The impact of droplets on dry and prewetted meshes was investigated using high-speed photography. The prewetting resulted from previous impacts. It was observed that an increase of the Weber number We resulted in a transition from no penetration of the mesh through an incomplete penetration to a complete penetration. It was found that both penetrations could be entirely suppressed by liquid trapped in the mesh (prewetted mesh), with the height $h$ of the sessile droplet being a key factor. The phase diagram in the $(\mathrm{We}, h)$ plane determining the expected type of impact has been determined. The transition Weber numbers for both types of penetration increased monotonically with $h$. A model for predicting the transition thresholds is proposed and compared with experimental results. It is suggested that the impact type is determined by the momentum exchange between the impacting droplet and the liquid trapped in the mesh.

Wind- and water-driven migrating sand dunes frequently interact with elevated natural and artificial topographical features. The dune-obstacle interaction can alter the migrating behavior of the dune and, depending on the nature of the obstacle, it may generate various societal and technological risks. Here we study the problem of dune-obstacle interaction in a paradigmatic quasi-two-dimensional domain realized in a subaqueous laboratory experiment. Generically, dunes interact with obstacles either by crossing over the obstacle or by being trapped. We describe how the selection of these two distinct dynamical behaviors depends on the size and shape of the obstacle, focusing in particular on the fluid flow in the immediate vicinity of the obstacle. Specifically, we perform a modal decomposition of the measured flow field and we discover that the outcome of the dune-obstacle interaction is closely related to the flow structure above the obstacle.

A nonintrusive data assimilation methodology is developed to improve the statistical predictions of large-eddy simulations (LES). The ensemble-variational (EnVar) approach aims to minimize a cost function that is defined as the discrepancy between LES predictions and reference statistics from experiments or, in the present demonstration, independent direct numerical simulations (DNS). This methodology is applied to adjust the Smagorinsky subgrid model and obtain data assimilated LES (DA-LES) which accurately estimate the statistics of turbulent channel flow. To separately control the mean and fluctuations of the modeled subgrid tensor, and ultimately the first- and second-order flow statistics, two types of model corrections are considered. The first one optimizes the wall-normal profile of the Smagorinsky coefficient, while the second one introduces an adjustable steady forcing in the momentum equations to independently act on the mean flow. Using these two elements, the data assimilation procedure can satisfactorily modify the subgrid model and accurately recover reference flow statistics. In a posteriori testing, the retrieved subgrid model significantly outperforms more elaborate baseline models such as dynamic and mixed models. The robustness of the present data assimilation methodology is assessed by changing the Reynolds number and considering grid resolutions that are away from usual recommendations. Taking advantage of the stochastic formulation of EnVar, the developed framework also provides the uncertainty of the retrieved model.

In statistically homogeneous and isotropic turbulence, the average value of the velocity increment ${\delta }_{r}u=u(x+r)-u\left(x\right)$, where $x$ and $x+r$ are two positions in the flow and $u$ is the velocity in the direction of the separation distance $r$, is identically zero, and so to characterize the dynamics one often uses the Reynolds number based on $\sqrt{\langle {\left({\delta }_{r}u\right)}^2\rangle }$, which acts as the coupling constant for scale-to-scale interactions. This description can be generalized by introducing structure functions of order $n$, $S_n=\langle {\left({\delta }_{r}u\right)}^n\rangle$, which allow one to probe velocity increments including rare and extreme events, by considering ${\delta }_{r}u\left(n\right)=O\left(S_n^{1/n}\right)$ for large and small $n$. If $S_n\propto r^{{\zeta }_n}$, the theory for the anomalous exponents ${\zeta }_n$ in the entire allowable interval $-1<n<\infty$ is one of the long-standing challenges in turbulence (one takes absolute values of ${\delta }_{r}u$ for negative $n$), usually attacked by various qualitative cascade models. We accomplish two major tasks here. First, we show that the turbulent microscale Reynolds number $R_{\lambda }^T$ (based on a suitably defined turbulent viscosity) is 8.8 in the inertial range with anomalous scaling, when the standard microscale Reynolds number $R_{\lambda }$ (defined using normal viscosity) exceeds that same number (which in practice could be by a large factor). When the normal and turbulent microscale Reynolds numbers become equal to or fall below 8.8, the anomaly disappears in favor of Gaussian statistics. Conversely, if one starts with a Gaussian state and increases $R_{\lambda }$ beyond 8.8, one ushers in the anomalous scaling; the inference is that $R_{\lambda }^T\approx 8.8$ and remains constant at that value with further increase in $R_{\lambda }$. Second, we derive expressions for the anomalous scaling exponents of structure functions and moments of spatial derivatives, by analyzing the Navier-Stokes equations in the form developed by Hopf. We present a novel procedure to close the Hopf equation, resulting in expressions for ${\zeta }_n$ in the entire range of allowable moment order $n$, and demonstrate that accounting for the temporal dynamics changes the scaling from normal to anomalous. For large $n$, the theory predicts the saturation of ${\zeta }_n$ with $n$, leading to several inferences, two among which are (a) the smallest length scale ${\eta }_n=L{\text{Re}}^{-1}\ll L{\text{Re}}^{-3/4}$, where Re is the large-scale Reynolds number, and (b) that velocity excursions across even the smallest length scales can sometimes be as large as the large-scale velocity itself. Theoretical predictions for each of these aspects are shown to be in excellent quantitative agreement with available experimental and numerical data.

This study considered how the presence of current impacted wave dissipation within a meadow of flexible marsh plants. A wave-damping model was developed from a prediction of current- and wave-induced force on individual plants. The model was validated with laboratory experiments. Wave decay was measured over a meadow of flexible model plants geometrically similar to Spartina alterniflora with and without a following current. Consistent with previous observations, the wave energy dissipation depended on the ratio of current velocity ($U_c$) to wave velocity ($U_w$). Compared to the same pure wave condition, wave energy dissipation was enhanced by large $U_c/U_w$ but can be decreased for small $U_c/U_w$. Once validated, the wave-damping model was used to explore a wider range of wave, current, and meadow conditions in order to illustrate the influence of reconfiguration on wave forces; the impact of current on wave group velocity; and the modification of in-canopy time-mean and wave orbital velocity associated with canopy drag.

We consider the influence of transverse confinement on the instability properties of velocity and density distributions reminiscent of those pertaining to exchange flows in stratified inclined ducts, such as the recent experiment of Lefauve et al. [J. Fluid Mech. 848, 508 (2018)]. Using a normal mode streamwise and temporal expansion for flows in ducts with various aspect ratios $B$ and nontrivial transverse velocity profiles, we calculate two-dimensional (2D) dispersion relations with associated eigenfunctions varying in the “crosswise” direction, in which the density varies, and the spanwise direction, both normal to the duct walls and to the flow direction. We also compare these 2D dispersion relations to the so-called one-dimensional (1D) dispersion relations obtained for spanwise invariant perturbations, for different aspect ratios $B$ and bulk Richardson numbers ${\text{Ri}}_b$. In this limited parameter space, the presence of lateral walls has a stabilizing effect, in that the 1D growth-rate predictions are almost systematically an upper bound to the 2D growth rates, which in turn decrease monotonically as lateral walls are brought together with increased spanwise confinement ($B\to 0$). Furthermore, accounting for spanwise-varying perturbations results in a plethora of unstable modes, the number of which increases as the aspect ratio is increased. These modes present an odd-even regularity in their spatial structures, which is rationalized by comparison to the so-called one-dimensional oblique dispersion relation obtained for oblique waves, characterized by a continuously varying spanwise wavenumber in addition to the streamwise wavenumber. Finally, we show that in most cases, the most unstable 2D mode is the one that oscillates the least in the spanwise direction, as a consequence of viscous damping. However, in a limited region of the parameter space and in the absence of stratification, we show that a secondary mode with a more complex “twisted” structure dominated by crosswise vorticity becomes more unstable than the least oscillating Kelvin-Helmholtz mode associated with spanwise vorticity.

We report existence of nonequilibrium turbulent dissipations in buoyant axisymmetric plumes at infinite Reynolds number limit. The plume statistical equations remain form invariant under one translation parameterized by $a_0$ and two unequal stretching transformations parameterized by $a_1$ and $a_2$ of flow variables, except the pressure-strain-rate equation. The dissipation coefficients, unlike Kolmogorov theory, in the scaling of dissipations ${\epsilon }_u$ of velocity fluctuation $u^{\prime }$ and ${\epsilon }_{\theta }$ of thermal fluctuation ${\theta }^{\prime }$ evolve linearly with spreading rate $d\delta /dz$. The spreading rate is expressed as inversely proportional to local Reynolds number ${\mathrm{Re}}_{\delta }$ raised to the exponent $m=3(a_1-a_2)/(a_1+a_2), a_1\ne -a_2$ and is varying with ${\mathrm{Re}}_{\delta }$ for $m\ne 0$. The components of Reynolds stress tensor have different streamwise (s) evolutions as ${\left(\overline{w^{\prime 2}}\right)}_s={\left(\overline{v^{\prime 2}}\right)}_s\propto {(d\delta /dz)}^2{\left(\overline{u^{\prime 2}}\right)}_s$ and ${\left(\overline{u^{\prime }{v}^{\prime }}\right)}_s\propto d\delta /dz{\left(\overline{u^{\prime 2}}\right)}_s$ unless $d\delta /dz$ is a constant, which holds only if $m=0$ giving $a_1=a_2$. This implies that Kolmogorov equilibrium theory ($m=0$) is intertwined inextricably with complete self-preservation. There is a direct universal relationship between turbulent dissipation and entrainment coefficient $\alpha$ as $d\delta /dz\propto \alpha$, the proportionality constant depends on integrals of mean axial velocity, temperature difference, and turbulent stresses. The power exponent in power-law streamwise evolutions of flow quantities are specified by the ratio $a_2/a_1$ and differs from the conventional results unless $m=0$. Both the local axial velocity and temperature difference widths are increasing with the increase of vertical distance from the source, as same power-law scaling exponents but differ due to different prefactors. However, the spreading rates and entrainment coefficient decrease in the non-Kolmogorov dissipation region, which occurs when $m\ne 0$ preferably lying in (0,1] ($a_2/a_1\in [1/2,1)$). Similar trends of spreading rate and entrainment were also measured experimentally in planar jet [Cafiero and Vassilicos, Proc. R. Soc. London A 475, 20190038 (2019)] and established theoretically in planar jet and plume [Layek and Sunita, Phys. Rev. Fluids 3, 124605 (2018); Layek and Sunita, Phys. Fluids 30, 115105 (2018)].

Extremely small amounts of surface-active contaminants are known to drastically modify the hydrodynamic response of the water-air interface. Surfactant concentrations as low as a few thousand molecules per square micron are sufficient to eventually induce complete stiffening. In order to probe the shear response of a water-air interface, we design a radial flow experiment that consists in an upward water jet directed to the interface. We observe that the standard no-slip effect is often circumvented by an azimuthal instability with the occurrence of a vortex pair. Supported by numerical simulations, we highlight that the instability occurs in the (inertia-less) Stokes regime and is driven by surfactant advection by the flow. The latter mechanism is suggested as a general feature in a wide variety of reported and yet unexplained observations.

We experimentally examine the formation of viscous fluid threads in hydrodynamic focusing sections using both miscible and immiscible fluid pairs at relatively low flow rates. A systematic comparative study is conducted between diffusive and capillary regimes using a viscous oil and a variety of polar organic solvents in a simple microflow geometry. Silicone oil and various low molecular weight alcohols are used as model fluids to investigate the dynamics of viscous multiphase flows at ultralow interfacial tension and with partially miscible systems. An original methodology based on analysis of thread width and detachment length in the viscous regime is developed to quantify various interfacial destabilization processes over a wide range of injection flow rates. For miscible fluid pairs, we investigate several regimes of thread swelling and, for immiscible fluid pairs, we discuss diverse modes of droplet formation and wetting dynamics. This work provides a comprehensive general classification of immiscible and miscible fluid dynamics with large viscosity contrasts in microchannels together with a unifying phenomenological description of thread behavior based on simple functional relationships to better delineate the role of flow parameters and fluid properties on viscous microflow processes.

Modeling realistic fluid and plasma flows is computationally intensive, motivating the use of reduced-order models for a variety of scientific and engineering tasks. However, it is challenging to characterize, much less guarantee, the global stability (i.e., long-time boundedness) of these models. Previous work provided a theorem outlining necessary and sufficient conditions to ensure global stability in systems with energy-preserving, quadratic nonlinearities, with the goal of evaluating the stability of projection-based models. In this work, we incorporate this theorem into modern data-driven models obtained via machine learning. First, we propose that this theorem should be a standard diagnostic for the stability of projection-based and data-driven models, examining the conditions under which it holds. Second, we illustrate how to modify the objective function in machine learning algorithms to promote globally stable models, with implications for the modeling of fluid and plasma flows. Specifically, we introduce a modified “trapping SINDy” algorithm based on the sparse identification of nonlinear dynamics (SINDy) method. This method enables the identification of models that, by construction, only produce bounded trajectories. The effectiveness and accuracy of this approach are demonstrated on a broad set of examples of varying model complexity and physical origin, including the vortex shedding in the wake of a circular cylinder.

Particles transported in fluid flows, such as cells, polymers, or nanorods, are rarely spherical. In this study, we numerically and theoretically investigate the dispersion of an initially localized patch of passive elongated Brownian particles in a two-dimensional Poiseuille flow, demonstrating that elongated particles exhibit an enhanced longitudinal dispersion. In a shear flow, the rods translate due to advection and diffusion and rotate due to rotational diffusion and their classical Jeffery's orbit. The magnitude of the enhanced dispersion depends on the particle's aspect ratio and the relative importance of its shear-induced rotational advection and rotational diffusivity. When rotational diffusion dominates, we recover the classical Taylor dispersion result for the longitudinal spreading rate using an orientationally averaged translational diffusivity for the rods. However, in the high-shear limit, the rods tend to align with the flow and ultimately disperse more due to their anisotropic diffusivities. Results from our Monte Carlo simulations of the particle dispersion are captured remarkably well by a simple theory inspired by Taylor's original work. For long times and large Péclet numbers, an effective one-dimensional transport equation is derived with integral expressions for the particles' longitudinal transport speed and dispersion coefficient. The enhanced dispersion coefficient can be collapsed along a single curve for particles of high aspect ratio, representing a simple correction factor that extends Taylor's original prediction to elongated particles.

The relaxation dynamics of a fluid-filled blister between an elastic sheet and a porous substrate are controlled by the deformation of the elastic sheet, the viscous stresses in the pores, and the capillary pressure at the liquid-air interface due to imbibition. We develop a mathematical model to study the effects of varying the permeability of the porous substrate, the bending stiffness of the elastic sheet, and the blister size on the relaxation dynamics. Experiments are conducted by injecting a finite volume of viscous fluid between a porous substrate and an elastic sheet, where fluid first invades the pores, and subsequently, as the pressure in the fluid increases, the elastic sheet is peeled and uplifted from the substrate to form a fluid-filled blister. After injection is stopped, the fracture front is static, and the elastic stresses in the overlying sheet and the capillary pressure at the liquid-air interface drive the drainage of the blister into the pores. We identify two regimes of drainage. For thick sheets and more permeable substrates, drainage is primarily due to the stresses in the deformed elastic sheet. For thin sheets and less permeable substrates, drainage is driven by the imbibition of the liquid into the pore space. Our model and experiments are relevant to the drainage of fluid-driven fractures in porous media.

The shear instability of stratified fluids is a well-studied problem in transition to turbulence. In temperate lakes, early springs typically lead to a weak thermal stratification involving water both above and below the temperature at which the density maximum occurs. This implies that mixing of two parcels with the same density, but different temperature, can lead to the creation of denser fluid, a phenomenon known as cabbeling. We report on simulations of shear instability in the cabbeling regime. We find that the initial stages of instability are dominated by shear instability, yielding billows. However, these billows are systematically located below the centerline of the shear layer. Three-dimensionalization occurs through Rayleigh-Taylor-like instabilities, and cabbeling efficiency is greatly increased in the fully three-dimensionalized state. By contrasting with initial states that have the same density profile, but a temperature well outside of the cabbeling regime, we demonstrate that the fully three-dimensional state of the density field is fundamentally different in the cabbeling regime.

Following recent evidence that the vortices in decaying two-dimensional turbulence can be classified into small mobile and large quasistationary, this paper examines the evidence that the latter might be considered a crystal whose formation embodies the inverse cascade of energy towards larger scales. Several diagnostics of order are applied to the ostensibly disordered large vortices. It is shown that their geometric arrangement is substantially more regular than random, that they move more slowly than could be expected from simple mean-field arguments, and that their energy is significantly lower than in a random reorganization of the same vortices. This is traced to screening of long-range interactions by the preferential association of vortices of opposite sign and it is argued that this is due to the mutual capture of corotating vortices, in a mechanism closer to tidal disruption than to electrostatic screening. Finally, the possible relation of these stochastic crystals to fixed points of the dynamical system representation of the turbulence flow is briefly examined.

The flow speedup generated by windbreaks can be used to increase the power production of wind turbines. However, due to the increased drag imposed by the windbreaks, their use in large wind turbine arrays has been questioned. We use large eddy simulations to show that windbreaks can increase the power production of large wind farms. A crucial finding is that windbreaks in a wind farm should be much lower than in the single-turbine case. In fact, the optimal windbreak for an isolated turbine can reduce wind-farm performance. The optimal windbreak height in a wind farm namely depends on the right balance between the flow speedup over the windbreak and the drag imposed by all windbreaks in the farm. The increased performance is a result of the favorable total pressure flux created by the windbreaks.

Building on the recent theoretical work of Wray et al. [J. Fluid Mech. 884, A45 (2020)] concerning the competitive diffusion-limited evaporation of multiple thin sessile droplets in proximity to each other, we obtain theoretical predictions for the spatially nonuniform densities of the contact-line deposits (often referred to as “coffee stains” or “ring stains”) left on the substrate after such droplets containing suspended solid particles have completely evaporated. Neighboring droplets interact via their vapour fields, which results in a spatially nonuniform “shielding” effect. We give predictions for the deposits from a pair of identical droplets, which show that the deposit is reduced the most where the droplets are closest together, and demonstrate excellent quantitative agreement with experimental results of Pradhan and Panigrahi [Colloids Surf. A Physicochem. Eng. Asp. 482, 562 (2015)]. We also give corresponding predictions for a triplet of identical droplets arranged in an equilateral triangle, which show that the effect of shielding on the deposit is more subtle in this case.

While wall modeling enables significant reduction in computational cost compared to wall-resolved large eddy simulations (LESs), it often fails to capture laminar-to-turbulence transition processes realistically. This issue arises in part because wall models typically assume that the near-wall flow is in a statistically quasiequilibrium turbulent state and hence incorrectly prescribe turbulent wall stresses in regions that are still laminar during transition. In this work we propose an approach in which the application of the wall model is retained within the turbulent regions of transitional flow where even nascent spots exhibit high-Reynolds-number characteristics, but the wall model is not applied in laminar regions. The local distinction between turbulent and laminar regions is performed using a self-organized map (SOM) [see Z. Wu et al., Phys. Rev. Fluids 4, 023902 (2019)], an unsupervised machine learning classifier. We demonstrate the capability of wall-modeled LES with SOM-based turbulent/nonturbulent classification (WMSOM) in predicting both bypass and orderly transitions in channel flow at target Reynolds numbers of ${\text{Re}}_{\tau }=130$ and 200, respectively. Predictions of bypass transition initiated from localized initial disturbances agree well with direct numerical simulation. For orderly transition, we simulate K- and H-type transitions, due to the interaction of two- and three-dimensional instability waves. We show good predictions for both scenarios, with a slight delay in the transition time. The WMSOM approach offers a significant reduction in computational cost compared to wall-resolved LES.

Nearly 150 years ago, Lord Kelvin proposed the isotropic helicoid, a particle with isotropic yet chiral interactions with a fluid so that translation couples to rotation. An implementation of his design fabricated with a three-dimensional printer is found experimentally to have no detectable translation-rotation coupling, although the particle point-group symmetry allows this coupling. We explain these results by demonstrating that in Stokes flow, the chiral coupling of such isotropic helicoids made out of nonchiral vanes is due only to hydrodynamic interactions between these vanes. Therefore it is small. In summary, Kelvin's predicted isotropic helicoid exists, but only as a weak breaking of a symmetry of noninteracting vanes in Stokes flow.

Some carnivorous mammals (e.g., cats and dogs) lap water with their tongues to drink water at high frequencies. Such a fast moving tongue creates a liquid column out of a bath which is bitten by the mouth for drinking. Presumably, the animals bite just before the pinch-off time of the water column to maximize the water intake. Otherwise, the water column falls back to the bath before being bitten. Such a pinch-off phenomenon in the liquid column can be described as the acceleration-induced (i.e., unsteady) inertia balances with the capillary force. The classical Rayleigh-Plateau instability explains the competition of the steady inertia with the capillarity, but not with the acceleration-induced inertia. In this study, we modify the Rayleigh-Plateau instability in the presence of the fluid acceleration, and show that the most unstable wavenumber and growth rate increase with acceleration. The pinch-off time is theoretically predicted as the $-1/3$ power of the Bond number (i.e, a ratio of the acceleration-induced inertia to capillarity). Finally, measured pinch-off times from previous physical experiments and dog and cat jaw-closing times are shown to be in good agreement with our theoretical pinch-off time. Therefore, our study shows that animals presumably modulate their lapping and jaw-closing time to bite down on the water column before the pinch-off to maximize the water intake.

The wavelength of undulatory kinematics of fish is an important parameter to determine their hydrodynamic performance. This study focuses on numerical examination of this feature by reconstructing the real physiological model and kinematics of steadily swimming Jack Fish. We perform three-dimensional numerical simulations for flows over these models composed of the trunk, and dorsal, anal, and caudal fins. Moreover, we prescribe the carangiform-like motion for its undulation for a range of wavelengths. Undulation with larger wavelengths improves the hydrodynamic performance of the carangiform swimmer in terms of better thrust production by the caudal fin, lower drag production on the trunk, and reduced power consumption by the trunk. This coincides with the formation of stronger posterior body vortices and leading-edge vortices with more circulation on the caudal fin. The real kinematics of Jack Fish surpasses the performance of those with prescribed motion owing to the flexibility of the caudal fin.