh phase diagrams. Our comprehensive study further reveals that eight salient flow structures are confined in these regions, including four previously reported flow structures: primary ring, secondary ring, jet, blob, and a combination of them. The characteristics of these flow structures along with their genesis are thoroughly examined. The thresholds of these flow structures are also quantified using nondimensional parameters. Subsequently, they are organized in an orderly manner in the phase diagram. This work thus delineates different regimes, subregimes, and their associated flow structures during the impact of a liquid drop on a liquid pool, and it constructs phase boundaries between them.

In recent years, deep learning approaches have shown much promise in modeling complex systems in the physical sciences. A major challenge in deep learning of partial differential equations is enforcing physical constraints and boundary conditions. In this work, we propose a general framework to directly embed the notion of an incompressible fluid into convolutional neural networks, and apply this to coarse-graining of turbulent flow. These physics-embedded neural networks leverage interpretable strategies from numerical methods and computational fluid dynamics to enforce physical laws and boundary conditions by taking advantage the mathematical properties of the underlying equations. We demonstrate results on three-dimensional fully developed turbulence, showing that this technique drastically improves local conservation of mass, without sacrificing performance according to several other metrics characterizing the fluid flow.

We report on the experimental observation of a transition from a dispersive wave turbulence regime to a nondispersive regime involving shock waves on the surface of a fluid. We use a magnetic fluid in a canal subjected to an external horizontal magnetic field to tune the dispersivity of the system. For a low magnetic field, gravity-capillary wave turbulence is observed, whereas for a high enough field, random steep coherent structures arise which are found to be shock waves. These shock waves create singularities in the second-order difference of the surface elevation, leading to an ${\omega }^{-4}$ frequency power spectrum. This spectrum is also found to be controlled by the number and amplitude of the shocks and is well captured by a model based on a random Dirac-$\delta$ distribution (Kuznetsov-like spectrum). Finally, the shock-amplitude statistics exhibits a power-law distribution with an exponent close to the predictions of the one-dimensional random-forced Burgers equation. To our knowledge this shock-wave regime has not previously been examined for surface waves and this work paves the way to better explore their properties.

Realistic rotating fluid under self-gravitation will be oblate due to the centrifugal force. In our previous paper [Li and Kong, Phys. Rev. Fluids 7, 103502 (2022)], for the first time, the problem of convective instabilities was formulated and tackled in rotationally flattened spheroids. Using that method, this paper demonstrates how extraordinary nonsphericity alters the linear onset of thermal inertial convection in internally heated Boussinesq fluid. A significant discovery is that the globally most unstable mode could switch from a non-axisymmetric quasigeostrophic wave to an equatorially symmetric zonal oscillation when the rotational flattening effect gets very strong. This was the only form of global convection not found so far.

We propose a simple model for the bottleneck effect in homogeneous isotropic turbulence as a bump in the compensated energy spectrum, based on Kolmogorov's hypotheses (of 1941 and 1962). The model of the longitudinal structure function consists of two quadratic functions representing large- and small-scale motions. The model parameters are derived from the asymptotic behavior of the structure function. The Kolmogorov and intermittency constants are fitted from direct numerical simulation (DNS) and experimental data. From the model, the height of the spectral bump in the compensated spectrum has a power-law $R_{\lambda }^{-0.0426}$, and the bump location scaled by the Kolmogorov scale is 0.153, which generally agree with various DNS results at moderate and large Reynolds numbers $R_{\lambda }$. Moreover, we derive that the incorporation of the intermittency exponent into the model leads to the decaying power law of the bump height with $R_{\lambda }$.

What constitutes the “extra stress” exerted by a liquid endowed with odd viscosity [for instance, the tensile or compressive stress imparted on a cylinder rotating in a viscous liquid as was calculated by Avron, J. Stat. Phys. 92, 543 (1998)], requires clarification. The nature of this extra stress depends on the character of the boundary conditions. We show that when only velocities are prescribed on the boundaries, it is not the full anomalous (odd) stress tensor that generates this “extra” stress but only its null divergence part, that is, the part of the odd stress whose divergence vanishes identically. We demonstrate this fine point by calculating the extra stress for a viscous liquid between concentric rotating cylinders and the corrections to the viscosity coefficient in liquid suspensions. Similar conclusions can be reached for a liquid with periodic boundary conditions. On the other hand, when stresses are prescribed on some part of the boundary, the state of stress due to odd viscosity becomes ambiguous. In general, it is the whole Cauchy stress tensor that now depends on odd viscosity. There are exceptions, however, to this rule which we briefly discuss. Finally, the decomposition of the Cauchy stress tensor into a part that is operative in the Navier-Stokes equations, and into a null part (whose divergence vanishes identically) gives rise to new fluid flow behavior and recovers previous results from the literature as special cases.

We propose an extension of the Maffettone-Minale (MM) model to predict droplet dynamics in shear flow. The parameters of the MM model are traditionally retrieved in the framework of the perturbation theory for small deformations, i.e., small capillary numbers ($\text{Ca}\ll 1$) applied to Stokes equations. In this work, we take a novel route, in that we determine the model parameters at finite capillary numbers ($\text{Ca}\sim \mathcal{O}\left(1\right)$) without relying on perturbation theory results, while retaining a realistic representation in loading time and steady deformation attained by the droplet for different realizations of the viscosity ratio $\lambda$ between the inner and the outer fluids. This extended MM (EMM) model hinges on an independent characterization of the process of droplet deformation via fully three-dimensional numerical simulations of Stokes equations employing the immersed boundary-lattice Boltzmann numerical techniques. Issues on droplet breakup are also addressed and discussed within the EMM model.

In this paper, water wave interaction with an array of thin submerged horizontal circular plates is investigated within the framework of linear potential flow theory. To consider a more general case, the circular plates studied in this paper are not limited to be rigid and impermeable and, instead, they can be perforated and/or elastic. A Hankel transform approach is employed to formulate integral equations in terms of unknown functions related to the jump in velocity potential across each plate. A Galerkin method is adopted to the solution of these integral equations, and the velocity potential jump across the plate is expressed in terms of Fourier-Gegenbauer series, incorporating the known square-root behavior at the edge of the plate in a rapidly convergent numerical scheme. For elastic plates, the plate motion is expanded in modes of free vibration with the edge constraint conditions accounted for intrinsically. The unknown coefficients of the plate motion are further expressed in terms of the unknown coefficients related to the velocity potential jump. The Hankel transform–based model is found to be valid for multiple plates distributed arbitrarily, including the staggered arrangement, for which the traditional eigenfunction matching method would not work. In-depth discussions have been made to the hydrodynamic responses of staggered arrangement of plates. It is found that the staggered arrangement of plates can result in notable wave focusing but with less energy dissipation. The largest principal strain is observed on the front region of the plate submerged at a shallower depth.

We study the two-dimensional motion of a self-propelling asymmetric bent rod. By employing slender body theory and the Lorentz reciprocal theorem, we determine particle trajectories for different geometric configurations and arbitrary surface activities. Our analysis reveals that all particle trajectories can be mathematically expressed through the equation for a circle. The rotational speed of the particle dictates the frequency of the circular motion and the ratio of translational and rotational speeds describes the radius of the circular trajectory. We find that even for uniform surface activity, geometric asymmetry is sufficient to induce a self-propelling motion. Specifically, for uniform surface activity, we observe (i) when bent rod arm lengths are equal, the particle only translates, (ii) when the length of one arm is approximately four times the length of the other arm and the angle between the arms is approximately $\frac{\pi }{2}$, the rotational and translational speeds are at their maximum. We explain these trends by comparing the impact of geometry on the hydrodynamic resistance tensor and the active driving force. Overall, the results presented here quantify self-propulsion in composite-slender bodies and motivate future research into self-propulsion of highly asymmetric particles.