We study the dynamic coarsening of wrinkles in an elastic sheet that is compressed while lying on a thin layer of viscous liquid. When the ends of the sheet are instantaneously brought together by a small distance, viscous resistance initially prevents the sheet from adopting a globally buckled shape. Instead, the sheet accommodates the compression by wrinkling. Previous scaling arguments suggested that a balance between the sheet's bending stiffness and viscous effects lead to a wrinkle wavelength $\lambda$ that increases with time $t$ according to $\lambda \propto t^{1/6}$. We show that taking proper account of the compression constraint leads to a logarithmic correction of this result, $\lambda \propto {(t/logt)}^{1/6}$. This correction is significant over experimentally observable time spans and leads us to reassess previously published experimental data.

The flow driven by a rapidly expanding and collapsing cavitation bubble in a narrow cylindrical gap is studied with the volume of fluid method. The simulations reveal a developing plug flow during the early expansion followed by flow reversal at later stages. An adverse pressure gradient leads to boundary layer separation and flow reversal, causing large shear stress near the boundaries. Analytical solution to a planar pulsating flow shows qualitative agreement with the CFD results. The shear stress close to boundaries has implications to deformable objects located near the bubble: Experiments reveal that thin, flat biological cells entrained in the boundary layer become stretched, while cells with a larger cross section are mainly transported with the flow.

This work uses the Mori-Zwanzig (M-Z) formalism, a concept originating from nonequilibrium statistical mechanics, as a basis for the development of coarse-grained models of turbulence. The mechanics of the generalized Langevin equation (GLE) are considered, and insight gained from the orthogonal dynamics equation is used as a starting point for model development. A class of subgrid models is considered which represent nonlocal behavior via a finite memory approximation [Stinis, arXiv:1211.4285 (2012)], the length of which is determined using a heuristic that is related to the spectral radius of the Jacobian of the resolved variables. The resulting models are intimately tied to the underlying numerical resolution and are capable of approximating non-Markovian effects. Numerical experiments on the Burgers equation demonstrate that the M-Z-based models can accurately predict the temporal evolution of the total kinetic energy and the total dissipation rate at varying mesh resolutions. The trajectory of each resolved mode in phase space is accurately predicted for cases where the coarse graining is moderate. Large eddy simulations (LESs) of homogeneous isotropic turbulence and the Taylor-Green Vortex show that the M-Z-based models are able to provide excellent predictions, accurately capturing the subgrid contribution to energy transfer. Last, LESs of fully developed channel flow demonstrate the applicability of M-Z-based models to nondecaying problems. It is notable that the form of the closure is not imposed by the modeler, but is rather derived from the mathematics of the coarse graining, highlighting the potential of M-Z-based techniques to define LES closures.

An intrinsic property of turbulent flows is the exponential deformation of fluid elements along Lagrangian paths. The production of enstrophy by vorticity stretching follows from a similar mechanism in the Lagrangian view, though the alignment statistics differ and viscosity prevents unbounded growth. In this paper, the stretching properties of fluid elements and vorticity along Lagrangian paths are studied in a channel flow at ${\text{Re}}_{\tau }=1000$ and compared with prior known results from isotropic turbulence. To track Lagrangian paths in a public database containing direct numerical simulation results, the task-parallel algorithm previously employed in the isotropic database is extended to the case of flow in a bounded domain. It is shown that above 100 viscous units from the wall, stretching statistics are equal to their isotropic values, in support of the local isotropy hypothesis. In the viscous sublayer, these stretching statistics approach values more consistent with an unsteady two-dimensional shear flow, in which exponential stretching no longer occurs. Normalized by dissipation rate, the stretching in the buffer layer and below is less efficient due to less favorable alignment statistics. The Cramér function characterizing cumulative Lagrangian stretching statistics shows that overall the channel flow has about half of the stretching per unit dissipation compared with isotropic turbulence.

The lifting Hele-Shaw cell problem is a variant of the classical constant-gap Hele-Shaw situation in which the cell gap width is time dependent. Experiments on Newtonian fluid flows in lifting Hele-Shaw cells with large lifting velocities reveal the development of dendriticlike fingered structures that compete among themselves. The usual Darcy law description of the problem, where inertial effects are neglected, has not been able to explain the origin of these competing sidebranched patterns. In this work we use a generalized Darcy law and a perturbative mode-coupling theory to investigate the impact of inertia on the pattern-forming dynamics of the system. Two main results are deduced: Inertia induces a mechanism for finger sidebranching formation and favors the intensification of finger competition events.

We present an extended thermodynamics (ET) theory of dissipative dense gases. In particular, we study the ET theory with six fields, where we neglect shear viscosity and heat conductivity. We postulate a simple principle of duality between rarefied and dense gases. This principle is based on the microscopic analysis of the energy exchange between different modes of the molecular motion. The basic system of equations satisfies all principles of ET, that is, Galilean invariance, entropy principle, and thermodynamic stability (entropy convexity), and, as in the ET theory of rarefied gases, the constitutive equations are completely determined by the thermal and caloric equations of state. The system is simplest after the Euler system, but, in contrast to the Euler system, we may have a global smooth solution due to the fact that the system is dissipative symmetric hyperbolic and satisfies the so-called K condition. There emerge two nonequilibrium temperatures; one is due to the translational modes, and the other is due to the internal modes such as rotation and vibration of a molecule. This viewpoint allows us to understand the origin of the dynamic pressure in a more clear way. Furthermore we evaluate the characteristic velocities associated with the hyperbolic system and address the fluctuation-dissipation relation of the bulk viscosity. As a typical example, we analyze van der Waals fluids based on the present theory.

Direct numerical simulation data for channel flow at a friction Reynolds number of 4200, generated by Lozano-Durán and Jiménez [J. Fluid Mech. 759, 432 (2014)], are used to examine the properties of near-wall turbulence within subranges of eddy-length scale. Attention is primarily focused on the intermediate layer (mesolayer) covering the logarithmic velocity region within the range of wall-scaled wall-normal distance of 80–1500. The examination is based on a number of statistical properties, including premultiplied and compensated spectra, the premultiplied derivative of the second-order structure function, and three scalar parameters that characterize the anisotropic or isotropic state of the various length-scale subranges. This analysis leads to the delineation of three regions within the map of wall-normal-wise premultiplied spectra, each characterized by distinct turbulence properties. A question of particular interest is whether the Townsend-Perry attached-eddy hypothesis (AEH) can be shown to be valid across the entire mesolayer, in contrast to the usual focus on the outer portion of the logarithmic-velocity layer at high Reynolds numbers, which is populated with very-large-scale motions. This question is addressed by reference to properties in the premultiplied scalewise derivative of the second-order structure function (PMDS2) and joint probability density functions of streamwise-velocity fluctuations and their streamwise and spanwise derivatives. This examination provides evidence, based primarily on the existence of a plateau region in the PMDS2, for the qualified validity of the AEH right down the lower limit of the logarithmic velocity range.

We present results from the simultaneous application of planar laser-induced fluorescence (PLIF), particle image velocimetry (PIV) and particle tracking velocimetry (PTV), complemented by direct numerical simulations, aimed at the detailed hydrodynamic characterization of harmonically excited liquid-film flows falling under the action of gravity. The experimental campaign comprises four different aqueous-glycerol solutions corresponding to four Kapitza numbers ($\text{Ka}=14$, 85, 350, 1800), spanning the Reynolds number range $\text{Re}=2.3–320$, and with forcing frequencies $f_{\mathrm{w}}=7$ and $10\mathrm{Hz}$. PLIF was employed to generate spatiotemporally resolved film-height measurements, and PIV and PTV to generate two-dimensional velocity-vector maps of the flow field underneath the wavy film interface. The latter allows for instantaneous, highly localized velocity-profile, bulk-velocity, and flow-rate data to be retrieved, based on which the effect of local film topology on the flow field underneath the waves is studied in detail. Temporal sequences of instantaneous and local film height and bulk velocity are generated and combined into bulk flow-rate time series. The time-mean flow rates are then decomposed into steady and unsteady components, the former represented by the product of the mean film height and mean bulk velocity and the latter by the covariance of the film-height and bulk-velocity fluctuations. The steady terms are found to vary linearly with the flow $\text{Re}$, with the best-fit gradients approximated closely by the kinematic viscosities of the three examined liquids. The unsteady terms, typically amounting to $5\%–10\%$ of the mean and peaking at approximately $20\%$, are found to scale linearly with the film-height variance. And, interestingly, the instantaneous flow rate is found to vary linearly with the instantaneous film height. Both experimental and numerical flow-rate data are closely approximated by a simple analytical relationship with only minor deviations. This relationship includes terms such as the wave speed $c$ and mean flow rate $\overline{Q}$, which can be obtained by relatively simple and inexpensive methods, thus allowing for spatiotemporally resolved flow-rate predictions to be made without requiring explicit knowledge of the full flow-field information underneath the wavy interface.

We study experimentally the occurrence of spontaneous spinning (Quincke rotation) of an ellipsoid in a uniform direct current (dc) electric field. For an ellipsoid suspended in an unbounded fluid, we find two stable states characterized by the orientation of the ellipsoid long axis relative to the applied electric field: spinless (parallel) and spinning (perpendicular). The phase diagram of ellipsoid behavior as a function of field strength and aspect ratio is in close agreement with the theory of Cēbers et al. [Phys. Rev. E 63, 016301 (2000)]. We also investigate the dynamics of the ellipsoidal Quincke rotor resting on a planar surface with normal perpendicular to the field direction. We find behaviors, such as swinging (long axis oscillating around the applied field direction) and tumbling, due to the confinement.

The relative role of convection and diffusion is characterized both numerically and experimentally for porous media flows due to a Rayleigh-Taylor instability of a horizontal interface between two miscible solutions in the gravity field. We show that, though globally convection dominates over diffusion during the nonlinear regime, diffusion can locally be as important as convection and even dominates over lateral convection far away from the fingertips. Our experimental and numerical computations of the temporal evolution of the mixing length, the width of the fingers, and their wavelength are in good agreement and show that the lateral evolution of fingers is governed by diffusion.

When a droplet is placed onto a vertically vibrated bath, it can bounce without coalescing. Upon an increase of the forcing acceleration, the droplet is propelled by the wave it generates and becomes a walker with a well-defined speed. We investigate the confinement of a walker in different rectangular cavities, used as waveguides for the Faraday waves emitted by successive droplet bounces. By studying the walker velocities, we discover that one-dimensional confinement is optimal for narrow channels of width of $D\simeq 1.5{\lambda }_F$. Thereby, the walker follows a quasilinear path. We also propose an analogy with waveguide models based on the observation of the Faraday instability within the channels.

The dynamics and statistical mechanics of $N$ chaotically evolving point vortices in the doubly periodic domain are revisited. The selection of the correct microcanonical ensemble for the system is first investigated. The numerical results of Weiss and McWilliams [Phys. Fluids A 3, 835 (1991)], who argued that the point vortex system with $N=6$ is nonergodic because of an apparent discrepancy between ensemble averages and dynamical time averages, are shown to be due to an incorrect ensemble definition. When the correct microcanonical ensemble is sampled, accounting for the vortex momentum constraint, time averages obtained from direct numerical simulation agree with ensemble averages within the sampling error of each calculation, i.e., there is no numerical evidence for nonergodicity. Further, in the $N\to \infty$ limit it is shown that the vortex momentum no longer constrains the long-time dynamics and therefore that the correct microcanonical ensemble for statistical mechanics is that associated with the entire constant energy hypersurface in phase space. Next, a recently developed technique is used to generate an explicit formula for the density of states function for the system, including for arbitrary distributions of vortex circulations. Exact formulas for the equilibrium energy spectrum, and for the probability density function of the energy in each Fourier mode, are then obtained. Results are compared with a series of direct numerical simulations with $N=50$ and excellent agreement is found, confirming the relevance of the results for interpretation of quantum and classical two-dimensional turbulence.

We investigate the flow over shallow cavities as a representative configuration for modeling small surface irregularities in wall-bounded shear flows. Due to the globally stable nature of the flow, we perform a frequency response analysis, which shows a significant potential for the amplification of disturbance kinetic energy by harmonic forcing within a certain frequency band. Shorter and more shallow cavities exhibit less amplified responses, while energy from the base flow can be extracted predominantly from forcing that impacts the cavity head on. A structural sensitivity analysis, combined with a componentwise decomposition of the sensitivity tensor, reveals the regions of the flow that act most effectively as amplifiers. We find that the flow inside the cavity plays a negligible role, whereas boundary layer modifications immediately upstream and downstream of the cavity edges contribute significantly to the frequency response. The same regions constitute preferred locations for implementing active or passive control strategies to manipulate the frequency response of the flow.

The effects of changing the trailing edge shape on the wake and propulsive performance of a pitching rigid panel are examined experimentally. The panel aspect ratio is $\text{AR}=1$, and the trailing edges are symmetric chevron shapes with convex and concave orientations of varying degree. Concave trailing edges delay the natural vortex bending and compression of the wake, and the mean streamwise velocity field contains a single jet. Conversely, convex trailing edges promote wake compression and produce a quadfurcated wake with four jets. As the trailing edge shape changes from the most concave to the most convex, the thrust and efficiency increase significantly.

The modal and nonmodal linear stability of the flow in a microchannel with either one or both walls coated with a superhydrophobic material is studied. The topography of the bounding wall(s) has the shape of elongated microridges with arbitrary alignment with respect to the direction of the mean pressure gradient. The superhydrophobic walls are modeled using the Navier slip condition through a slip tensor, and the results depend parametrically on the slip length and orientation angle of the ridges. The stability analysis is carried out in the temporal framework; the modal analysis is performed by solving a generalized eigenvalue problem, and the nonmodal, optimal perturbation analysis is done with an adjoint optimization approach. We show theoretically and verify numerically that Squire's theorem does not apply in the present settings, despite the fact that Squire modes are found to be always damped. The most notable result is the appearance of a streamwise wall-vortex mode at very low Reynolds numbers when the ridges are sufficiently inclined with respect to the mean pressure gradient, in the case of a single superhydrophobic wall. When two walls are rendered water repellent, the exponential growth of the instability results from either a two-dimensional or a three-dimensional Orr-Sommerfeld mode, depending on the ridges' orientation and amplitude. Nonmodal results for either one or two superhydrophobic wall(s) display but a mild modification of the no-slip case.

We quantify the diffusiophoresis and electrophoresis of a uniformly charged, spherical colloid in a binary electrolyte using modified Poisson-Nernst-Planck equations that account for steric repulsion between finite sized ions. Specifically, we utilize the Bikerman (Bik) lattice gas model and the Carnahan-Starling (CS) and Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equations of state for monodisperse and polydisperse, respectively, hard spheres. We compute the phoretic mobility for weak applied fields using an asymptotic approach for thin diffuse layers, where ion steric effects are expected to be most prevalent. The thin diffuse layer limit requires ${\lambda }_D/R\to 0$, where ${\lambda }_D$ is the Debye screening length and $R$ is the particle radius; this limit is readily attained for micron-sized colloids in concentrated electrolytic solutions. It is well known that the classic Poisson-Boltzmann (PB) model for pointlike, noninteracting ions leads to a prediction of a maximum in both the diffusiophoretic and electrophoretic mobilities with increasing particle zeta potential (at fixed ${\lambda }_D/R$). In contrast, we find that ion sterics essentially eliminate this maximum (for reasonably attainable zeta potentials) and increase the mobility relative to PB. Next, we consider the more experimentally relevant case of a particle with a constant surface charge density and vary the electrolyte concentration, neglecting charge regulation on surface active sites. Rather surprisingly, there is little difference between the predictions of the four models (PB, Bik, CS, and BMCSL) for electrophoretic mobility in concentrated solutions, at reasonable surface charge densities ($\sim 1–10\mu \mathrm{C}/{\mathrm{cm}}^2$). This is because as the concentration increases, the zeta potential is reduced (to below the thermal voltage for concentrations above about 1 M) and therefore the diffuse layer structure is largely unaffected by ion sterics. For gradients of symmetric electrolytes (equal diffusivities, charge, and size) diffusiophoresis is also essentially unaffected by ion sterics, with a mobility that approaches zero with increasing concentration, just as in electrophoresis. For gradients of asymmetric electrolytes, the difference in diffusivities of the cation and anions leads to an induced electric field that acts on the charged particle. Importantly, we show that ion sterics leads to an excess contribution to the induced electric field, which increases rapidly with concentration. This increase overwhelms the accompanying decrease in zeta potential. The result is the diffusiophoretic mobility increases with concentration, rather than approaching zero. Therefore, diffusiophoresis could be an appealing alternative transport mechanism to electrophoresis in concentrated electrolyte solutions.

We investigate the large-scale transport of inertial particles. We derive explicit analytic expressions for the eddy diffusivities for generic Stokes times. These latter expressions are exact for any shear flow while they correspond to the leading contribution either in the deviation from the shear flow geometry or in the Péclet number of general random Gaussian velocity fields. Our explicit expressions allow us to investigate the role of inertia for such a class of flows and to make exact links with the analogous transport problem for tracer particles.

Topological features of vortices in terms of local flow geometry in an isotropic homogeneous turbulence and relationships between the topology and development of a vortex are investigated. Swirlity and sourcity represent the unidirectionality and intensities of the azimuthal and radial flows, respectively. Skewness reflects the symmetry quantity of the vortical flow. Together, the three quantities characterize the details of the invariant flow geometry. The analysis shows that flow symmetry is correlated with swirlity, and associated with its development or decay, especially for weak vortices. Stronger vortices exhibit lower correlations between the two and lack sufficient flow symmetry for inflow in all directions. This clarifies why highly intense vortices cannot attain effective vortex stretching. Vortex stretching is formulated in terms of the radial flow in the swirl plane. It shows that stretching is not entirely characterized by the eigenvalues of the rate-of-strain tensor, and depends on the eigenvalues of the radial flow classified by sourcity. Sourcity shows that numerous vortices, which have been classified as inflow (convergent) vortices using the complex eigenvalues of the velocity gradient tensor, have a mixture of inflow and outflow. These vortices break the orthogonality of the vortical axis to the swirl plane during vortex stretching. Stretching in vortices with complete inflow increases vorticity normal to the swirl plane effectively and improves axis orthogonality. Sourcity classifies these characteristics, and flow symmetry and sourcity are important quantities for effective stretching. The present topological analysis provides important details of vortical flow features in turbulent flows or realistic vortex models, and sourcity extracts the specific vortical region supported by the flow geometry itself.

Extensional rheometry and Brownian dynamics simulations of flexible polymer solutions confirm predictions based on blob concepts that coil-stretch hysteresis in extensional flows increases with concentration, reaching a maximum at the critical overlap concentration $c^{*}$ before progressively vanishing in the semidilute regime. These observations demonstrate that chain stretching strengthens intermolecular hydrodynamic screening in dilute solutions, but weakens it in semidilute solutions. Flow can thus strongly modify the concentration dependence of viscoelastic properties of polymer solutions.