The stability of the circular Couette flow with two differentially heated cylinders is studied in the special cases of hydrodynamically stable rotation regimes. A one-dimensional model is developed to derive the condition of flow stability. This condition combines the curvature of the cylinders, the applied temperature difference between the two cylinders, and the diffusion properties of the fluid. The three-dimensional analysis is performed for two different rotation regimes: the Keplerian regime and the regime where the inner cylinder is stationary. The main results of this analysis is that, for a given radius ratio of the two cylinders, a single parameter combining the Prandtl number and the thermal expansion parameter can describe the critical state of the system. The description is in good agreement with the result of the one-dimensional model. An energy analysis shows a subtle role played by the shear stress in these two rotation regimes.

Liquid slip significantly affects confined fluid flow. The physical origin of slip flow with the Knudsen number ranging from 0.001 to 0.1 can be attributed to the long-range intermolecular fluid-solid interaction (FSI) force. To this end, in the framework of the mesoscopic lattice Boltzmann model (LBM), an exponentially decaying force function between fluid particles and two confined flat walls is proposed herein. For the parallel walls of symmetric FSI forces, we explicitly link density profile, velocity profile, apparent slip length, and permeability-enhancement ratio with the mesoscale FSI parameters (strength and decay length); by nondimensionalization of the exact solutions, we also acquire two dimensionless numbers that indicate the role of complex FSI strength and gap size of the flow channel in the slip-flow system. For the walls with asymmetric FSI properties, the numerical profiles of density and velocity as well as the amount of slip can be provided by the LBM simulations. The curve for continuous FSI force with two free parameters is calibrated for the hydrophobic surfaces in two benchmark flow experiments. Results show that the proposed FSI force function provides a robust model framework to mesoscopically elucidate the physical process of liquid slip flow.

The propulsive performance and acoustic emission of undulatory swimmers are investigated using an integrated unsteady potential flow and acoustic boundary element solver. Anguilliform and carangiform swimming gaits are modeled by a deforming NACA 0012 airfoil section for various reduced frequencies and dimensionless wave numbers based on the body length. The most efficient swimming motions are achieved when the reduced frequency and dimensionless wave number are approximately equal, a condition which also minimizes the thrust, required power, and radiated acoustic pressure. A vertically oriented dipole dominates the transient acoustic response in the near and far fields for both classes of swimming gait. The effect of a ground plane on undulatory swimming and its associated noise generation is examined as a function of reduced frequency and altitude above the plane using the method of images. Ground effect becomes pronounced when swimming within half of a chord length from the ground plane, where the thrust, power, propulsive efficiency, and peak acoustic pressure all increase for both gaits. All swimming configurations simulated in this study experience positive period-averaged lift at proximal distances where increased thrust and other hydrodynamic performance benefits associated with ground effect occur.

The understanding of the mechanics of turbulent dispersion is of primary importance in estimating the effects of mixing processes involved in a variety of events playing a significant role in our daily life. This motivates research on the characterization of statistics and the complex temporal evolution of passive scalars in turbulent flows. A key aspect of these studies is the modeling of the probability density function (PDF) of the passive scalar concentration and the identification of its link with the mixing properties. In order to investigate the dynamics of passive scalars as observed in nature and in laboratory experiments, we perform here direct numerical simulations of a passive tracer injected in the stationary phase of homogeneous isotropic turbulence flows in a setup mimicking the evolution of a fluid volume in the reference frame of the mean flow. In particular, we show how the gamma distribution proves to be a suitable model for the PDF of the passive scalar concentration and its temporal evolution in a turbulent flow throughout the different phases of the mixing process. Then, assuming a gamma distribution, we develop a simple mixing model by which we can estimate a mixing timescale, which regulates the decay rate of the intensity of the concentration fluctuations.

Detailed investigation of spatial evolution of mechanically generated regular water waves in a wind-wave tank under the action of steady wind is carried out. Deterministic waves are excited by a wavemaker driven at a range of frequencies and wavemaker displacement amplitudes. Prolonged measurements of the temporal variation of the instantaneous surface elevation carried out at multiple locations along the test section at numerous airflow rates enable obtaining reliable statistical parameters characterizing the wave-field evolution. Particular attention is given to the development along the tank of the wave frequency spectra as a result of wind input and interaction of the deterministic mechanical and the random wind waves. The interrelation between the regular and the random parts of the resulting wave field is studied in detail using auto- and cross-covariance analysis. Spatial coherence of the wave field is evaluated as a function of frequency for different wavemaker operation parameters and wind. The accumulated results allow us to draw conclusions regarding the effect of the high-frequency waves at short fetches evolving under the action of wind-wave field at more remote locations.

A viscous filament falling from a certain height onto a surface can form coils resulting from a buckling instability. This coiling phenomenon has been extensively studied for Newtonian fluids. However, the effect of liquid viscoelasticity has not been fully explored. Here we present experimental measurements of the coiling performance using Newtonian fluids and viscoelastic Boger fluids. Compared to Newtonian fluids with a comparable viscosity, the onset of viscoelastic fluid coiling is delayed; the coiling frequency is found to be smaller for viscoelastic fluids under the same experimental conditions. We show that these differences in coiling performance are due to the prevalence of extensional viscosity in viscoelastic fluids. Moreover, we find that the coiling frequency curves of different Newtonian fluids can be collapsed using a gravitational frequency and length scaling. This frequency and length scaling can also be used to collapse the data for Boger fluids considering the extensional viscosity instead of shear viscosity, confirming the importance of this property on filament coiling phenomenon for viscoelastic liquids.

Dispersions of bubbles with a compound interface in liquids are ubiquitous in nature and various industrial processes, such as marine oil transport and froth flotation, hence understanding surface phenomena effect on bubble formation in liquids remains as a canonical topic in fundamental multiphase flows. Here, we experimentally investigate the formation of an oil-coated bubble at submerged coaxial orifices in quiescent liquids. The air bubble is initially injected inside a confined oil domain and then exits into the surrounding water under buoyancy, forming an oil-coated bubble. Compared with the bubble formation in a single-phase liquid, the bubble size is significantly modified due to the presence of the oil phase. We develop a force balance model to predict the oil-coated bubble size, considering the orifice geometry as well as the compound air/oil/water interface, which agrees well with the experimental results. We further discuss the dependencies of the bubble size on the Bond number, size ratio of the coaxial orifices, and the interfacial tension ratio of oil-water and oil-air interfaces. Our study could contribute to further understandings on the dynamics of bubble formation with a compound interface.

Gamma ($\gamma$) instability theory, originally proposed in 2003, continues to provide the most promising explanation of salt-fingering engendered thermohaline staircases that are ubiquitously present in both the global ocean and lakes. Our purpose herein is to extend $\gamma$ instability theory to salt-fingering systems in which the vertical gradients of temperature and salinity are not constant. Our goal is to explain why the characteristic “step size” in a salt-fingering staircase is larger in regions characterized by weak gradients. Through application of an appropriately modified linear stability analysis, we first demonstrate that the most quickly growing mode of instability is unaltered by the inhomogeneity of the background stratification in most cases. We then perform numerical simulations based upon the mean field equations to show that staircases tend to form and thereafter merge much more quickly in the low gradient regions than the high gradient regions. After explaining this difference of timescale within the framework of our model, we argue that the differences in background gradients of physical properties may arise naturally in a quasiequilibrium staircase environment. We further invoke observations from the Tyrrhenian Sea to support a quasiequilibrium staircase hypothesis.

Phase synchronization between the vortex shedding behind a two-dimensional circular cylinder and its vibrations is investigated using the phase-reduction analysis. Leveraging this approach enables the development of a one-dimensional, linear model with respect to the limit-cycle attractor of the laminar wake, which accurately describes the phase dynamics of the high-dimensional, nonlinear fluid flow and its response to rotational, transverse, and longitudinal vibrations of the cylinder. This phase-based model is derived by assessing the phase response and sensitivity of the wake dynamics to impulse perturbations of the cylinder, which can be performed in simulations and experiments. The resulting model in turn yields the theoretical conditions required for phase-locking between the cylinder vibrations and the wake. We furthermore show that this synchronization mechanism can be employed to stabilize the wake and subsequently reduce drag. We also uncover the circumstances under which the concurrent occurrence of different vibrational motions can be used to promote or impede synchronization. These findings provide valuable insights for the study of vortex-induced body oscillations, the enhancement of aerodynamic performance of flyers, and the mitigation of structural vibrations by synchronizing or desynchronizing the oscillatory motions of a body to the periodic wake.

The characteristics of the internal layers of intense shear are examined in a mixing layer and in a jet, in the range of Reynolds numbers $134<{\text{Re}}_{\lambda }<275$. Conditionally averaged profiles of streamwise velocity conditioned on the identified internal layers present strong velocity jumps, which account for approximately $10\%$ of the characteristic large-scale velocity of the flow. The thickness $\langle {\delta }_{\text{w}}\rangle$ of the internal layers from the combined analysis of both the mixing layer and the jet scales with $\langle {\delta }_{\text{w}}\rangle /\lambda \sim {\text{Re}}_{\lambda }^{-1/2}$, which suggests a scaling with the Kolmogorov length scale ($\eta$), analogous to recent observations on the turbulent/nonturbulent interface (TNTI). The thickness of the internal shear layers within the mixing layer is found to be between $9\eta$ and $11\eta$. The concentration of a passive scalar across the internal layers is also examined, at the Schmidt number $\text{Sc}=1.4$. The scalar concentration does not show any jumps across the internal layers, which is an important difference between the internal layers and the TNTI. This can be explained from the analysis of the internal layers of intense scalar gradient, where the flow topology node/saddle/saddle dominates, associated with strain, whereas the internal layers of intense shear are characterized by a prevalence of focus/stretching. A topological content analogous to that obtained in layers of intense scalar gradient is found in proximity to the TNTI, at the boundary between the viscous superlayer and the turbulent sublayer. These observations evidence that the TNTI and the internal layers of intense scalar gradient are similar in several respects.

The wall-attached structures of velocity fluctuations over a traveling wavy boundary are explored here by performing large eddy simulation (LES) at a moderate Reynolds number (${\mathrm{Re}}_{\tau }\approx 1000$). The wave slope is $ak=0.1$, where $a$ is the wave amplitude and $k$ is the wave number. The prescribed wave age is $c/u_{*}=2,$ where $c$ is the wave phase speed and $u_{*}$ is the friction velocity. For comparison, the results of a LES over a smooth wall are also discussed. The wall-attached structures are self-similar with respect to their heights, and in particular the population density of their streamwise components scales inversely with their heights, which is reminiscent of a hierarchy of attached eddies. The wall-attached structures in the flow over the traveling wavy boundary retain geometric self-similarity; however, their streamwise length scale is decreased by the wavy boundary while their spanwise length scale is increased. By conditionally averaging the streamwise velocity fluctuations within the wall-attached structures, the reconstructed streamwise turbulent intensity was found to exhibit logarithmic behavior. The turbulent intensity carried by the small-scale wall-attached structures in the near-wall region is weakened by the traveling wavy boundary, while that of the large-scale wall-attached structures in the outer region is enhanced. The streamwise velocity corresponding to the highest uniform momentum zone for the large-scale wall-attached structures in the presence of the wavy boundary is larger than that for the smooth wall.

Strong shear localization effects are observed in large amplitude oscillatory shear (LAOS) simulations of a particulate suspension. Here, the structural response of this complex fluid is completely viscous and governed by the general shear-driven diffusion model by Phillips et al. [Phys. Fluids 4, 30 (1992)]. When coupled to oscillatory shear in LAOS, this model is shown to produce concentration gradients, which imply the existence of regions of disparate viscosities across the simulated measurement gap. This suggests the presence of strong shear localization which is conceived even though the intrinsic flow curve of the model is monotonic, and the simulated geometry is a planar Couette setup, expected to display simple shear flow characteristics. This shear localization is generated due to the oscillatory shear at the shearing plate, which, therefore, induces accelerating motion. The subsequent inertial effects act as perturbations in the nonlinear response of the fluid structure to shear and are sufficient to trigger significant localization in the flow. Due to the ubiquitous nature of shear-driven diffusive mechanisms in complex fluids, these results suggest shear localization to be an integral feature of a LAOS measurement of many complex fluids.

Droplets impacting on a surface are key to a wide range of applications such as spray deposition and inkjet printing. Yet, a full understanding of how they spread and retract is still lacking. Surfactants are often added to improve spreading and coverage of aqueous solutions, resulting in variations of the surface tension at timescales beyond the reach of conventional dynamic surface tension measurement methods. Here we study the impact dynamics of aqueous surfactant solutions on hydrophobic surfaces at millisecond timescales. We find that the spreading and retraction of droplets cannot be adequately described by the equilibrium surface tension. We infer the dynamic surface tension in the first milliseconds after impact from the spreading dynamics of droplets. “Slow” surfactants that take a lot of time to reach newly created droplet surface, only slightly decrease or even increase the surface tension, while “fast” surfactants, on the other hand, allow efficient wetting of aqueous solutions on hydrophobic surfaces. Our findings allow us to tailor surfactants for efficient drop deposition or spray application.

New reduced -order models (ROMs) are derived for sinusoidal shear flow (also known as Waleffe flow) and plane Couette flow in small periodic domains. A first derivation for Waleffe flow exploits Fourier modes that form a natural orthonormal basis for the problem. A ROM for such basis is obtained by a Galerkin projection of the Navier-Stokes equation. A large basis was reduced to 12 modes that contribute significantly in maintaining chaotic, turbulent dynamics. A key difference from earlier ROMs is the inclusion of two roll-streak structures, with spanwise wavelengths equal to $L_z$ and $L_z/2$, where $L_z$ is the spanwise length of the computational box. The resulting system was adapted to Couette flow by rewriting the Galerkin system for the same 12 modes, modified so as to satisfy no-slip conditions on the walls. The resulting dynamical systems lead to turbulence with finite lifetimes, in agreement with earlier ROMs and simulations in small domains. However, the present models display lifetimes that are much longer than in earlier ROMs, with differences of more than an order of magnitude. The Couette-flow model is compared to results of direct numerical simulation (DNS), with statistics displaying fair agreement. The inclusion of the $L_z$ and $L_z/2$ length scales is seen to be a key feature for longer turbulence lifetimes: Neglecting any of the roll modes, or their nonlinear interaction, leads to drastic reductions of turbulence lifetimes. The present ROMs thus highlight some of the dominant nonlinear interactions that are relevant in maintaining turbulence for long lifetimes.

The appearance of detached recirculation regions in wakes with base bleed determines the aerodynamic properties of many natural organisms and technological applications. In this work we introduce an analytical model which captures certain key dimensions of the recirculation region in the wake of porous plates of infinite aspect ratio, along with the porosity range over which it exists when vortex shedding is absent or suppressed. The model is used to interpret why the recirculation region (i) emerges, (ii) migrates away from the body with increasing base bleed, (iii) disappears at a critical bleed, and (iv) is partially insensitive to variations in the Reynolds number. The model predictions show considerable agreement with data from laboratory experiments and numerical simulations.

Complex but coherent motions form and rapidly evolve within wall-bounded turbulent flows. Research over the past two decades broadly indicates that the momentum transported across the flow largely derives from the dynamics of these coherent motions. The associated spatial organization, and its inherent connection to the dynamics, motivates the present research on streamline curvature and torsion. All the present results have been calculated and compared using the existing direct numerical simulation databases for boundary layers and channel flows. Here we have investigated the statistical properties of the local curvature $\left(\kappa \right)$ and torsion $\left(\tau \right)$ of streamlines for the considered wall-bounded flows. The computation of $\kappa$ (deviation from a straight line-bending) and $\tau$ (out of plane motion-twisting) uses the local construction of the Frenet-Serret coordinate frame. The analysis shows that the statistics of these geometrical properties change significantly with wall-normal position. Even though the mean wall-normal velocity is zero (e.g., for channel flow), the wall-normal curvature component shows a notable positive peak close to the wall. The correlation coefficient and the conditional average of the wall-normal velocity corresponding to the wall-normal curvature exhibit an anticorrelation between them. The probability density function of the curvatures have been calculated across the flow and compared with the ${\kappa }^{-4}$ scaling proposed by Schaefer [J. Turbul., N28 (2012)] for both the total and fluctuating field. Although in isotropic turbulence this scaling of curvature pertains to scales that are near to and smaller than the Kolmogorov scale $\left(\eta \right)$, in wall-bounded turbulence we find the onset of this scaling to occur at slightly larger length scales of $\approx 10\eta$. In fact, the start of this scaling with wall distance coincides with the three-dimensionalization of the vorticity field and agrees with the stagnation point structure in the inertial domain observed by Dallas et al., [Phys. Rev. E 80, 046306 (2009)]. In this region, the mean radius of curvature scales like the Taylor microscale. The standard deviation of torsion exhibits a decreasing trend with distance from the wall. The torsion to curvature intensity ratio reveals that the out of plane motion of the streamlines exceeds in-plane bending. The joint pdf of curvature and velocity magnitude supports the notion that large curvature values correspond to the region near a stagnation point. Furthermore, the joint pdf results between curvature components provides information about the orientation of the streamlines at different wall-normal locations.

This work deals with the simulation of hypersonic flows past a copper sphere by using a finite-rate catalysis model coupled with either a state-to-state (StS) or a multitemperature thermochemical nonequilibrium approach. Without detailed state-specific data for copper catalytic recombination, molecules formed on the surface are described with three different statistics: one reproducing the incoming distribution, one considering a uniform distribution, and the third populating only the highest vibrational level. Following recent experimental and theoretical results, very high enthalpy and very low pressure conditions have been considered. The finite-rate partial catalysis model provides results that are closer to the experimental ones than those obtained by a fully catalytic approach. The multitemperature model shows better agreement with experiments, whereas among the StS catalytic approaches the outcomes have shown that the surface recombination on only the highest energy level gives more accurate results.

We study the driven collective dynamics of a colloidal monolayer sedimenting down an inclined plane. The action of the gravity force parallel to the bottom wall creates a flow around each colloid, and the hydrodynamic interactions among the colloids accelerate the sedimentation as the local density increases. This leads to the creation of a universal “triangular” inhomogeneous density profile, with a traveling density shock at the leading front moving in the downhill direction. Unlike density shocks in a colloidal monolayer driven by applied torques rather than forces [Phys. Rev. Fluids 2, 092301(R) (2017)], the density front during sedimentation remains stable over long periods of time even though it develops a roughness on the order of tens of particle diameters. Through experimental measurements and particle-based computer simulations, we find that the Burgers equation can model the density profile along the sedimentation direction as a function of time remarkably well, with a modest improvement if the nonlinear conservation law accounts for the sublinear dependence of the collective sedimentation velocity on density.

The existence of the large-scale structures appearing in turbulent Couette flows is studied by means of a direct numerical simulation data set of active thermal Couette flows for different friction Richardson numbers, at the Prandtl number of air, $\mathrm{Pr}=0.71$. The existence of these structures is linked to the nonexistence of an active thermal flow. As soon as the Richardson number is greater than 1.5, the structures are less energetic, and for a value of only 3, the structures have vanished. This is due to the reorganization of the intense Reynolds stress events. Thus, large-scale structures will hardly appear in real-life Couette flows of air with a stable wall-normal gradient of temperature.