Flagellated bacteria on nutrient-rich substrates can differentiate into a swarming state and move in dense swarms across surfaces. A recent experiment measured the flow in the fluid around an Escherichia coli swarm [Wu, Hosu, and Berg, Proc. Natl. Acad. Sci. USA 108, 4147 (2011)]. A systematic chiral flow was observed in the clockwise direction (when viewed from above) ahead of the swarm with flow speeds of about $10\mu \mathrm{m}/\mathrm{s}$, about 3 times greater than the radial velocity at the edge of the swarm. The working hypothesis is that this flow is due to the action of cells stalled at the edge of a colony that extend their flagellar filaments outward, moving fluid over the virgin agar. In this work we quantitatively test this hypothesis. We first build an analytical model of the flow induced by a single flagellum in a thin film and then use the model, and its extension to multiple flagella, to compare with experimental measurements. The results we obtain are in agreement with the flagellar hypothesis. The model provides further quantitative insight into the flagella orientations and their spatial distributions as well as the tangential speed profile. In particular, the model suggests that flagella are on average pointing radially out of the swarm and are not wrapped tangentially.

A theoretical model for predicting and interpreting blood-spatter patterns resulting from a gunshot wound is proposed. The physical process generating a backward spatter of blood is linked to the Rayleigh-Taylor instability of blood accelerated toward the surrounding air, allowing the determination of the initial distribution of drop sizes and velocities. Then the motion of many drops in air is considered with governing equations accounting for gravity and air drag. Based on these equations, a numerical solution is obtained. It predicts the atomization process, the trajectories of the back-spatter drops of blood from the wound to the ground, the impact angle, and the impact Weber number on the ground, as well as the distribution and location of bloodstains and their shape and sizes. A parametric study is undertaken to predict patterns of backward blood spatter under realistic conditions corresponding to the experiments conducted in the present work. The results of the model are compared to the experimental data on back spatter generated by a gunshot impacting a blood-impregnated sponge.

This work addresses the study of the behavior of the excited electronic states of CO molecules in the nonequilibrium relaxation zone behind a normal shock for a ${\mathrm{CO}}_2\text{−}{\mathrm{N}}_2$ mixture representative of the Mars atmosphere. The hybrid state-to-state (StS) model developed accounts for thermal nonequilibrium between the translational energy mode of the gas and the vibrational energy mode of individual molecules. The electronic states of CO molecules are treated as separate species, allowing for non-Boltzmann distributions of their populations. The StS model is coupled with a nonequilibrium radiation solver, hpc-rad, allowing for the calculation of the radiation signature from the molecular and atomic species in the gas. This study focuses on the radiation from the fourth positive system of CO, which dominates the radiation heating on the forebody for higher speed Mars entry applications. In the rapidly dissociating regime behind strong shock waves, the population of the ground electronic state of CO $\mathrm{[}{\mathrm{CO}(\mathrm{X}}^1\mathrm{\Sigma }\left)\right]$, departs from Maxwell-Boltzmann distributions, owing to the efficient collisional excitation to the electronically excited ${\mathrm{CO}(\mathrm{A}}^1\mathrm{\Pi })$ state. In general the assumption of the equilibrium between electronic and vibration fails when the excitation of electronic states is driven by heavy particles. The comparison of the radiation heating predictions obtained using the conventional quasi-steady-state (QSS) approach and the physics-based StS approach revealed differences in radiative heating predictions of up to 50%. These results demonstrate that the choice of nonequilibrium model can have a significant impact on radiative heating simulations, and more importantly, they cast serious doubts on the validity of the QSS assumption for the condition of interest to this work.

We present results from numerical reconstructions of magnetic obstacle experiments performed in liquid metal flows. The experimental setup consists of an open rectangular container filled with a thin layer of liquid metal (GaInSn). A permanent magnet is installed on a rail beneath the container and is moved with a constant velocity $U_0$, which in turn induces a flow inside the liquid metal due to Lorentz forces. The setup allows experiments in a parameter range that is accessible by direct numerical simulations (DNS). We present results from realizations with four different parameter sets, covering flows with stable stationary vortex structures in the reference system of the moving magnet as well as time-dependent flow regimes. Although the liquid metal layer is very thin, the flow shows a highly three-dimensional character in the near and in the far wake of the magnetic obstacle. We conclude that the streamline visualization in the experiment (using gas bubbles at the surface of the liquid metal layer) is insufficient to picture the flow structure occurring in the liquid metal. To underpin our conclusions, we introduce a modified numerical model which aims to mimic the movement of these gas bubbles. Although this model is a strong simplification of the highly complicated behavior of bubbles at a fluid-fluid interface, it captures the main effects and provides a good reproduction of the experimental results. Furthermore, transient effects are investigated when the flow is initiated, i.e., when the magnet approaches the container and crosses its front wall. We conclude that the process of vortex formation is accompanied by a decrease of the streamwise component of the Lorentz force compared to the time when the fluid is still quiescent. This decrease occurs only for flows with stable vortex structures, which might be of interest for practical applications like Lorentz force velocimetry. The Lorentz forces obtained from our DNS are in good agreement with the values measured in experiment.

The spatiotemporal aspects of the transition to turbulence are considered in the case of a boundary-layer flow developing above a flat plate exposed to free-stream turbulence. Combining results on the receptivity to free-stream turbulence with the nonlinear concept of a transition threshold, a physically motivated model suggests a spatial distribution of spot nucleation events. To describe the evolution of turbulent spots a probabilistic cellular automaton is introduced, with all parameters directly obtained from numerical simulations of the boundary layer. The nucleation rates are then combined with the cellular automaton model, yielding excellent quantitative agreement with the statistical characteristics for different free-stream turbulence levels. We thus show how the recent theoretical progress on transitional wall-bounded flows can be extended to the much wider class of spatially developing boundary-layer flows.

A spheroidal particle in simple shear flow shows surprisingly complicated angular dynamics; caused by effects of fluid inertia (characterized by the particle Reynolds number ${\text{Re}}_p$) and particle inertia (characterized by the Stokes number $\text{St}$). Understanding this behavior can provide important fundamental knowledge of suspension flows with spheroidal particles. Up to now only qualitative analysis has been available at moderate ${\text{Re}}_p$. Rigorous analytical methods apply only to very small ${\text{Re}}_p$ and numerical results lack accuracy due to the difficulty in treating the moving boundary of the particle. Here we show that the dynamics of the rotational motion of a prolate spheroidal particle in a linear shear flow can be quantitatively analyzed through the eigenvalues of the log-rolling particle (particle aligned with vorticity). This analysis provides an accurate description of stable rotational states in terms of ${\text{Re}}_p,\text{St}$, and particle aspect ratio $\left(r_p\right)$. Furthermore we find that the effect on the orientational dynamics from fluid inertia can be modeled with a Duffing-Van der Pol oscillator. This opens up the possibility of developing a reduced-order model that takes into account effects from both fluid and particle inertia.

Direct numerical simulations are used for investigating the effects of stable stratification on the turbulent/nonturbulent (T/NT) interface in stably stratified mixing layers whose buoyancy Reynolds number ${\text{Re}}_b$ on the centerline is large enough for small-scale three-dimensional turbulence to exist. The stratification changes the interface geometry, and a large part of the interface is oriented with normal in the vertical direction in the stratified flows. The structures of the T/NT interface layer are similar between the nonstratified and stratified flows, and the T/NT interface consists of the viscous superlayer and the turbulent sublayer. The stratification is locally strengthened near the T/NT interface as evidenced by the large vertical density gradient, resulting in the decrease in ${\text{Re}}_b$ in the T/NT interface layer. Thus, even the small-scale dissipation range is directly affected by the buoyancy near the T/NT interface, although the small scales are somewhat free from the direct effects of the buoyancy in the turbulent core region. The production rates of enstrophy and scalar dissipation, which arise from the strain/vorticity and strain/density-gradient interactions, are decreased near the T/NT interface because the stratification modifies the alignments among the vorticity, density gradient, and strain-rate eigenvectors near the T/NT interface. This influence on the small-scale turbulence dynamics is not observed in the turbulent core region because of the large ${\text{Re}}_b$. A possible explanation is given for the influence of buoyancy on the alignment statistics based on the suppression of the vertical turbulent motions by buoyancy.

We present a modification of the integral length-scale approximation (ILSA) model originally proposed by Piomelli et al. [Piomelli et al., J. Fluid Mech. 766, 499 (2015)] and apply it to plane channel flow and a backward-facing step. In the ILSA models the length scale is expressed in terms of the integral length scale of turbulence and is determined by the flow characteristics, decoupled from the simulation grid. In the original formulation the model coefficient was constant, determined by requiring a desired global contribution of the unresolved subfilter scales (SFSs) to the dissipation rate, known as SFS activity; its value was found by a set of coarse-grid calculations. Here we develop two modifications. We de-fine a measure of SFS activity (based on turbulent stresses), which adds to the robustness of the model, particularly at high Reynolds numbers, and removes the need for the prior coarse-grid calculations: The model coefficient can be computed dynamically and adapt to large-scale unsteadiness. Furthermore, the desired level of SFS activity is now enforced locally (and not integrated over the entire volume, as in the original model), providing better control over model activity and also improving the near-wall behavior of the model. Application of the local ILSA to channel flow and a backward-facing step and comparison with the original ILSA and with the dynamic model of Germano et al. [Germano et al., Phys. Fluids A 3, 1760 (1991)] show better control over the model contribution in the local ILSA, while the positive properties of the original formulation (including its higher accuracy compared to the dynamic model on coarse grids) are maintained. The backward-facing step also highlights the advantage of the decoupling of the model length scale from the mesh.

The flow on the centerline of grid-generated turbulence is characterized via hot-wire anemometry for three grids with different geometry: a regular grid (RG60), a fractal grid (FSG17), and a single-square grid (SSG). Due to a higher value of the thickness $t_0$ of its bars, SSG produces greater values of turbulence intensity $\text{Tu}$ than FSG17, despite SSG having a smaller blockage ratio. However, the higher $\text{Tu}$ for SSG is mainly due to a more pronounced vortex shedding contribution. The effects of vortex shedding suppression along the streamwise direction $x$ are studied by testing a three-dimensional configuration, formed by SSG and a set of four splitter plates detached from the grid (SSG+SP). When vortex shedding is damped, the centerline location of the peak of turbulence intensity $x_{\mathrm{peak}}$ moves downstream and $\text{Tu}$ considerably decreases in the production region. For FSG17 the vortex shedding is less intense and it disappears more quickly, in terms of $x/x_{\mathrm{peak}}$, when compared to all the other configurations. When vortex shedding is attenuated, the integral length scale $L_u$ grows more slowly in the streamwise direction, this being verified both for FSG17 and for SSG+SP. In the production region, there is a correlation between the vortex shedding energy and the skewness and the flatness of the velocity fluctuations. When vortex shedding is not significant, the skewness is highly negative and the flatness is much larger than 3. On the opposite side, when vortex shedding is prominent, the non-Gaussian behavior of the velocity fluctuations becomes masked.

We report a combined experimental-numerical study of the effects of background rotation on large- and small-scale isotropy in rotating Rayleigh-Bénard convection (RBC) from both Eulerian and Lagrangian points of view. Three-dimensional particle-tracking velocimetry (3D-PTV) and direct numerical simulations (DNS) are employed at three different heights within the cylindrical cell. The Lagrangian velocity fluctuation and second-order Eulerian structure function are utilized to evaluate the large-scale isotropy for different rotation rates. Furthermore, we examine the experimental measurements of the Lagrangian acceleration of neutrally buoyant particles and the second-order Eulerian structure function to evaluate the small-scale isotropy as a function of rotation rate. It is found that background rotation enhances large-scale anisotropy at the cell center and close to the top plate, while decreases it at intermediate height. The large-scale anisotropy, induced by rotation, has negligible effect on the small scales at the cell center, whereas the small scales remain anisotropic close to the top plate.

An array of model rotating wind turbines is compared experimentally to an array of static porous disks in order to quantify the similarities and differences in the mean kinetic energy transport within the wakes produced in these two cases. Stereo particle image velocimetry measurements are done in a wind tunnel bracketing the center turbine in the fourth row of a $4\times 3$ array of model turbines. Equivalent sets of rotors and porous disks are created by matching their respective induction factors. The primary difference in the mean velocity components is found in the spanwise mean velocity component, which is as much as 190% different between the rotor and disk case. Horizontal averages of mean kinetic energy transport terms in the region where rotation is most important show percent differences in the range 3%–41%, which decrease to 1%–6% at streamwise coordinates where rotation is less important. Octant analysis is performed on the most significant term related to vertical mean kinetic energy flux $\overline{u^{\prime }{v}^{\prime }}U$. The average percent difference between corresponding octants is as much as 68% different in the near wake and as much as 17% different in the far wake. Furthermore, octant analysis elucidates the three-dimensional nature of sweeps and ejections in the near wake of the rotor case. Together, these results imply that a stationary porous disk adequately represents the mean kinetic energy transport of a rotor in the far wake where rotation is less important, while significant discrepancies exist at streamwise locations where rotation is a key phenomenon. This comparison has implications in the use of an actuator disk to model the wind turbine rotor in computational simulations specifically for studies where Reynolds stresses, turbulence intensity, or interactions with the atmosphere are of interest.

This study experimentally investigates the phenomenon of leading-edge-vortex burst on rotating flat plate wings. An aspect-ratio-2 wing was driven in pure rotation at a Reynolds number of $\text{Re}=2500$. Of primary interest is the evolution of the leading-edge vortex along the wing span over a single-revolution wing stroke. Direct force measurements of the lift produced by the wing revealed a single global lift maximum relatively early in the wing stroke. Stereoscopic particle image velocimetry was applied to several chordwise planes to quantify the structure and strength of the leading-edge vortex and its effect on lift production. This analysis revealed opposite-sign vorticity entrainment into the core of the leading-edge vortex, originating from a layer of secondary vorticity along the wing surface. Coincident with the lift peak, there emerged both a concentration of opposite vorticity in the leading-edge-vortex core, as well as axial flow stagnation within the leading-edge-vortex core. Planar control volume analysis was performed at the midspan to quantify the contributions of vorticity transport mechanisms to the leading-edge-vortex circulation. The rate of circulation annihilation by opposite-signed vorticity entrainment was found to be minimal during peak lift production, where convection balanced the flux of vorticity resulting in stagnation and eventually reversal of axial flow. Finally, vortex burst was found to be correlated with swirl number, where bursting occurs at a swirl threshold of $S_w<0.6$.

Motivated by diving semiaquatic mammals, we investigate the mechanism of dynamic air entrainment in hairy surfaces submerged in liquid. Hairy surfaces are cast out of polydimethylsiloxane elastomer and plunged into a fluid bath at different velocities. Experimentally, we find that the amount of air entrained is greater than what is expected for smooth surfaces. Theoretically, we show that the hairy surface can be considered as a porous medium and we describe the air entrainment via a competition between the hydrostatic forcing and the viscous resistance in the pores. A phase diagram that includes data from our experiments and biological data from diving semiaquatic mammals is included to place the model system in a biological context and predict the regime for which the animal is protected by a plastron of air.

We study experimentally the rate of chaotic mixing in viscoplastic fluids by using a rod-stirring protocol with a rotating vessel. Only a limited zone localized around the stirring rods is highly sheared at a given time. Using a dyed spot as the initial condition, we measure the decay of concentration fluctuations of dye as mixing proceeds. The mixing rate is found to be proportional to the volume of highly sheared fluid during a rotation period of the rods and inversely proportional to the number of rotations of the rods over a rotation of the vessel. Due to numerical simulations and experimental measurements, we relate the volume of highly sheared fluid to the parameters of the flow. We propose a quantitative two-zone model for the mixing rate, taking into account the geometry of the highly sheared zone as well as the rate at which fluid is renewed inside this zone. For all experiments, the model predicts correctly the scaling of the exponential mixing rates during a first rapid stage and a second slower one.

While chemically active homogeneous spherical particles do not undergo self-diffusiophoresis in free solution, they may do so when suspended in the vicinity of a solid boundary. We explore this possibility using a first-order kinetic model of solute absorption, where the relative magnitude of reaction to diffusion is characterized by the Damköhler number $\mathrm{Da}$. When the particle is remote from the wall, it is repelled from it with a velocity that scales inversely with the square of distance. The opposite extreme, when the ratio $\delta$ of separation distance to particle size is small, results in the anomalous scaling ${\delta }^{\frac{\sqrt{1+2\mathrm{Da}}-1}{2}}$ of the solute concentration in the narrow gap separating the particle and wall. This irrational power may only be obtained by asymptotic matching with solute transport outside the gap. For $\mathrm{Da}<4$ the self-propulsion speed possesses the same scaling, being set by the large pressures forming in the gap through a lubrication-type mechanism. For $\mathrm{Da}>4$ the particle velocity is $O\left(\delta \right)$, set by the flow in the region outside the gap. Solute advection is subdominant to diffusion in both the remote and near-contact limits and accordingly affects neither the above scaling nor the resulting approximations.

We show that the transition to a $k^{-1}$ spectrum in the enstrophy inertial range of generalized two-dimensional turbulence can be derived analytically using the eddy damped quasinormal Markovianized (EDQNM) closure. The governing equation for the generalized two-dimensional fluid system includes a nonlinear term with a real parameter $\alpha$. This parameter controls the relationship between the stream function and generalized vorticity and the nonlocality of the dynamics. An asymptotic analysis accounting for the overwhelming dominance of nonlocal triads allows the $k^{-1}$ spectrum to be derived based upon a scaling analysis. We thereby provide a detailed analytical explanation for the scaling transition that occurs in the enstrophy inertial range at $\alpha =2$ in terms of the spectral dynamics of the EDQNM closure, which extends and enhances the usual phenomenological explanations.

A cantilevered-capillary force apparatus is used to study the time scale for the coalescence of two droplets compressed together with a constant force. Power-law trends for the coalescence time as a function of droplet radius and compression force are experimentally measured. The measurements are compared against several different scaling theories from the literature. One of the existing theories is found to correctly predict the dependence on the droplet radius, but all of the theories overpredict the dependence on the force. A transition is also observed in the measured drainage time from a small variation around a single deterministic value for droplets with a radius of 125 $\mu \mathrm{m}$ or less to a broad distribution of drainage times for droplets with a radius of 150 $\mu \mathrm{m}$. A qualitative explanation for this transition is provided via scaling arguments.

Plane Couette flow under spanwise, anticyclonic system rotation [rotating plane Couette flow (RPCF)] is studied experimentally using stereoscopic particle image velocimetry for different Reynolds and rotation numbers in the fully turbulent regime. Similar to the laminar regime, the turbulent flow in RPCF is characterized by roll cells, however both instantaneous snapshots of the velocity field and space correlations show that the roll cell structure varies with the rotation number. All three velocity components are measured and both the mean flow and all four nonzero Reynolds stresses are obtained across the central parts of the channel. This also allows us to determine the wall shear stress from the viscous stress and the Reynolds stress in the center of the channel, and for low rotation rates the wall shear stress increases with increasing rotation rate as expected. The results show that zero absolute vorticity is established in the central parts of the channel of turbulent RPCF for high enough rotation rates, but also that the mean velocity profile for certain parameter ranges shows an $\mathsf{S}$ shape giving rise to a negative velocity gradient in the center of the channel. We find that from an analysis of the Reynolds stress transport equation using the present data there is a transport of the Reynolds shear stress towards the center of the channel, which may then result in a negative mean velocity gradient there.

The linear stability of plane Couette flow past a deformable solid is analyzed in the creeping-flow limit with an objective towards elucidating the consequences of employing two widely different formulations for the dissipative stresses in the deformable solid. One of the formulations postulates that the dissipative stress is proportional to the strain-rate tensor based on the left Cauchy-Green tensor, while in the other the dissipative stress in the solid is proportional to the rate-of-deformation tensor. However, it is well known in continuum mechanics that the rate-of-deformation tensor obeys the fundamental principle of material-frame indifference while the strain-rate-tensor formulation does not and hence it is more appropriate to employ the rate-of-deformation tensor in the description of dissipative stresses in deformable solids. In this work we consider the specific context of stability of plane Couette flow past a deformable solid and demonstrate that the results concerning the stability of the system from both models differ drastically. In the rate-of-deformation formulation for the dissipative stress, there is a range of solid-fluid thickness ratios (between 1.21 and 1.46) wherein the system is always stable for nonzero values of solid viscosity, unlike the strain-rate-tensor formulation wherein the system is unstable at all values of solid thickness. Further, for a solid-fluid thickness ratio less than 1, incorporation of dissipative effects in the solid using the rate-of-deformation formulation shows that the flow is more unstable compared to a purely elastic neo-Hookean solid, while for strain-rate-tensor formulation the flow is stabilized with an increase in viscosity of the solid. Using the fundamentally correct dissipative stress formulation, we also address the stability of pressure-driven flow in a deformable channel, wherein previous work carried out for an elastic neo-Hookean solid has shown that only the short-wave instability (driven by the first normal stress difference in the solid) exists while the finite-wave instability is absent in the creeping-flow limit. Using a consistent formulation for viscous stresses in the solid, we show that the short-wave instability is completely stabilized beyond a critical viscosity of the solid. Thus the present study clearly demonstrates the importance of consistent modeling of dissipative effects in the solid in order to accurately predict the stability of fluid flow past deformable solid surfaces.

Expressions for the ratio of the turbulent Schmidt (${\text{Sc}}_t$) to Prandtl (${\text{Pr}}_t$) numbers are derived for an idealized atmospheric surface layer flow over water surfaces. Conditions where the ansatz ${\text{Sc}}_t/{\text{Pr}}_t\approx 1$ are then discussed. It is shown that ${\text{Sc}}_t/{\text{Pr}}_t\approx 1$ is consistent with the active role of temperature in turbulence generation or destruction even when perfect similarity between turbulent transport of heat and water vapor is absent.