This paper demonstrates the efficient extraction of unstable recurrent flows from two-dimensional turbulence by using nonlinear triads to diagnose recurrence in direct numerical simulations. Nearly recurrent episodes are identified from simulations and then converged using a standard Newton-GMRES-hookstep method, however with much greater diversity than previous studies which performed this “recurrent flow analysis.” Unstable periodic and relative periodic orbits are able to be identified which span larger values of dissipation rate, i.e., corresponding to extreme bursting events. The triad variables are found to provide a more natural way to weight the greater variety of spatial modes active in such orbits than a standard Euclidian norm of complex Fourier amplitudes. Moreover, the triad variables build in a reduction of the continuous symmetry of the system which avoids the need to search over translations when obtaining relative periodic orbits. Armed with these orbits we investigate optimal weightings when reconstructing the statistics of turbulence and suggest that, in fact, a simple heuristic weighting based on the solution instability provides a very good prediction, provided enough dynamically relevant orbits are included in the expansion.

This paper briefly reprises, with added commentary, a talk I gave on transport and flows within living cells at an APS-DFD meeting. Directed transport is especially important in large cells, such as eggs where developmental factors need to be properly localized, and early embryos whose organelles and genetic material must be properly positioned before cell division. I discuss two cases—a nematode single-cell embryo and a fruit fly egg cell—where advances in mathematical modeling and large-scale simulation of fluid-structure interactions have helped us understand fundamental mechanisms of force transduction and self-organization within the cell.

Cloud droplets grow via vapor condensation and collisional aggregation. Upon reaching approximately $\approx 100\mu \mathrm{m}$, their inertia allows them to capture smaller droplets during descent, initiating rain. Here we show that raindrop formation is not primarily governed by gravity or thermal diffusion, but by a critical range of drop sizes ($3–30\mu \mathrm{m}$) where collisions are largely ineffective and controlled by van der Waals and electrostatic interactions. We identify four pathways to rain. The coalescence pathway, which is slow, involves the broadening of the drop size distribution across the $3–30\mu \mathrm{m}$ low-efficiency gap through collisions, until enough large individual droplets achieving efficient collisions have formed. The mixing pathway, which is faster, requires mixing at the cloud top with drop-free, cold, humid air to create locally supersaturated conditions that grow droplets above the low-efficiency gap. The electrostatic pathway bypasses the gap through a static vertical field creating attractive interactions between droplets. The turbulence pathway relies on air turbulence to bring the droplets together at an increased rate, but we show that this pathway is unlikely. For all dynamical mechanisms, we demonstrate that the initiation time for rainfall occurs at the crossover between the broadening of the drop size distribution and the emergence of individual droplets large enough to trigger the onset of the rainfall cascade.

Two different adjoint-based approaches are developed here for gust mitigation of two-dimensional or three-dimensional wing models in oscillatory heaving-pitching motion. One approach is based on a full-order model (FOM), i.e., Navier-Stokes equations, where noncylindrical calculus is implemented for moving boundary effect, and the other is based on a global reduced-order model (ROM), which models fluid flow and moving solid boundary in a global framework. When the lift performance was affected by either streamwise or transverse gusts, an objective function was designed to reduce the oscillation and keep the same lift to maintain a stable flight in gust. The goal was achieved by the optimal control of wing motions using the adjoint-FOM approach or the adjoint-ROM approach. In the study, the streamwise gust was successfully mitigated by reducing the amplitude of the heaving-pitching motion, and the transverse gust was mitigated by reducing the oscillation amplitude and decreasing the mean angle of attack at the same time. The adjoint-FOM approach provides better accuracy and can handle stronger gusts at the cost of longer computational time. The adjoint-ROM approach has lower accuracy and can only handle two-dimensional cases with weaker gusts, but it has its own advantage of requiring much less computational time and makes real-time control possible.

Understanding the nanoscale effects controlling the dynamics of a contact line—defined as the line formed at the junction of two fluid phases and a solid—has been a longstanding problem in fluid mechanics pushing experimental and numerical methods to their limits. A major challenge is the multiscale nature of the problem, whereby nanoscale phenomena manifest themselves at the macroscale. To probe the nanoscale, not easily accessible to other methods, we propose a reductionist model that employs elements from statistical mechanics, namely, dynamic-density-functional theory (DDFT), in a Navier-Stokes-like equation—an approach we name hydrodynamic DDFT. The model is applied to an isothermal Lennard-Jones fluid with no slip on a flat solid substrate. Our computations reveal fluid stratification with an oscillatory density structure close to the wall and the emergence of two distinct regions as the temperature increases: a region of compression on the vapor side of the liquid-vapor interface and an effective slip region of large shear on the liquid side. The compressive region spreads along the fluid interface at a lengthscale that increases faster than the width of the fluid interface with temperature, while the width of the slip region is bound by the oscillatory fluid density structure and is constrained to a few particle diameters from the wall. Both compressive and shear effects may offset contact line friction, while compression in particular has a disproportionately high effect on the speed of advancing contact lines at low temperatures.

This study aims to evaluate the effect of freestream turbulence (FST) on wakes produced by disks with different porosity. The wakes are exposed to various freestream turbulence “flavors,” where turbulence intensity and integral length scale are independently varied. The turbulent wakes are interrogated through hot-wire anemometry from 3 to 15 diameters downstream of the disks. It is found that disks with low porosity behave similarly to a solid body, in terms of both entrainment behavior and scaling laws for the centerline mean velocity evolution. Far from the disks, the presence of FST reduces both the wake growth rate and entrainment rate, with a clear effect of both turbulence intensity and integral length scale. As porosity increases, these “solid body” FST effects gradually diminish and are reversed above a critical porosity. The entrainment behavior in disk-generated wakes is significantly influenced by the presence of large-scale coherent structures, which act as a shield between the wake and the surrounding flow, thus impeding mixing in the near wake. We found that higher porosity, turbulence intensity, or integral length scale weakens the energy content of these structures, thereby limiting their influence on wake development to a shorter distance downstream of the disk. This, in turn, potentially reduces the influence of large-scale engulfment on the overall entrainment mechanism to a shorter distance downstream of the disks as well. For low-porosity disks, freestream turbulence intensity initially promotes near-wake growth through the suppression of large-scale structures; however, farther downstream, the wakes grow faster when the background is nonturbulent.

Though internal waves cannot propagate vertically through weakly stratified fluid, if the depth of the weak stratification is sufficiently shallow, these waves can partially reflect from and transmit through it. In this paper, we quantitatively extend the results of Sutherland and Yewchuk [J. Fluid Mech. 511, 125 (2004)] on Cartesian internal wave tunneling to the case of axisymmetric wave fields and discuss their tunneling through a weakly stratified layer. A simple three-layer model allowing for the computation of transmission coefficients for the velocity fields is proposed and tested on a case study. We notably show that there exists a smooth transition between the fully propagating and the tunneling regimes. We further reflect on the challenges set by the measurement of internal wave mode amplitudes in confined domains, and we discuss an innovative method to measure said amplitudes in this experimental and numerical context.

This study investigates the role of grain-fluid interactions, and especially those related to viscous dissipation, in the generation process of landslide tsunamis. For this purpose, original laboratory experiments on the collapse of a dry granular mass into a liquid are presented, in which only the grain size and liquid viscosity are varied to modify grain-scale viscous dissipation. By following the temporal evolution of the granular and free-surface height profiles, our results first reveal a surprising wealth in dynamics of granular collapses entering the liquid. Three distinct regimes are identified, namely, dense-inertial, dilute-inertial, and dense-viscous regimes. These regimes are described in terms of the flow Reynolds number $Re$ and the Stokes number $St$ that prescribe the relative importance of flow and particle inertia, respectively, to viscous dissipation of the liquid. Whereas the two inertial regimes are characterized by relatively fast and far propagation of, either dense or dilute, granular flows once immersed, the dense-viscous regime consists of the sudden arrest of the granular material on the incline, possibly accompanied by lift-off from the front. Although the collapse dynamics and deposition are very different for each of these regimes, they barely affect the first and largest wave, which suggests that (i) the generation of the leading wave is mainly governed by the impact process depending on subaerial flow conditions, and (ii) large-amplitude waves are not necessarily associated with long depositional runouts. In fact, granular flow regimes contribute mainly to the total energy transferred to the free-surface and the resulting wave train, rather than only the leading wave. Accordingly, we show that the leading wave to total wave train energy ratio follows a master curve depending only on $St$, for dense granular flow regimes. Altogether, these results help to understand better physical mechanisms involved in landslide-tsunami generation, for which $St$ can varied significantly at large $Re$, while offering an original and relevant benchmark for numerical models.

We study the locomotion of helical-tailed robots through a granular matter by varying the length of their tails. The swimming robots were built with a rigid helix attached to a magnetic cylindrical head, and were driven using a rotating magnetic field, which produced their spinning and forward self-propel across the media. Experiments show that the forward speed of the swimmers in granular matter increases with the tail length (with more turns), contrary to what was observed in viscous Newtonian fluids. A modified resistive force theory model was used to predict the forward velocity of the swimmers (including head and tail) in the granular medium, leading to good agreement with the experimental data, especially when the number of tail loops is higher than three. The findings of this research highlight the key role that tail length and head drag play in the swimming performance in a granular environment. This insight can be valuable in designing robots and vehicles optimized for such medium.

We investigate granular flows over an inclined rigid base, which is vibrated externally in a direction normal to itself, through the discrete element method. We vary the base's inclination angle $\theta$, vibration frequency $f$, and amplitude $A$ to study changes in the granular flow's profile and the mass flow rate $Q$. We find that the flow velocity profiles for the vibrated bases are nonlinear, unlike their fixed-base counterparts. Our study reveals that $Q$ may be maintained nearly constant in flows over vibrated bases utilizing appropriate combinations of $\theta$, $A$, and $f$. At the same time, by vibrating the base depending on the inclination angle, we may increase the mass flow rate by 25 to 100 times, compared to the values for the fixed base. Finally, we characterize $Q$ in terms of a nondimensional number $S$, which is the ratio of vibrational and gravitational energies.

Steady-state numerical simulations are conducted to analyze viscoplastic flows in a two-dimensional channel with two superhydrophobic surfaces, featuring grooves with air trapped and a nearly flat liquid-air interface. The Bingham model with the Papanastasiou regularization is used, and the thin channel limit is considered. By focusing on the creeping flow limit, the impact of varying the groove misalignment, via the offset number ($\varepsilon$), along with the other dimensionless flow parameters, including the Bingham number (Bn), slip number ($b$), groove periodicity ($\ell$), and slip area fraction ($\phi$), are examined. The results reveal that varying $\varepsilon$ significantly affects the velocity profiles, center plug morphology, and yielded and unyielded zones. Also, the deviation velocity field and deviation strain rate magnitude are particularly influenced by $\varepsilon$ and Bn, and they play crucial roles in the morphology of the center plugs, leading to deformation, breakage, and asymmetry in both velocity and strain rate profiles. Finally, influenced by the interaction of these parameters, four regimes of plug behavior are identified, highlighting the complex dynamics of our viscoplastic flow in channels with misaligned superhydrophobic surfaces.

We revisit the recent study of a gravity-driven Newtonian viscous falling film conducted by Mukhopadhyay et al. [J. Fluid Mech. 952, R3 (2022)]. As a result, the depth-averaged two-equation model is derived in terms of the film layer thickness $h(x,t)$ and the flow rate $q(x,t)$ based on the assumption of a combined parabolic and elliptic velocity profile, where the two-equation model is consistent up to first order in inertia terms and second order in viscous diffusion terms. The aim is to validate the outcomes of the two-equation model in the linear regime when the wavelength of the infinitesimal disturbance is finite and to perform spatiotemporal numerical simulations in the nonlinear regime. The current results demonstrate that as the free parameter $A$, relating to the eccentricity of the ellipse, increases, the two-equation model adequately captures the findings of the Orr-Sommerfeld equation obtained by Brevdo et al. [J. Fluid Mech. 396, 37 (1999)] and the findings of the finite element-based numerical simulation obtained by Malamataris et al. [Phys. Fluids 14, 1082 (2002)] in the linear regime, as well as the experimental results of Liu and Gollub [Phys. Fluids 6, 1702 (1994)] and the three-equation-based numerical result of Richard et al. [J. Fluid Mech. 804, 162 (2016)] in the nonlinear regime. However, the amplitudes of the sinusoidal-type periodic waves and the solitary-type waves differ slightly from the existing ones at higher values of $A$. Comparing our spatiotemporal-based numerical results, we can report that $A=2.23219$ provides a relatively more accurate result than the other values of $A$. In addition, we notice that the maximum amplitude and speed of the steady-state traveling wave increase with rising values of $A$. The backflow phenomenon occurs in the capillary regime, as observed in the parabolic profile-based two-equation model by Oron et al. [Eur. J. Mech. B: Fluids 28, 1 (2009)]. Interestingly, the combined parabolic and elliptic velocity profile detects the point of inflection in the capillary region at $A=2.23219$, but it disappears at higher values of $A$, signaling a strong influence of the elliptic part of the combined velocity profile in the capillary region.

The separated and reattached flow over backward-facing steps with different spanwise widths is experimentally investigated in a wind tunnel. The height and streamwise length of steps are fixed at 19 mm and 3.95 m, respectively. Five different spanwise aspect ratios ($\mathrm{AR}$), defined as the ratio of step width to height, 1, 2, 4, 8, and 16, are tested. The Reynolds number based on the step height and free-stream velocity is 11 300, and a well-developed turbulent boundary layer is present before the flow encounters the step. Planar particle image velocimetry is employed to measure the velocity field along the centerline over and behind the steps. Results show that the three-dimensional effect becomes more significant as $\mathrm{AR}$ increases up to 4 and persists when $\mathrm{AR}=8$, likely attributed to the corner vortices formed alongside the step, as well as rolled up the sidewall shear layer. Surface oil-film flow visualization shows that the effect of side edges on the central flow remains significant until $\mathrm{AR}$ reaches 16. For $\mathrm{AR}=16$, the step flow is nominally two dimensional and exhibits similar characteristics as a typical two-dimensional backward-facing step flow. The mean reattachment length increases with $\mathrm{AR}$ and then tends to approach an asymptotic level, while a much larger $\mathrm{AR}$ may be required for the saturation in the span of the reattachment zone. For $\mathrm{AR}=4$ and 8, a distinct flow structure is observed, characterized by jettisoned flow away from the floor after reattachment, and the distributions of Reynolds stresses are therefore not confined within a narrow region below the step height. The highest Reynolds stresses are observed when $\mathrm{AR}=4$ while the largest-scale turbulence appears when $\mathrm{AR}=2$. Furthermore, as $\mathrm{AR}$ increases, the evolution of vortical structures becomes more complex and the spreading of the shear layer slows down.

Typical unsteady vortex-dominated flows like those involved in bio-inspired propulsion, airfoil separation, bluff body wakes, and vortex-induced vibrations can be prohibitively expensive to simulate and impossible to measure comprehensively. These examples are governed by nonlinear interactions, and often involve moving boundaries, high-dimensional parameter spaces, and multiscale flow structures. The classical way to get around these challenges has been to reduce the experimental complexity by using canonical motions or simplified unsteady inflow conditions. A paradigm shift is emerging in the form of self-exploring automated experiments that combine the automation of the experimental pipeline with data-science tools to increase experimental throughput and expedite scientific discovery. Such automated experiments can explore and exploit higher-dimensional parameter spaces and cover more realistic and technically relevant unsteady conditions compared to what is traditionally feasible with supervised canonical experiments. This alternative approach can yield robust and generalizable models and control solutions, as well as the discovery of rare and extreme events. Here, we provide a perspective on the transformative potential of self-exploring automated experiments for the discovery, optimization, and control of unsteady vortex-dominated flow phenomena.

The predictability of isotropic turbulence is studied with unprecedented detail using massive Monte Carlo ensembles. Predictability loss is characterized by the smoothing of the ensemble-averaged flow field with the forecasting time, which is accurately captured by the ensembles. It is shown that this process is well described in scale and physical space by a Gaussian low-pass filter, with a characteristic length scale that increases in time following a self-similar scaling. These results simplify the quantification of uncertainty in turbulence forecasts and open the possibility to efficiently assess the predictability of local inertial- and large-scale flow patterns.

Impact of particle-in-liquid compound drops on solid wall is investigated numerically using a diffuse-interface immersed-boundary method. We focus on the effect of the properties of the particles on the spreading and retraction dynamics of the compound drops. Numerical simulation results reveal that with an increase in the particle volume fraction ($\alpha$), there is a corresponding decrease in the volume of fluid involved in spreading. As a result, the presence of particles within the drops inhibits the spreading of the compound drops. Specifically, the maximal spreading ratio (${\beta }_{\max }$) can be scaled by $1-\alpha$, analogous to the scaling observed in pure drops. Conversely, both the rebound coefficient and particle density exert minimal effect on ${\beta }_{\max }$ at same $\alpha$. Additionally, the presence of particles is found to promote compound drop rebound, leading to a reduction in droplet-wall contact time.

Vertical soap films drain under the influence of gravity, as indicated by the downward motion of colorful horizontal interference fringes observed on their surfaces. In this study conducted with rectangular soap films, we experimentally characterize the descent dynamics of these isothickness fringes and report its self-similar nature, which additionally features a power law relationship between thickness and time. We also show that this result is equivalent to thickness profiles exhibiting a separation of space and time. By integrating new measurements with data from the literature across various conditions, we validate these properties and establish the universality of the dynamics by collapsing all data onto a single master curve. Our findings provide a general framework to compare studies with each other and thus pave the way toward a comprehensive characterization of the drainage of vertical soap films, along with the mechanism of marginal regeneration at the origin of the process.

We investigate the two-dimensional shock-induced instability of a dual-layer gas-particle (DLGP) mixture, with particle volume fractions on the order of ${10}^{-3}$ and moderate mass loading at the initial time. We elucidate the mechanism underlying the instability in the DLGP mixture using vorticity budgets, wave system analysis, and particle dynamics. The mechanism is distinct from that in the dual-layer gas (DLG) mixture. In the DLG mixture, the shock-induced instability is driven by the baroclinic vorticity. By contrast, in the DLGP mixture, the vorticity budgets suggest that the instability is not triggered by the baroclinic vorticity, because its contribution is negligible. Instead, the shock-induced instability in the DLGP mixture is induced by the pressure perturbation near the perturbed interface. The particle dynamics show that the velocity difference in particles near the perturbed interface is driven by the velocity difference in gas through the drag force. Thus, the velocity difference in- gas induced by the pressure perturbation drives the particle interface to grow via dragcoupling effects. Inspired by the interfacial instability mechanism, we estimate the growth of the particle interface in the linear stage. The model incorporates the multiphase Atwood number and the Stokes number, and well captures the linear growth rate of the particle-phase interface amplitude at moderate Atwood and Stokes numbers.

We demonstrate the existence of interface-induced turbulence, an emergent nonequilibrium statistically steady state (NESS) with spatiotemporal chaos, which is induced by interfacial fluctuations in low-Reynolds-number binary-fluid mixtures. We uncover the properties of this NESS via direct numerical simulations (DNSs) of cellular flows in the Cahn-Hilliard-Navier-Stokes (CHNS) equations for binary fluids. We show that, in this NESS, the shell-averaged energy spectrum $E\left(k\right)$ is spread over more than one decade in the wavenumber $k$ and it exhibits a power-law region, indicative of turbulence but without a conventional inertial cascade. To characterize the statistical properties of this turbulence, we compute, in addition to $E\left(k\right)$, the time series $e\left(t\right)$ of the kinetic energy and its power spectrum, scale-by-scale energy transfer as a function of $k$, and the energy dissipation resulting from interfacial stresses. Furthermore, we analyze the mixing properties of this low-Reynolds-number turbulence via the mean-square displacement (MSD) of Lagrangian tracer particles, for which we demonstrate diffusive behavior at long times, a hallmark of strong mixing in turbulent flows.

The Atlantic Meridional Overturning Circulation (AMOC) is a much studied component of the climate system, because its suspected multistability is associated with tipping behavior yielding potentially large regional and global climatic impacts. In this paper we investigate the global stability properties of the system using an ocean general circulation model. We construct an unstable AMOC state, i.e., an unstable solution of the flow that resides between the stable regimes of a vigorous and collapsed AMOC. Such a solution, also known as a melancholia or edge state, is a dynamical saddle embedded in the boundary separating the competing basins of attraction. It is physically relevant since it lies on the most probable path of a noise-induced transition between the two stable regimes, and because tipping occurs when one of the attractors and the melancholia state collide. Its properties may thus give hints towards physical mechanisms and predictability of the critical transition. We find that while the AMOC melancholia state as viewed from its upper ocean properties lies between the vigorous and collapsed regimes, it is characterized by an Atlantic deep ocean that is fresher and colder compared to both stable regimes. The melancholia state has higher dynamic enthalpy than either stable state, representing a state of higher potential energy that is in good agreement with the dynamical landscape view on metastability.