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.

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

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

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

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

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

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

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

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

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