The structure of homogeneous rotating turbulence at moderate Reynolds number is investigated by analyzing the instantaneous statistics of the scale-dependent velocity gradient tensor perceived by a set of four fluid elements equally spaced. The relative orientations between dynamical vectors such as vorticity, rate-of-strain eigenframe, and vortex stretching vector, together with their orientations with the rotating frame, are measured by direct numerical simulation at different rotation rates. Measurements are performed in the entire inertial range of scales. The preferential orientation of turbulence with the rotating frame is found to be maximal at the scale of the horizontal large structures of the flow. The relative orientations between dynamical vectors exhibit a continuous and monotonic evolution with scale. Overall, the orientation properties reflect the Gaussianization and two-dimensionalization of turbulence under the effect of rotation. In particular, rotation suppresses some alignment properties valid in isotropic turbulence, which in turn induces a strong decrease of the enstrophy production and strain production rates. These results are found to be valid at all scales.

We show that in decaying hydromagnetic turbulence with initial kinetic helicity, a weak magnetic field eventually becomes fully helical. The sign of magnetic helicity is opposite to that of the kinetic helicity—regardless of whether the initial magnetic field was helical. The magnetic field undergoes inverse cascading with the magnetic energy decaying approximately like $t^{-1/2}$. This is even slower than in the fully helical case, where it decays like $t^{-2/3}$. In this parameter range, the product of magnetic energy and correlation length raised to a certain power slightly larger than unity is approximately constant. This scaling of magnetic energy persists over long timescales. At very late times and for domain sizes large enough to accommodate the growing spatial scales, we expect a crossover to the $t^{-2/3}$ decay law that is commonly observed for fully helical magnetic fields. Regardless of the presence or absence of initial kinetic helicity, the magnetic field experiences exponential growth during the first few turnover times, which is suggestive of small-scale dynamo action. Our results have applications to a wide range of experimental dynamos and astrophysical time-dependent plasmas, including primordial turbulence in the early universe.

The low-Reynolds-number gravitational settling of a sphere through a fluid interface is investigated experimentally. By varying the viscosity ratio between the two fluids and the Bond number, two different modes of interfacial deformation are observed: a tailing mode and a film drainage mode. In the tailing mode, the interface deforms significantly as the sphere approaches, and the sphere becomes enveloped by a layer of the upper fluid. A tail forms, connecting the sphere to the bulk of the upper phase. In the film drainage mode, the interface deforms much less and the sphere impacts onto the interface, which either ruptures to form a contact line on the sphere or leaves a very thin wetting film. Additionally, two types of sinking profiles are observed: steady sinking, where the sphere velocity changes monotonically as it sinks, and stalled sinking, where the sphere's progress is inhibited by the interface, before it accelerates into the lower fluid. We present a regime diagram showing the different behaviors. Finally, the dependence of the sinking time on the Bond number and viscosity ratio is investigated. For the film drainage regime a simple scaling law is deduced; the tailing regime exhibits more complicated dynamics, possibly explained by a multistage sinking process.

We determine experimentally, with an unprecedented spatiotemporal resolution, the evolution of the liquid free surface during the pinching of a pendant droplet. We observe the transition from the inertio-capillary regime to the inertio-viscous-capillary final stage for a low viscosity liquid. Experiments with 5-cSt silicone oil show the formation of a micrometer subsatellite droplet in the vicinity of the pinching region. This phenomenon does not occur for a glycerine-water mixture with the same Ohnesorge number, which indicates the existence of complex effects during the breakup of the silicone oil droplet. The comparison between the experimental results and numerical simulations of the full Navier-Stokes equations shows that experiments deviate from the Newtonian theoretical predictions when the subsatellite droplet forms. Viscoelasticity might explain that deviation.

We investigate the process of formation of large-scale structures in a turbulent flow confined in a thin layer. By means of direct numerical simulations of the Navier-Stokes equations, forced at an intermediate scale $L_f$, we obtain a split of the energy cascade in which one fraction of the input goes to small scales generating the three-dimensional direct cascade. The remaining energy flows to large scales producing the inverse cascade which eventually causes the formation of a quasi-two-dimensional condensed state at the largest horizontal scale. Our results show that the connection between the two actors of the split energy cascade in thin layers is tighter than what was established before: the small-scale three-dimensional turbulence acts as an effective viscosity and dissipates the large-scale energy thus providing a viscosity-independent mechanism for arresting the growth of the condensate. This scenario is supported by quantitative predictions of the saturation energy in the condensate.

The unsteady loading on an airfoil due to the inflow turbulence is the primary source of broadband noise in turbomachinery, which makes the modeling of the inflow conditions a crucial task. This Rapid Communication presents an advanced method to model isotropic turbulent inflow conditions for a two-dimensional vortex particle method. The method relies on the classical view of turbulence as a superposition of random vortices convected with the mean flow. The fluctuating velocity is formulated using the scalar potential given by a convolution product which furnishes a solenoidal velocity field. The system is then optimized stochastically to create a realistic turbulence field based on a target energy spectra using an evolutionary optimization algorithm.

For the past 50 years or so, Kolmogorov's (1962) correction (K62) to his 1941 hypotheses (K41) has been embraced by an overwhelming majority of turbulence researchers. However, we show in this paper that there are no valid reasons for abandoning K41, a similarity framework known for its simplicity and elegance. In particular, analytical considerations, based on the Navier-Stokes equations, which take into account the finite Reynolds number (FRN) effect, together with all available experimental laboratory data, confirm a tendency towards the universal predictions of K41 as the Reynolds number continues to increase. This is especially true when the focus is on the energy spectrum and velocity structure function in the dissipative range. Incorrectly accounting for the FRN effect, which has been almost invariably mistaken for the intermittency effect, and the inclusion of the atmospheric surface layer data are the major factors which have contributed to the heretofore almost unrivalled acceptance of K62.

Several vortex formulations for computing the lift and drag/thrust forces on a flapping foil are compared in terms of simplicity, accuracy, and suitability for using with experimental data of measured velocity and vorticity fields. These methods are very useful to physically understand the aerodynamic performance of the flapping foil, and therefore the mechanisms of animal swimming and flight. In particular, we consider the case of a two-dimensional heaving foil at high Reynolds numbers and, using the results of accurate numerical simulations, we compare the performance of three force formulations based on the vortical impulse and Lamb's vector, projection of Lamb's vector, and wake integrals. We find that the formulation based on the vortical impulse is appropriate when all vortices generated by the flapping foil remain close to the foil, such as in a starting motion or in hovering, but may become quite inaccurate for analyzing forward flight or swimming. In these latter cases, the projection method is much more appropriate because it only takes into account vorticity close to the moving solid body at each instant. In fact, we find that, for high Reynolds numbers, the performance of the projection method is always better, even in hovering, due to its simplicity and because it neatly separates the contribution of the added-mass force from the circulatory or vortical force component. Finally, it is shown that the standard integral momentum method, which is quite simple to implement in a forward motion using experimental data of the velocity field in the wake behind the solid body, is much less accurate than the methods based on vortex force formulas.

We experimentally study the time evolution of the distance between two identical spheres settling down in polyacrylamide shear-thinning solutions in mixtures of water and glycerin. In order to analyze the behavior of the spheres under different rheological conditions, we varied the concentration of the polymer and glycerin. To examine the influence of wall effects, the experiments were performed in two containers of different size. We found that depending on the fluids' rheological properties, two different regimes are revealed for the same diluted polymer. In one of them (I), the separation between the spheres grows in time if the initial separation $S_i$ is beyond a critical distance $S_c$, while the separation decreases for an initial distance shorter than $S_c$. In the second observed regime (II), the spheres aggregate if $S_i<S_c$ while they remain unchanged in their separation if $S_i>S_c$, i.e., repulsion is not detected. The transition from one to another regime can be produced at constant polymer concentration by changing the solvent viscosity ${\eta }_s$. In our experiments this shift has been done modifying the glycerin-water proportion. Although these two behaviors were reported in previous works for different viscoelastic fluids, a result that we show is that both regimes can be observed for the same polymer. The elusive regime I, in which far-field repulsion is exhibited, is of particular interest since it has been previously reported only by Riddle et al. [J. Non-Newtonian Fluid Mech. 2, 23 (1997)]. Thus, our results confirm that this behavior is also feasible.

It has recently been shown by Wei and Klewicki [Phys. Rev. Fluids 1, 082401 (2016)] that in a zero-pressure-gradient turbulent boundary layer flow, the product of the nondimensional free-stream velocities in the streamwise $\left(U_{\infty }^{+}\right)$ and wall-normal $\left(V_{\infty }^{+}\right)$ directions is the flow shape parameter $\left(H\right)$: $U_{\infty }^{+}{V}_{\infty }^{+}=H$. It is suggested here that this result is a consequence of the variation of the Reynolds shear stress with $U_{\infty }V$ in the outer region of the boundary layer.

The asymptotic scaling structure of the total scalar variance equation is investigated for fully developed turbulent channel flow subjected to uniform scalar generation. The total scalar variance balance has a four-layer structure similar to that of the total kinetic energy balance, as previously investigated by Zhou and Klewicki [Phys. Rev. Fluids 1, 044408 (2016)]. Direct numerical simulation data are used to quantify the leading balance structure. These data cover the friction Reynolds number up to ${\delta }^{+}=4088$ and Prandtl number ranging between $\text{Pr}=0.2$ and 1.0. Of the layers empirically characterized, the inner-normalized width of the third layer is analytically verified to be ${\delta }^{+}-\sqrt{{\delta }^{+}/\text{Pr}}$. This result agrees closely with the empirical observations. Consistent with previous observations, the Kármán constant, $k_{\theta }$, for the mean scalar profile for $\text{Pr}=1$ is shown to be greater than the Kármán constant, $k$, for the mean velocity profile. Unlike previous studies, the present problem formation yields identical mean equations and boundary conditions for the scalar and velocity, and this allows unambiguous comparisons regarding the noted differences between $k$ and $k_{\theta }$. Results from the mean transport equations and streamwise velocity and scalar variance budget equations, as well as the relevant correlation coefficient profiles, are used to clarify the source of the differences between $k$ and $k_{\theta }$. Through the present theory, the results reported herein connect the statistical structure of the scalar and velocity fields to the mean profile slopes.

When a confined long gas bubble rises in a vertical tube in a cocurrent liquid flow, its translational velocity is the result of both buoyancy and mean motion of the liquid. A thin film of liquid is formed on the tube wall and its thickness is determined by the interplay of viscous, inertial, capillary and buoyancy effects, as defined by the values of the Bond number ($\mathrm{Bo}\equiv \rho g{R}^2/\sigma$ with $\rho$ being the liquid density, $g$ the gravitational acceleration, $R$ the tube radius, and $\sigma$ the surface tension), capillary number (${\mathrm{Ca}}_{\mathrm{b}}\equiv \mu U_b/\sigma$ with $U_b$ being the bubble velocity and $\mu$ the liquid dynamic viscosity), and Reynolds number (${\mathrm{Re}}_{\mathrm{b}}\equiv 2\rho U_{b}R/\mu$). We perform experiments and numerical simulations to investigate systematically the effect of buoyancy ($\mathrm{Bo}=0\text{–}5$) on the shape and velocity of the bubble and on the thickness of the liquid film for ${\mathrm{Ca}}_{\mathrm{b}}={10}^{-3}\text{–}{10}^{-1}$ and ${\mathrm{Re}}_{\mathrm{b}}={10}^{-2}\text{–}{10}^3$. A theoretical model, based on an extension of Bretherton's lubrication theory, is developed and utilized for parametric analyses; its predictions compare well with the experimental and numerical data. This study shows that buoyancy effects on bubbles rising in a cocurrent liquid flow make the liquid film thicker and the bubble rise faster, when compared to the negligible gravity case. In particular, gravitational forces impact considerably the bubble dynamics already when $\mathrm{Bo}<0.842$, with ${\mathrm{Bo}}_{\mathrm{cr}}=0.842$ being the critical value below which a bubble does not rise in a stagnant liquid in a circular tube. The liquid film thickness and bubble velocity in a liquid coflow may vary by orders of magnitude as a result of small changes of $\mathrm{Bo}$ around this critical value. The reduction of the liquid film thickness for increasing values of the Reynolds numbers, usually observed for ${\mathrm{Re}}_{\mathrm{b}}\lesssim {10}^2$ when $\mathrm{Bo}\ll 1$, becomes more evident at larger Bond numbers. Buoyancy effects also have a significant influence on the features of the undulation appearing near the rear meniscus of the bubble, as they induce a substantial increase in its amplitude and decrease in its wavelength.

Sorting cells based on their intrinsic properties is a highly desirable objective, since changes in cell deformability are often associated with various stress conditions and diseases. Deterministic lateral displacement (DLD) devices offer high precision for rigid spherical particles, while their success in sorting deformable particles remains limited due to the complexity of cell traversal in DLD devices. We employ mesoscopic hydrodynamics simulations and demonstrate prominent advantages of sharp-edged DLD obstacles for probing deformability properties of red blood cells (RBCs). By consecutive sharpening of the pillar shape from circular to diamond to triangular cross-section, a pronounced cell bending around an edge is achieved, serving as a deformability sensor. Bending around the edge is the primary mechanism which governs the traversal of RBCs through such a DLD device. This strategy requires an appropriate degree of cell bending by fluid stresses, which can be controlled by the flow rate, and exhibits good sensitivity to moderate changes in cell deformability. We expect that similar mechanisms should be applicable for the development of novel DLD devices that target intrinsic properties of many other cells.

Understanding the wake characteristics of wind turbines under the influence of atmospheric turbulence is crucial for developing advanced turbine control algorithms, such as the coordinated turbine control for improving the performance of the entire wind farm as an integrated system. In this work, we systematically investigate the wake of a utility-scale wind turbine for different thrust coefficients, which is relevant to the coordinated axial induction control. Large-eddy simulation (LES) with novel actuator surface models for turbine blades and nacelle is employed to simulate turbine wakes. Different thrust coefficients are achieved by varying the tip-speed ratio, i.e., $\lambda =6.8,7.8,8.8,9.3$. The inflow is generated from a precursory simulation using a very large computational domain to include the large-scale flow structures in atmospheric turbulence. The computed results show that varying the tip-speed ratio gives rise to differences in wake statistics, such as the wake recovery rate and the turbulence intensity. However, the computed results also reveal similarities in wakes from different tip-speed ratios. It is found that the characteristic velocity defined by the thrust on the rotor scales the turbine-added turbulence kinetic energy computed based on different wake center locations. For all considered tip-speed ratios, two dominant frequencies of the large-scale motion of the wake are observed, one is the dominant low frequency of the large-scale flow structures in the inflow prevailing at almost all downwind locations, the other one is the frequency of Strouhal number about 0.15 prevailing at far wake locations ($>3\sim 4$ rotor diameters). The existence of the inflow frequency in the large-scale motion of wakes shows the effects of incoming large-scale flow structures on wake meandering. The Strouhal number of the second frequency, however, is typical for that of vortex shedding behind bluff bodies. This finding suggests the coexistence of the two mechanisms for wake meandering, i.e., inflow large-scale turbulent flow structures and the wake shear layer instability, with the corresponding motion termed inflow-driven wake meandering and shear-induced wake meandering, respectively. The effects of wake and turbine energy extraction on motion of different frequencies are examined for different tip-speed ratios. As approaching the turbine upwind, the energy of the low-frequency motion of the inflow is significantly attenuated, while the energy of the motion at frequencies higher than the inflow low frequency are observed to increase for most cases. In the near wake, decreases of energy are observed for all the frequencies in almost all the cases. At far wake locations, the energy of the motion at all frequencies is increased to a level higher than that of the inflow (at $2D$ turbine upwind) in almost all the cases. At last, the statistics of wake centers in the spanwise and vertical directions are examined. It is found that the probability density function (PDF) profiles of wake center fluctuations nearly collapse with each other for different tip-speed ratios. The Gaussian distribution is found to be an acceptable approximation for the PDF of wake center locations at near wake locations (e.g., $2D,4D$, and $6D$ turbine downwind), while it is a poor approximation at far wake locations (greater than $8D$ turbine downwind). Downwind variations of the mean values and the standard deviations of wake center fluctuations are also observed to nearly collapse with each other for different tip-speed ratios. The observed similarities of turbine wake statistics illuminate the possibility of developing advanced engineering models taking into account the unsteady features of turbine wakes for advanced turbine controls.

Using a recent alternative form of the Kolmogorov-Monin exact relation for fully developed hydrodynamics (HD) turbulence, the incompressible energy cascade rate $\varepsilon$ is computed. Under this current theoretical framework, for three-dimensional (3D) freely decaying homogeneous turbulence, the statistical properties of the fluid velocity $\left(\mathbf{u}\right)$, vorticity $\left(\mathbf{\omega }=\mathbf{\nabla }\times \mathbf{u}\right)$, and Lamb vector $(\mathcal{L}=\mathbf{\omega }\times \mathbf{u})$ are numerically studied. For different spatial resolutions, the numerical results show that $\varepsilon$ can be obtained directly as the simple products of two-point increments of $\mathbf{u}$ and $\mathcal{L}$, without the assumption of isotropy. Finally, the results for the largest spatial resolutions show a clear agreement with the cascade rates computed from the classical four-thirds law for isotropic homogeneous HD turbulence.

We propose a reciprocal, self-propelled model swimmer at intermediate Reynolds numbers (Re). Our swimmer consists of two unequal spheres that oscillate in antiphase, generating nonlinear steady streaming (SS) flows. We show computationally that the SS flows enable the swimmer to propel itself, and also switch direction as Re increases. We quantify the transition in the swimming direction by collapsing our data on a critical Re and show that the transition in swimming directions corresponds to the reversal of the SS flows. Based on our findings, we propose that SS can be an important physical mechanism for motility at intermediate Re.

Liquid-ice interactions are becoming increasingly relevant for many applications including hydraulic fracturing, arctic drilling, and liquid-impregnated surfaces. It is therefore surprising that the capillary action of a liquid wicking across the surface of ice has never been characterized. We observe silicone oil as it wicks up sheets of frost grown on vertically oriented aluminum surfaces of varying wettability. Superhydrophilic and hydrophilic surfaces promote the growth of continuous frost sheets which displace oil with a power-law slope of 1/3 with respect to time. While in contrast to the 1/2 slope of Washburn's law governing most porous media, the 1/3 slope can be rationalized by considering the dendritic frost structure as an array of vertical wedges incapable of supporting the liquid's weight. Nonwetting surfaces grow frost from a more dilute distribution of frozen dropwise condensate, resulting in lower slopes of 1/4 for hydrophobic surfaces and nearly zero for superhydrophobic surfaces promoting jumping-droplet condensation. When switching to a near-horizontal orientation, Washburn's law is obtained for continuous frost sheets. The spreading rate of a liquid across frost can therefore be controlled by tuning the underlying surface wettability or surface orientation. Finally, we show that oils cannot wick inside of a bulk volume of frozen water due to the small pore size of the hexagonal lattice structure.

Particle image velocimetry and particle tracking velocimetry have been employed to investigate the dynamics of finite-size spherical particles, slightly heavier than the carrier fluid, in a horizontal turbulent square duct flow. Interface resolved direct numerical simulations (DNSs) have also been performed with the immersed boundary method at the same experimental conditions, bulk Reynolds number ${\text{Re}}_{2H}=5600$, duct height to particle-size ratio $2H/d_p=14.5$, particle volume fraction $\mathrm{\Phi }=1\%$, and particle to fluid density ratio ${\rho }_p/{\rho }_f=1.0035$. Good agreement has been observed between experiments and simulations in terms of the overall pressure drop, concentration distribution, and turbulent statistics of the two phases. Additional experimental results considering two particle sizes $2H/d_p=14.5$ and 9 and multiple $\mathrm{\Phi }=1\%$, 2%, 3%, 4%, and 5% are reported at the same ${\text{Re}}_{2H}$. The pressure drop monotonically increases with the volume fraction, almost linearly and nearly independently of the particle size for the above parameters. However, despite the similar pressure drop, the microscopic picture in terms of fluid velocity statistics differs significantly with the particle size. This one-to-one comparison between simulations and experiments extends the validity of interface resolved DNS in complex turbulent multiphase flows and highlights the ability of experiments to investigate such flows in considerable detail, even in regions where the local volume fraction is relatively high.

Numerical simulations were carried out to examine a ${24}^{\circ }$ compression ramp interaction in which the confinement effect of sidewalls was very strong. The ratio of turbulent boundary-layer thickness to domain width at the start of the interaction was $\delta /w=0.12$. Inflow conditions of $M_{\infty }=2.25$ and ${\mathrm{Re}}_{\theta i}=1800$ were chosen to match previous simulations. Comparing to the limited data available from similar computations, the centerline separation length scale $L_s/\delta$ was seen to vary with the flow confinement parameter $\delta /w$, as previously recognized in reflected shock interactions. Significant differences in flow structure were observed between these computations with confining sidewalls and previous computations with periodic boundary conditions at the lateral boundaries of the domain. The most intense turbulent fluctuations occurred in the corners of the domain. Symmetric and antisymmetric motions of the separation region were identified in the instantaneous flow using conditional averages and spatial correlations. The presence of the sidewalls was found to influence both the mean and unsteady flow. Accurately capturing the sidewall flows is judged to be essential in realistic modeling of confined flows.

Historically, there has been little faith in particle tracking velocimetry (PTV) as a tool to make quantitative measurements of thermal counterflow in He II, since tracer particle motion is complicated by influences from the normal fluid, superfluid, and quantized vortex lines, or a combination thereof. Recently, we introduced a scheme for differentiating particles trapped on vortices (G1) from particles entrained by the normal fluid (G2). In this paper, we apply this scheme to demonstrate the utility of PTV for quantitative measurements of vortex dynamics in He II counterflow. We estimate $\ell$, the mean vortex line spacing, using G2 velocity data, and $c_2$, a parameter related to the mean curvature radius of vortices and energy dissipation in quantum turbulence, using G1 velocity data. We find that both estimations show good agreement with existing measurements that were obtained using traditional experimental methods. This is of particular consequence since these parameters likely vary in space, and PTV offers the advantage of spatial resolution. We also show a direct link between power-law tails in transverse particle velocity probability density functions (PDFs) and reconnection of vortex lines on which G1 particles are trapped.