Is it possible to reconstruct all the scales of turbulence from limited observations? If so, what is the minimum resolution of observations for a successful reconstruction? How much information about a turbulent flow field can be decoded from an isolated, instantaneous measurement? These fundamental questions are addressed using variational data assimilation, where the observations are infused in simulations and are decoded using the Navier-Stokes equations. We highlight the “dual butterfly effect” and how the stochasticity of turbulence obfuscates the interpretation of measurements.

We develop a wave damping model based on a prediction of current- and wave-induced force on individual plants. The model captures 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, all of which affect the wave dissipation by vegetation. The model explains why weak current reduces wave dissipation while strong current increases wave dissipation, as observed both in the present and previous studies. Further, we explore the impact of plant flexibility and leaf morphology on wave dissipation over a wide range of current to wave velocity ratio.

The figures on the left show the effect of the Prandtl number (Pr) of the Rayleigh-Bénard problem with Boussinesq conditions, for the same Grashof number of ${10}^9$. Top: Pr = 12.73; bottom, Pr = ${10}^{-4}$. The plot on the right shows that low molecular Pr yields an inversely varying turbulent Prandtl number; that is, the flow behaves effectively as a high Prandtl number fluid. The data are for non-Boussinesq conditions. The qualitative effect is the same for the Boussinesq case as well, but the dependence has a weaker power law exponent of about $-1/3$.

This article reviews the recent theories and models of space-time energy spectra in turbulent shear flows. The review is based on the picture of turbulent passage proposed by Taylor’s frozen-flow hypothesis and Kraichnan-Tennekes random sweeping hypothesis: convection of small-scale eddies by large-scale eddies with a certain distortion, which determines the peaks and bandwidths of space-time energy spectra. The data-refined stochastic models and data-based reconstruction models are examined. The linearized Navier-Stokes equations with random forcing for space-time energy spectra are also discussed.

Experiments and simulations of a non-Brownian suspension of particles demonstrate that weak van der Waals (adhesive) interactions induce rate dependence of the rheological response in oscillatory shear flow, with enhanced particle diffusivities and cluster formations below a critical shear rate, even though the steady shear behavior remains rate-independent. Phase diagrams showing the influence of volume fraction, strain amplitude, and oscillation frequency, for a given Hamaker constant, highlight the connection between irreversibility and suspension rheology.

When a soap film drains, marginal regeneration refers to the rise of patches that are thinner than the rest of the film. In this work the rise velocities and sizes of buoyant patches are measured and found to be in good agreement with a Rayleigh-Taylor like instability and a model based on a balance of gravitational and surface viscous forces, as suggested in the literature. Thus, in an environment saturated in humidity, to eliminate evaporation effects, marginal regeneration approximately describes the film drainage at the apex of a draining bubble.

The effects of the liquid trapped in a mesh on droplet penetration were investigated. It was found that penetrations could be entirely suppressed by the trapped liquid. 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.

In our work, we motivate and rederive the Large-eddy simulation (LES) framework by coarse-graining of Lagrangian fluid elements making use of a statistical mechanics approach. Consequently, we understand that LES is much more than a numerical turbulence model, namely a perspective commonly taken by modern fluid dynamicists, not only in numerical simulations but also in experiments. From this point of view, we see the potential to develop a unified theory for LES and the Reynolds-averaged Navier-Stokes (RANS) framework and additionally reveal a link to uncertainty quantification in particle image velocimetry (PIV).

A small flag attached to the surface of an airfoil near the leading-edge exhibits self-excited oscillations when the airfoil is set at a post-stall angle of attack. The limit cycle oscillations of the flag between the airfoil surface and the freestream produce leading-edge vortices periodically, resulting in a remarkable increase in the maximum lift coefficient and stall angle. There are strong similarities between this passive flow control method, which relies on the fluid-structure interactions, and the active flow control methods in producing post-stall lift enhancement.

Small-amplitude peristaltic flows occur in many biological systems, and may occur in the inner ear. We present a simple analytic model for such flows, validated using simulations and measurements from a laboratory model of the inner ear. We demonstrate that Lagrangian transport dynamics can be reproduced accurately with our simple analytic model.

A model bacterium with a flexible flagellar hook generically swims along a helical trajectory, even when incorporating detailed hydrodynamics. A bifurcation in the hook’s equilibrium bending angle below a critical bending stiffness can have a dramatic effect on the trajectory’s helical pitch angle. Analytical predictions for the bifurcation’s dependence on the hook’s spontaneous curvature, the shape of the cell body, and the flagellum geometry are provided.

The introduction of a particle into a preexisting nonuniform viscosity field will generally modify the viscosity field in order to satisfy boundary conditions on the particle surface. Here we discuss the effect of this disturbance viscosity on the dynamics of active particles, as well as characterize the relative importance of the local changes in stress versus the nonlocal flow changes due to nonuniform viscosity.

The first observations of colliding jamming fronts show some interesting behavior. After jamming fronts collide, the stress releases and an unjammed region appears.

We study the fall of pancake-shaped drops in a Hele-Shaw cell filled with a more viscous ambient fluid in the case where the drop and ambient fluid are miscible. We propose a theoretical expression for the falling velocity of the drops which takes into account elongated drops with width smaller than the gap of the cell. We also provide experimental evidence for the break-up of miscible drops, which can be caused by internal fluid motion within the drop, or by an instability in the shape of the drop.

The physical mechanism of converting the kinetic energy of turbulence to magnetic energy is known as a dynamo. Fluctuation dynamo amplifies magnetic fields at scales smaller than the driving scale of turbulence. We show that the fluctuation dynamo in subsonic turbulent plasma is similar to the supersonic case in some aspects and very different in others.

We conduct experimental research on binary liquid metal droplet collisions under the influence of a horizontal magnetic field. For magnetic intensity smaller than 1.5 T, only reflexive separation is obviously facilitated, but other collision regimes show little difference with zero magnetic intensity. We infer that when magnetic intensity is larger than a critical value of 4 T, remarkable influences on all regimes would be observed.

We study electrohydrodynamic instabilities in a freely suspended liquid film subject to a normal electric field. The behavior of the system is characterized as a function of the relevant dimensionless groups during the linear and nonlinear regimes of growth. We demonstrate how the coupling of flow and surface charge transport in different modes of instability can give rise to manifold nonlinear phenomena such as tip streaming or pinching of the film into droplets.

This manuscript presents a derivation of path equations to describe the dynamics of thin jets evolving along temperature fronts. The results show spiral-like solutions, as opposed to the case of jets arising at potential vorticity fronts.

A predator-prey model of plankton dynamics in a turbulent flow past an idealized island is studied through fully-resolved numerical simulations to understand the complex interplay between biological excitable behavior and flow transport. We provide evidence that for a certain relation between advective and biological time scales, plankton accumulates in localized filamentary regions where velocity gradients compete with reaction-diffusion spreading, favoring persistence and primary production. The impact of small turbulent scales and of the geometrical details of the obstacle are investigated as well, quantifying their effects on plankton dynamics and patchiness.

We study the influence of transverse confinement on the linear instability properties of velocity and density distributions evoking exchange flows in stratified inclined ducts. In the chosen parameter space, we find that the presence of lateral walls has a stabilizing effect. The growth-rate predictions for the spanwise-invariant cases are almost systematically an upper bound to the growth-rate corresponding to the confined geometry. In addition, accounting for spanwise-varying perturbations result in the proliferation of unstable modes that present an odd-even regularity in their spatial structures, which is rationalized by comparison to the dispersion relation obtained for oblique waves.

We study the primary bifurcations of a plane parallel flow in a channel with Kolmogorov forcing. We find a new type of bifurcation with both the oscillation frequency and the amplitude of the growing mode being zero at the threshold. We call this a stationary drift bifurcation. The laminar steady flow can display different types of bifurcation depending on the forcing wave number of the base flow. This is in contrast to the case of doubly periodic boundary conditions for which the primary bifurcation is stationary.

Different regimes of temperature modulated breakup were studied using a slender jet model. The instability is induced through capillary and Marangoni stresses and can be used to control droplet formation in terms of intact length and resultant drop size distribution, which is otherwise irregular due to the inevitable presence of background noise. When thermal modulation is weak, the surface tension gradient forces act only as a trigger and curvature-gradient forces soon take over and grow exponentially downstream of the jet due to inertio-capillary growth. When thermal modulation is strong, the surface tension gradient forces not only act as a trigger, but remain significant till breakup.

The Richtmyer-Meshkov (RM) instability has long been an interesting subject due to its fundamental significance in scientific research. In the current study, the contribution of shock Mach number on the evolution of the RM instability induced by a shock-accelerated square light bubble is investigated numerically. The shock Mach number causes significant changes in flow morphology, resulting in complex wave patterns, vorticity generation, vortex formation, and bubble deformation. The Mach number effects are explored in detail through various physical phenomena such as vorticity production, kinetic energy, dissipation rate, and enstrophy.

When two droplets with different surface tensions collide, the shape evolution of the merging droplets is asymmetric. Here, we reveal the importance of capillary waves in this process, and systematically study the influence of both inertia and surface tension. Counterintuitively, the Marangoni effect reduces the asymmetry.

Motivated by small-scale natural and industrial processes involving flow over and/or through a layer of a porous medium, a mathematical model for the steady gravity-driven flow of a slowly varying and thin rivulet of fluid over and through an even thinner permeable membrane is formulated and analyzed. The three-dimensional shape of the free surface of a rivulet with either fixed semi-width or fixed contact angle is determined, and it is shown how the length, base area and volume of the rivulet on the permeable part of the membrane depend on the physical properties of the system.

We show for the first time that only one similarity solution that describes the break-up of viscous liquid threads is linearly stable, while other similarity solutions are unstable. Complex eigenvalues lead to the presence of oscillations close to the break-up.

A two-layer falling film consisting of two viscous fluids with identical density but different viscosity lining the interior of a vertical tube is studied using a long-wave asymptotic model. The impact of the viscosity ratio on the film linear stability and nonlinear dynamics are explored. It is shown that a less viscous outer layer can decrease the total film thickness required for plugs to form; the significance of this study for applications, including human airways, is briefly discussed.

Interfacial swimmers self-propel by maintaining a surface tension gradient around them, often through the release of a surfactant. The symmetry-breaking mechanism underlying motion of symmetric swimmers is qualitatively understood but the role of Marangoni flows in self-propulsion has never been elucidated. We address this question by numerical methods, which can handle the complex couplings at play. We find that Marangoni flows play a key role near the onset of swimming but have only a modest influence at large velocities. We discuss the generality of those conclusions and their relation to experiments.

We consider the formation of liquid marbles via impact onto powder beds. Experimentally we analyze how much powder the surface of the drop is able to harvest and discover how this determines the threshold for marble formation. This motivates the development of the first mathematical model for this process and simulations based on this model qualitatively recover many features of the experiments, while also highlighting avenues for future research.

In 1851, Stokes (in insert) calculated the friction force on a cylinder in oscillating motion, neglecting the nonlinear term of the Navier-Stokes equation, an approximation valid for vanishing values of the Reynolds number Re. Previous tests were performed with Re>0.1 and frequently with Re»1. We have measured the oscillation of a macroscopic gravity pendulum. Our position detector with a submicrometer sensitivity enables us to record very small oscillation amplitudes, corresponding to Re=0.0002. The friction force deduced from the damping time constant is in very good agreement with Stokes’ calculation.

A study of caking in a concertinaed filtration membrane uncovers potential inaccuracies in using flux–throughput curves to determine filter-blocking behavior, and further explores the effect of membrane properties and configuration on flow and blocking dynamics.

Interface-resolved direct numerical simulations are performed to investigate the effects of clean (top) and contaminated (bottom) bubbles driven upward in Newtonian and viscoelastic turbulent channel flows. It is found that the viscoelasticity promotes formation of the bubble-wall layers and thus the polymer drag reduction is completely lost for the surfactant-free bubbly flows. An addition of a minute amount of Triton X-100 to the viscoelastic turbulent bubbly flow system is found to be sufficient to revive the polymer drag reduction effects.

Direct Numerical Simulations are employed to investigate preferential concentration of heavy inertial particles in a system in which turbulence is mechanically-driven. Using the two-fluid equations, we study this process and the resulting particle concentration enhancement for particles with $\text{St}\lesssim O(0.01)$. The results are similar to those found in previous work, where we established scaling laws to predict maximum and typical particle concentration enhancements in the context of the particle-driven convective instability.

We explore the behavior of granular avalanches of nonconvex cross-shaped particles as a step forward in the modeling of entangled granular media. We conduct experiments and simulations of a dam break setup and report several flow regimes such as the top-driven collapse and the intermittent regime, in which the granular column sometimes remains stable and the flow outcome is determined by the random initial microstructure.

A generalization of Stokesian dynamics is formulated to describe hydrodynamic interactions between two spheres in a viscous fluid. The analysis quantifies transient mutual interactions in terms of frequency-dependent friction coefficients of both spheres as well as their temporally varying mobility response to an impulsive force. The analysis also contributes to work on many-body unsteady Brownian motions.

The phase interaction force in a multiphase flow is decomposed into a particle-mean field force and a divergence of a Particle-Fluid-Particle (PFP) stress. The particle mean field force is mainly accounted for through drag models, while the PFP stress arising from the interparticle interactions is seldom reported. Using the nearest particle statistics, the PFP stress is calculated from particle-resolved simulations. The PFP stress represents the macroscopic effect of the drafting-kissing-tumbling mechanism.

Wettability characterization of a porous material has been mainly addressed so far in terms of an average contact angle. Here, a methodology is proposed to determine the contact angle spatial distribution of the medium in a statistical sense and the hydrophilic pore fraction, assuming the contact angle to take binary values. This is achieved by means of a minimization procedure on the relative permeability and capillary pressure curves with an inverse method based on pore network model and genetic and hill climbing algorithms.

Wind- and water-driven migrating sand dunes frequently interact with elevated natural and artificial topographical features. Generically, dunes interact with obstacles either by ‘crossing’ over the obstacle or by being ‘trapped’. We study this problem in an idealized quasi-two-dimensional laboratory experiment. We show that the outcome – crossing or trapping – depends on the size and shape of the obstacle and we relate these observations to the flow structure in the immediate vicinity of the obstacle.

Drag and lift forces experienced by a rigid spherical particle translating close to a flat wall in a linear shear flow are determined through fully resolved simulations. Particles are assumed to obey either a non-rotating or a torque-free condition and may either lead the fluid or lag behind it. The simulations cover a wide range of flow regimes, from low-but-finite Reynolds numbers to conditions close to the onset of wake unsteadiness. Results are used to build accurate semiempirical expressions for the two force components valid at arbitrary Reynolds number, relative shear rate, and separation distance from the wall.

Higher order equations governing long surface waves in shallow water beyond the standard Korteweg-de Vries and Kadomtsev-Petviashvili equations are derived from the full water wave equations. The higher order dispersive and nonlinear terms in these equations lead to resonance between nonlinear wave structures and dispersive radiation. This resonance between solitary waves and dispersive shock waves (undular bores) is studied numerically and analytically using exponential asymptotic theory. A key result is that there is a near node in the resonant wave amplitude for the higher order equations with the water wave coefficients.

The flow fields of direct numerical simulation of turbulent channel flow are decomposed into large scales and small scales based on the interscale energy transfer spectra. The former is characterized by streaks and quasi-streamwise vortices even in the outer layer, and the latter is characterized by hairpin-like vortical structures that are similar to the original flow fields. We further investigated the coherent structures associated with the real-space energy transfer. The formation of small-scale hairpin-like vortices is related to the large-scale shear layer.

This paper established the existence of non-Kolmogorov turbulence in free shear flows. The authors propose a set of dissipation laws and link them with the spreading rates as well as the entrainment coefficient, which varies with the rise of the plume in contrast to the Kolmogorov case. The work also show how the parameters of two stretching transformations determine both Kolmogorov and non-Kolmogorov turbulence.

A self-consistent closure theory of the passive scalar turbulence has been developed on the basis of the Hessian of the scalar field, where the characteristic timescale of the scalar is properly incorporated via Lagrangian time-advancement of the Hessian. Without relying on any empirical parameter, the theory reasonably predicts the Obukhov-Corrsin spectrum of the inertial-convective range with its universal constant.

Turbulent flows contain occasional, well-separated sharp features, as illustrated in this picture by Bonn et al. (1993), reproduced with permission, surrounded mostly by low levels of activity. Both interacting structures contribute to the complexity of turbulence. A full theory requires the understanding of both, which is what our paper attempts to do. We predict quantitatively the multi-scaling exponents for these singular-like features of different strengths, while also showing that the background flow is Gaussian. The large spatial separation between the sharp structures enables one to treat them as a “weakly interacting gas”.

Due to the inverse energy cascade, when the energy dissipation length scale in two-dimensional turbulence is larger than the domain size, energy is expected to condense into the lowest allowed mode. Thus, the appearance of large-scale structures is often taken as a proxy for spectral condensation, particularly in laboratory realizations of two-dimensional turbulence. We show that large-scale flows alone, however, are not robust indicators of spectral condensation, because small domains may both weaken the inverse cascade and introduce new dissipation mechanisms.

Is an autonomous large eddy simulation (LES) possible where a subgrid-scale (SGS) model is extracted in a bootstrapping way from LES fields? We show how the SGS energy transfer among resolved scales and its wave number distribution can be obtained from evolving LES fields. This information, supplemented by known asymptotic properties of energy flux in the inertial range, allows self-contained LES without prescribing extraneous SGS models. The method is tested in LES of isotropic turbulence at high Reynolds number (Re) where inertial range dynamics is expected and for lower Re decaying turbulence under conditions of the classical Comte-Bellot and Corrsin experiments (energy spectra in figure).

Data assimilation is employed to improve the accuracy of large-eddy simulation (LES) of wall-bounded flows. The methodology is adjoint-free and can assimilate any reference statistical quantities that are available from experiments or direct simulations. The outcome is enhanced fidelity LES that outperforms a variety of traditional subgrid models.

In the statistical point of view, the skewness of the longitudinal velocity gradient is usually related to energy transfer in turbulence, for example, the Kolmogorov forward energy cascade in fully developed turbulence implies negative skewness, while Gaussian random noise and infinitesimal perturbations lead to zero skewness. We show by two DNS cases that, in the early transition stage, the skewness can be positive, in contrast to the energy cascade in equilibrium turbulence.

Using direct numerical simulations, we studied the effects of roughness in a turbulent plane Couette flow where one wall is rough and the other one is smooth. Two different roughness configurations are simulated, and the results are compared with the case where both walls are smooth. Upon roughening a wall, roughness would generate vortical structures near the vicinity of the roughness elements and enhance turbulence locally. In the current study, however, we report that turbulence is enhanced near both the rough and the smooth walls.

Vortex rings are self-propagating structures that can transport mass and momentum to locations remote from the ring creation. We focus on the reorganization of a light vortex ring impinging, at a given angle to the vertical, a layer of fluid stably stratified in density, as in many environmental applications. We also examine the stratified layer response with regard to baroclinic vorticity and internal gravity wave generation. The symmetry of both the flow and wave field is preserved over time for normal impacts. For inclined impacts, the flow reorganizes into a vertically flattened dipolar structure and internal gravity waves radiate from two sources that match with the dipole cores.

We investigated how vortex rings disintegrate across several geometries: head-on collisions between two rings and the impact of a single ring against a wall. We found that at sufficiently large Reynolds number, vortices produce a turbulent cloud regardless of the underlying geometry, but the instability leading to the decay is very dependent on the geometry and the radius ratio, and this determines the main flow dynamics. We also found that the ejection of secondary rings can happen for impact against a stress-free wall and in the head-on collision of two rings under very specific circumstances which depend on traveling distance and noise levels.

A circular hydraulic jump is a discontinuous rise of the downstream height of a radially outflowing liquid (water). The discontinuous circular front, which can be easily seen in a kitchen sink, is a hydrodynamic white hole. When two such impenetrable white holes collide, rather than yielding any ground to each other, they force a wall of liquid to stand between themselves. We associate surface tension with this phenomenon.

A horizontal vortex in a moving stratified flow will have the density field overturn along the axis of the vortex. Gravity distorts this steady vortex, ultimately leading to three instabilities. The twirling and rolling instabilities are strong for small Froude number and small pitch. The streaming instability is strong for large pitch and is independent of Froude number.

The distinctive wave pattern that forms behind the stern of a moving ship is the result of a combination of divergent and transverse waves across all wavenumbers. At a fixed point in space, as a ship travels past, these waves produce a surface elevation signal in which properties of the ship are encoded in a complicated way. Motivated by the challenge of how to decode such signals, we explore their frequency spectrum using spectrograms. Recent findings are extended to allow for the ship to accelerate along arbitrary paths instead of simply traveling steadily in a straight line.