Active colloidal systems with nonequilibrium self-organization constitute a long-standing, challenging area in material sciences and biology. To understand how hydrodynamic flow may be used to actively control self-assembly of Janus particles (JPs), we developed a model for the many-body hydrodynamics of amphiphilic JPs suspended in a viscous fluid with imposed far-field background flows [Fu et al., J. Fluid Mech. 941, A41 (2022)]. In this paper we alter the hydrophobic distribution on the JP-solvent interface to investigate the hydrodynamics that underlies the various morphologies and rheological properties of the JP assembly in the suspension. We find that JPs assemble into unilamellar, multilamellar, and striated structures. To introduce dynamics, we include a planar linear shear flow and a steady Taylor-Green mixing flow and measure the collective dynamics of JP particles in terms of their (a) free energy from the hydrophobic interactions between the JPs, (b) order parameter for the ordering of JPs in terms of alignment of their directors, and (c) strain parameter that captures the deformation in the assembly. We characterize the effective material properties of the JP structures and find that the unilamellar structure increases orientation order under shear flow, the multilamellar structure behaves as a shear thinning fluid, and the striated structure possesses a yield stress. These numerical results provide insights into dynamic control of nonequilibrium active biological systems with similar self-organization.

For periodic acoustic fields of sufficient intensity inside a cylindrical tube, a nonlinear mechanism is responsible for the generation of vorticity at the open end of the tube. It has been observed that as the magnitude of the acoustic velocity is increased, different regimes are possible. At first, we consider the inner edge of the duct to be straight. In the first regime, vorticity appears only in the immediate vicinity of the open end of the tube. For higher acoustic velocities, vortex rings are formed at this same location, and finally, for even larger velocities, they are advected outwards. In all cases roundingoff the inner edge of the tube to different degrees leads to a suppression of the mechanism responsible for the generation of vorticity, with the more noticeable suppression occurring for the smoother edges. The parameter that determines the scale at which different behaviors occur is a Reynolds number $R_{\delta }$ associated with the width of the acoustic boundary layer inside the duct. We use a three-dimensional Lattice Boltzmann Method (LBM) to simulate the velocity and the pressure fields at the exit of the tube, for different values of $R_{\delta }$, allowing for validation of the numerical method against experimental measurements. In this regard, we conduct experiments with 2D phase-locked particle image velocimetry (PL-PIV) within a similar range of values of $R_{\delta }$. The expected behavior is observed in both experimental and numerical results, and the results obtained by means of the numerical scheme are consistent with those obtained through PIV measurements, with different regimes exhibiting varying combinations of acoustic streaming, boundary-layer separation, and vortex shedding.

We investigate experimentally the effect of wind on the dynamics of a viscous liquid film flowing down a thread. The liquid film is well known to destabilize into an axisymmetric bead-like pattern in stagnant air. When the flowing thin film is exposed to side wind, the beads are pushed downstream of the wind, breaking the symmetry and leading to a modification of the film flow. The viscous dissipation in the liquid film decreases with increasing side wind, leading to a faster slide speed of the liquid beads. The inertia in the film is then increased, which can induce a regime shift, triggering an instability. When the film becomes unstable, it switches from a periodic pattern of equally sized liquid beads to an irregular film pattern where large beads collide with smaller ones.

An efficient method is reported to determine correction tensors at successive orders in the Knudsen number (i.e., the Klinkenberg and higher corrections) to approximate the apparent permeability tensor characterizing one-phase, creeping, Newtonian, isothermal slip flow in homogeneous porous media. It is shown that the Klinkenberg correction tensor can be obtained from the solution of the same ancillary (closure) problem that is required to compute the intrinsic permeability tensor. More generally, correction tensors up to the $(2M-1)\mathrm{th}$ order are shown to be obtained from the solution of the first $M$ closure problems, instead of the $2M$ ones suggested by the upscaling procedure and associated closure scheme. Moreover, it is demonstrated that all the correction tensors are symmetric, the odd and even order ones being respectively positive and negative. In particular, this indicates that the apparent permeability tensor at the first order in the Knudsen number is symmetric positive. The model is validated by analytical solutions in the simple cases of flow in parallel plates and bundle of parallel cylindrical tubes and by numerical simulations performed in a model two-dimensional structure. An improvement in the apparent permeability prediction is shown using a Padé approximant.

The mechanics of curved, heterogeneous, surfactant-laden surfaces and interfaces are important to a variety of engineering and biological applications. To date, most models of rheologically complex interfaces have focused on homogeneous systems of planar or fixed curvature. In this paper, we investigate a simple, dynamical model of a two-phase surface fluid on a curved interface: a condensed, surface-viscous domain embedded within a surface-inviscid, spherical interface of time-varying radius of curvature. Our aim is to understand how changes in surface curvature generate two-dimensional Stokes flows inside the domain, thereby resisting curvature deformation and distorting the domain shape. We model the surface stress within the domain using the classical Boussinesq-Scriven constitutive equation, simplified for a near-spherical cap undergoing a small-amplitude curvature deformation. We then analyze the frequency-dependent dynamics of the surface stress and curvature within the domain when the pressure difference across the surface is sinusoidally oscillated. We find that the curvature relaxes diffusively, and thus define a Peclet number (Pe) relating the rate of diffusion to the oscillation frequency. At small enough Pe, the surface deforms quasistatically, whereas at high Pe the curvature varies sharply within a thin boundary layer adjacent to the domain border. Consequently, the curvature of the domain appears discontinuous from the rest of the surface under rapid oscillation. We then examine the linear stability of the domain shape to small, nonaxisymmetric perturbations when the surface is steadily compressed (i.e., the pressure difference across it is increased). While the line tension at the domain border tends to maintain circular symmetry, surface-viscous stresses generated by surface compression tend to destabilize the perimeter. A shape instability arises above a critical surface capillary number (Ca) that relates surface-viscous stresses to line tension. Moreover, we show that the mechanism of instability is distinct from that of the famous Saffman-Taylor fingering instability. Various extensions of our model are discussed, including materials with finite dilatational surface viscosity, linear and nonlinear (visco)elasticity, and large-amplitude deformations.

Intermittency is one of the central obstacles for understanding small-scale dynamics in the fully developed hydrodynamic turbulence. The modern approach is largely based on the multifractal theory of Parisi and Frisch which is, however, phenomenological. It was shown recently that the intermittency can be related to the hidden scale invariance. The latter is a statistical scaling symmetry unbroken in a rescaled (projected) formulation of equations of motion. In the present paper, we consider a shell model of turbulence and describe how the hidden symmetry manifests itself through all scales, both in the inertial interval and in the transition to forcing and dissipation ranges. In the inertial interval, we derive anomalous scaling laws from the hidden symmetry. Then we show how a complicated form of the dissipation range is controlled by intermittent rescaled Reynolds numbers within a large range of dissipation scales. This dissipative intermittency can be removed by using a special class of dissipation models. For such models, the hidden scale invariance is restored both in the inertial interval and the dissipation range. Overall, the presented approach deduces the multifractal theory and some of its basic conclusions from the hidden scaling symmetry of equations of motion.

We present a numerical study of finite-temperature superfluid turbulence using the vortex filament model for superfluid helium. We examine the phenomenon of vorticity locking between the normal and superfluid components across a wide range of temperatures, using two different structures of external normal fluid drive. Our analysis is restricted to one-way coupling between the two components, and subject to this simplification, we show that vorticity locking increases with temperature leading to the superfluid flow being more influenced by the characteristics of the normal fluid. This results in stronger superfluid polarization and deviations from Gaussian statistics with a more probable occurrence of extreme fluctuations. We also examine how these properties influence the pressure field and attempt to verify a longstanding $P_k\propto k^{-7/3}$ theoretical quantum signature within the spatial pressure spectrum.

The influence of planform and Strouhal number (St) on the propulsive performance of bio-inspired pitching panels is investigated for $0.09\le \text{St}\le 0.66$. Aspect ratio (AR) is varied in the range $3.0\le \text{AR}\le 6.6$ by changing the trailing edge sweep of a trapezoidal planform, resulting in panels of forked, straight, and pointed trailing edges. Positive mean thrust only develops for panels of reduced AR with straight or pointed trailing edges, contrary to expectations from biology. Planform and St have significant impacts on force amplitudes and improved performance is associated with larger force amplitudes. All panels experience positive thrust during significant portions of a cycle, but positive mean thrust only occurs when thrust maxima exceed drag maxima. Strong lateral forces develop for panels with the best mean performance, showing that low AR pointed panels may provide better maneuverability, as well as high thrust and efficiency. Decomposition of the thrust force into its normal and axial forces components in the frame of the panel reveal the relative impact of these components on mean performance. When mean axial forces are small or negative, a thrust-producing panel has relatively large propulsive efficiency and thrust is due primarily to normal forces. Once a thrust-producing panel reaches a local maximum in efficiency, further increases in St result in increases in mean thrust due to larger axial forces. Additionally, thrust-producing panels experience time-varying axial forces that contribute more effectively to thrust in a way not observed in forked planforms.

We consider the flow of an inertial supercritical gravity current sustained by a constant source at $x=0$ and free drainage edge at $x=x_D$. We analyze time-dependent flows provided by an analytical model and shallow-water finite-difference solution and compare them with the predictions of steady-state formulations [Ellison and Turner, J. Fluid Mech. 6, 423 (1959); Haddad et al., Phys. Rev. Fluids 7, 084802 (2022)]. Entrainment and drag (expressed as $Eu$ and $c_D{u}^2$, respectively, where $u$ is velocity), with coefficients modeled as some simple functions of the Richardson number $\mathrm{Ri}$, play a significant role in the first domain of propagation. The solution shows that an internal forward-moving jump appears, separating the supercritical, significantly mixed, domain at the rear and the free nose at $x_N\left(t\right)$ that propagates toward $x_D$, where $t$ is time. The behavior of the subcritical domain between the jump and the nose depends strongly on the entrainment-drag model, as follows: (a) If $E$ and $c_D$ decay to zero for $\mathrm{Ri}>{\mathrm{Ri}}_{\mathrm{crit}}<1$, eventually the jump overflows $x_D$, leaving behind a steady-state domain of supercritical flow. This contradicts the steady-state model of Haddad et al. that postulates a stationary internal jump at $x_S<x_D$ with a critical outflow at $x_D$. (b) If finite values $E$ and $c_D$ prevail for $\mathrm{Ri}>1$, the internal jump propagates to a position $x_J>x_S$ but does not overflow $x_D$ for a long time. Some oscillations at $x_D$ appear, which may indicate a backward-moving adjustment wave, but this is a long-time process beyond the accuracy of our shallow-water simulation. The reasons for the discrepancy with the steady-state solutions, and the connections with the experiment of Ellison and Turner, are discussed. A noteworthy insight is that the time-dependent stage is important for the understanding and use of the steady-state results. The free edge may admit a supercritical outflow, and hence the application of a critical flow condition may lead to nonphysical results; outflow over a weir may reflect the internal jumps, and this needs a separate investigation.

We derive the flow field disturbance produced by point viscosity variations in a heterogeneous fluid when subject to a background flow while neglecting fluid inertia. The disturbance flow field is found to be identical to that generated by a force dipole called a stresslet. Using a combination of theory and numerical simulations, we show how the hydrodynamics of an active rigid particle is altered due to the presence of point viscosity variations, and how this can be exploited to manipulate and steer them in microfluidic environments.

The question of whether buoyancy forces arising in a turbulent flow in a stratified medium can influence the cascade in the inertial range was posed independently by Obukhov and Bolgiano more than 60 years ago, but has not been answered up to now. Here, we show that the Obukhov-Bolgiano scaling (OBs) is possible only if the injection rates of kinetic energy and thermal variance by force acting at a large scale, strictly correspond to the given buoyancy parameter. We found an analytical solution of energy balance equations which demonstrates both the OBs and Kolmogorov scaling as well as a transition between them. A new characteristic scale is introduced which characterizes the role of buoyancy in the spectral cascade of energy and determines the Bolgiano scale. The feasibility of the solution is illustrated by a fixed point of a shell model of turbulence. However, the quasistationary solutions obtained within the framework of essentially dynamic shell models do not reveal the OBs. We come to conclusion that the idealized conditions required to implement the OBs should be extended considering real turbulent flows.

Building efficient, accurate, and generalizable reduced-order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for turbulent flows, and it investigates the effects of enforcing physical structure through smoothed particle hydrodynamics (SPH) versus relying on neural networks (NNs) as universal function approximators. Starting from NN parametrizations of a Lagrangian acceleration operator, this hierarchy of models gradually incorporates a weakly compressible and parameterized SPH framework, which enforces physical symmetries, such as Galilean, rotational, and translational invariances. Within this hierarchy, two new parameterized smoothing kernels are developed to increase the flexibility of the learn-able SPH simulators. For each model we experiment with different loss functions which are minimized using gradient based optimization, where efficient computations of gradients are obtained by using automatic differentiation and sensitivity analysis. Each model within the hierarchy is trained on two data sets associated with weakly compressible homogeneous isotropic turbulence: (1) a validation set using weakly compressible SPH; and (2) a high-fidelity set from direct numerical simulations. Numerical evidence shows that encoding more SPH structure improves generalizability to different turbulent Mach numbers and time shifts, and that including the novel parameterized smoothing kernels improves the accuracy of SPH at the resolved scales.

The enhancement of skin-friction drag and surface heat flux by the transition to turbulence is a crucial physical phenomenon for the design of high-speed vehicles. An interpretable mapping of how various flow phenomena such as turbulence and the streamwise growth of the boundary layer (BL) thickness influence these key surface quantities is desirable for advancing our understanding of fundamental flow physics, as well as informing engineering design analysis. To accomplish such a mapping, an angular momentum integral (AMI) equation, originally derived for incompressible flows by Elnahhas and Johnson [J. Fluid Mech. 940, A36 (2022)], is here introduced for compressible turbulent BL flows of a calorically perfect gas. By isolating the laminar BL friction at the same Reynolds number, the AMI equation obtains a straightforward interpretation for skin-friction alteration by other flow phenomena relative to an equivalent laminar BL. Similarly, a moment of total enthalpy integral (MTEI) equation is proposed to quantitatively map the effects of turbulence and other physical flow phenomena to the Stanton number relative to an equivalent laminar BL. Direct numerical simulations (DNSs) of zero pressure gradient isothermal flat plate BLs up to edge Mach number of 7 are used to demonstrate the utility of the AMI and MTEI equations. The DNS cases span a variety of wall-temperature boundary conditions ranging from nominally adiabatic to strongly cooled walls. The derivation of the AMI equation itself suggests the use of shear stress-weighted average viscosity, which collapses the relative influence of turbulence on compressible BL skin friction over the wide range of edge Mach numbers and temperature boundary conditions considered. The AMI results quantify how the variation of mean density inside a turbulent BL impacts the ability of correlated velocity fluctuations to transport momentum and enhance the skin friction coefficient relative to the equivalent laminar BL. From an alternative viewpoint, the results demonstrate how the effect of compressibility on laminar BLs can be used to gain insight into turbulent BLs. The MTEI results similarly demonstrate how the mean density alters the impact of turbulence on the transport of total enthalpy and Stanton number. In doing so, the MTEI results highlight the relative role of turbulent fluxes of enthalpy and mean kinetic energy on the Stanton number. In light of these results, the AMI and MTEI equations provide a quantitative perspective on the fundamental physics of skin friction and surface heat flux in high-speed BLs, which may prove useful for evaluating flow control schemes and complementing existing analysis tools.

While understanding breaking waves is crucial for the development of parametrizations used in ocean wave modeling for both deep and shallow water, the complete process of wave breaking is not well understood. Here we present direct numerical simulations of two-dimensional solitary waves that shoal and break on a uniform beach in shallow water, with the presence of storm surge represented by an inshore region. The storm surge depth, beach slope, and wave amplitude are varied to study the dependence of energy dissipation in the breaker on wave and bathymetric parameters. We classify wave breaker types and find a separation between plunging and spilling breakers when scaled by breaking amplitude and depth. We compare energy dissipation during the breaking process with results from the literature without storm surge. A representation of energy dissipation in this solitary wave breaker data is also compared with prior experiments and simulations of breakers in deep water, and possibilities of a unifying model are explored. We conclude that a previously developed shallow-water inertial dissipation model for wave breaking on a uniform slope can be extended to this storm surge environment with good data collapse, and we further discuss possibilities for a general parametrization of wave breaking valid across different depth regimes.

A detailed study of small-scale Hall magnetohydrodynamic dynamos has been performed both analytically and numerically. Assuming the magnetic field and the current to be separate fields, the contribution of the Hall term has been decomposed into two parts and their individual contributions have been studied separately. Calculating the scale-separated transfer rates described in Dar et al. [Physica D 157, 207 (2001)], it is found that the small-scale current fields are the primary contributors in sustaining large-scale magnetic fields. Furthermore, the nature of the scale-to-scale fluxes are found to be globally intact with the ion inertial scale.

We study numerically and theoretically the gravity-driven flow of a viscous liquid film coating the inner side of a horizontal cylindrical tube and surrounding a shear-free dynamically inert gaseous core. The liquid-gas interface is prone to the Rayleigh-Plateau and Rayleigh-Taylor instabilities. Here we focus on the limit of low and intermediate Bond numbers, $\mathrm{Bo}$, where the capillary and gravitational forces are comparable and the Rayleigh-Taylor instability is known to be suppressed. We first study the evolution of the axially invariant draining flow, initiating from a uniform film thickness until reaching a quasistatic regime as the bubble approaches the upper tube wall. We then investigate the flow's linear stability within two frameworks: frozen time-frame (quasisteady) stability analysis and transient growth analysis. We explore the effect of the surface tension $\left(\mathrm{Bo}\right)$ and inertia (measured by the Ohnesorge number, $\mathrm{Oh}$) on the flow and its stability. The linear stability analysis suggests that the interface deformation at large $\mathrm{Bo}$ results in the suppression of the Rayleigh-Plateau instability in the asymptotic long-time limit. Furthermore, the transient growth analysis suggests that the initial flow evolution does not lead to any considerable additional amplification of initial interface perturbations, a posteriori rationalizing the quasisteady assumption. The present study yields a satisfactory prediction of the stabilization threshold found experimentally by Duclaux et al. [J. Fluid Mech. 556, 217 (2006)].

Bubbles appear when a carbonated drink is poured in a glass. Very stable bubble chains are clearly observed in champagne, showing an almost straight line from microscopic nucleation sites from which they are continuously formed. In some other drinks such as soda, such chains are not straight (not stable). Considering pair interactions for spherical clean bubbles, bubble chains should not be stable, which contradicts these observations. The aim of this work is to explain the conditions for bubble chain stability. For this purpose, experiments and direct numerical simulation are conducted. The bubble size as well as the level of interface contamination are varied to match the range of parameters in typical drinks. Both factors are shown to affect the bubble chain stability. The transition from stable to unstable behavior results from the reversal of the lift force, which is induced by the bubble wake. A criteria based on the production of vorticity at the bubble surface is proposed to identify the conditions of transition from stable to unstable bubble chains. Beyond carbonated drinks, understanding bubble clustering has impact in many two-phase problems of current importance.

We study, by means of extensive direct numerical simulations, the turbulent flow produced by a two-dimensional cellular forcing in a cubic box with periodic boundary conditions. We find that, in spite of the developed turbulence that recovers isotropic features at small scales, the signature of forcing remains in the mean flow (averaged over time and over the homogeneous direction). This allows us to introduce a friction factor, whose dependence on the Reynolds number is investigated. We further show that the flow is characterized by large temporal fluctuations of the total energy, as a consequence of the exchange between the forced mean flow at large scales and turbulent fluctuations at small scales. Such temporal fluctuations produce a correction to the energy spectrum that can be explained by a simple dimensional argument.

Stokesian dynamics is a well-established computational method for simulating dynamics of many particles suspended in a conventional passive fluid medium. Active fluids composed of self-driving particles with broken time-reversal symmetry permit the emergence of a so-called odd viscosity. In this work, we extended the conventional Stokesian dynamics formalism to incorporate the additional hydrodynamic effects due to odd viscosity, which enables simulating collective behavior of many particles suspended in an active fluid medium with both even viscosity and odd viscosity.

Cleaning surfaces with air bubbles in an aqueous medium has been a topic of discussion in recent years due to the growing interest in sustainable methods for cleaning biological surfaces such as agricultural produce. Specifically, in a bubble-injection method, inclined surfaces are targeted by many millimetric air bubbles that collide with and slide along the surface. The collision and subsequent sliding of these air bubbles exert shear stress on the surface, causing contaminants to be removed. The shear stress is proportional to the tangential speed of the bubble with respect to the surface divided by the thickness of the thin film of liquid between the bubble and the solid surface. In this study, we conduct experiments to test the cleaning efficacy at different angles of inclination of a contaminated surface. We use two different types of surface coated with either a protein solution or a bacterial biofilm. Our experimental results indicate that bubbles exhibit the highest cleaning efficacy at the surface angle of $\theta \approx {20}^{\mathrm{o}}$ with respect to the horizontal plane for polydisperse bubbles in the range of 0.3–2 mm and with an average radius of 0.6 mm. To gain a better understanding of the underlying mechanism, we perform a numerical analysis of a single air bubble colliding with a clean surface at various angles. Our numerical and theoretical results show that the average shear force that the bubble exerts on the surface reaches a maximum at $\theta \approx 22.5^{\mathrm{o}}$ which agrees well with the experiments. We also compare the maximum shear stress in sliding phase with the shear stress required for removing different types of bacteria as a fluid-mechanics-based guideline for geometrical design of bubble cleaning devices.