We present a model appropriate to the initial motion of a flat-plate airfoil accelerating in an inviscid fluid. The model is based on the one presented in Pullin and Wang [J. Fluid Mech. 509, 1 (2004)] and is intended to extend the range of validity to lower angles of attack and longer distances traveled. The separated flow structures are represented as vortex sheets in the conventional manner and similarity expansions locally applicable to the leading and trailing edges of the plate are developed. In our approach, an expansion is applied to the attached outer flow rather than the vortex sheet circulations and positions. This allows the asymmetric effect of the sweeping component of the free-stream flow parallel to the plate to be built in to the same governing equation as the singular-order flow. Additionally, we develop a time-dependent self-similarity procedure that allows the modeling of more complex evolution of the flow structures. This is accomplished through an implicit time variation of the similarity variables. As a collective result, the predicted vortex dynamics and forces on the plate compare favorably to Navier-Stokes simulations. The model is split into high and low angles of attack regimes. The former assumes that the leading-edge and trailing-edge flows evolve independently, while the latter makes a further simplification to couple the two flows.

Turbulent signals are intermittent with large instantaneous fluctuations. Such large fluctuations lead to small Kolmogorov scales that are hard to resolve in numerical simulations [P. K. Yeung, K. R. Sreenivasan, and S. B. Pope, Effects of finite spatial and temporal resolution in direct numerical simulations of incompressible isotropic turbulence, Phys. Rev. Fluids 3, 064603 (2018)]. The present paper follows the above basic logic, but instead of dissipation events in isotropic turbulence, we study wall-shear stress events in plane channel flow. Wall-shear stress fluctuations are increasingly more intermittent as the Reynolds number increases. Hence, one has to employ higher grid resolutions as the Reynolds number increases in order to resolve a given percentage of wall-shear stress events. The objective of this paper is to quantify effects of the grid resolutions on the rare and high intensity wall-shear stress events. We find that the standard grid resolution resolves about 99% of the wall-shear stress events at ${\text{Re}}_{\tau }=180$. A slightly higher grid resolution has to be employed in order to resolve 99% of the wall-shear stress events at higher Reynolds numbers, and if the standard grid resolution is used for, e.g., a ${\text{Re}}_{\tau }=10000$ channel flow, one resolves about 90%–95% wall-shear stress events.

Empirical formulas describing the Darcy-Weisbach friction factor remain indispensable for applications in sciences and engineering dealing with turbulent flows. Despite their practical significance, these formulas have remained without theoretical interpretation for many decades. To close this knowledge gap, much research has been devoted to the development of the so-called “spectral link” introduced in the early 2000s. Such a theory is entirely based on elegant phenomenological arguments that make no contact with equations describing turbulent wall flows. The spectral link spawned alternative approaches, now labeled “cospectral budget” (or CSB) models, that describe how turbulent eddies contribute to wall stresses. The CSB overcomes some of the shortcomings of the phenomenological approach and is here employed to provide a thorough clarification of the link between spectral properties of velocity fluctuations and the scaling of friction factors in turbulent pipe flows in the hydraulically smooth and fully rough regimes.

Space-time energy spectra describe the distribution of energy density over space and timescales, which are fundamental to studying dynamic coupling at spatial and temporal scales and turbulence-generated noise. The present paper develops a dynamic autoregressive (DAR) random forcing model for space-time energy spectra in turbulent shear flows. This model includes the two essential mechanisms of statistical decorrelation: the convection proposed by Taylor's model and the random sweeping proposed by the Kraichnan-Tennekes model. The new development is that DAR random forcing is introduced to represent the random sweeping effect. The resulting model can correctly reproduce the convection velocity and spectral bandwidths, while a white-in-time random forcing model makes erroneous predictions on spectral bandwidths. The DAR model is further combined with linear stochastic estimation (LSE) to reconstruct the near-wall velocity fluctuations of the desired space-time energy spectra. Direct numerical simulation of turbulent channel flows is used to validate the DAR model and evaluate the Werner-Wengle wall model and the LSE approach. Both the wall model and LSE incorrectly estimate the spectral bandwidths.

This work extends the input-output approach to the study of wall-bounded shear flows manipulated using actuators common in experimental flow control studies. In particular, we adapt this powerful analytical framework to investigate the flow response to specified geometric actuation patterns (e.g., different plasma actuators) that can be applied over a range of different temporal input signals. For example, the commonly studied steady-state (time-averaged) flow response corresponds to a superposition of step responses in our modeling framework. The approach takes advantage of the linearity of the transfer function representation to construct the actuated flow field as a weighted superposition of the flow responses to point sources of varying intensity comprising the actuation model. We first validate the proposed method through comparisons with numerical and experimental studies of the time-averaged behavior of a transitional boundary layer actuated using a dielectric-barrier discharge plasma actuator operating in constricted discharge mode. The method is shown to reproduce the streamwise velocity field and the vortical structures observed downstream from the tested plasma actuator configurations. We then demonstrate that the method provides even better agreement with the steady-state response of the boundary layer subject to actuation from arrays of symmetric plasma actuators arranged in both spanwise and serpentine geometries. These results indicate the utility of this extension to the widely used input-output framework in analyzing the effects of certain actuation modalities that have shown promise in flow manipulation strategies for drag reduction. An important benefit of this analytical method is the low computational cost associated with its use in extensive parametric studies that would be cost-prohibitive using experiments or high-fidelity simulations.

Dispersion of active Brownian particles is a fundamental issue in biological, environmental, and related applications. However, due to the restriction in former models, a detailed analysis of Taylor dispersion of gyrotactic microorganisms in a horizontal plane Poiseuille flow is still lacking. In the present paper, with a recently proposed method [Jiang and Chen, J. Fluid Mech. 877, 1 (2019)], we illustrate the influences of the swimming ability, gyrotaxis intensity, shape anisotropy of microorganisms, and velocity of the ambient fluid on the dispersion process. Compared with nongyrotactic ones, there is a double accumulation mechanism for gyrotactic microorganisms: gravitactic focusing and wall accumulation. By using different boundary conditions, we show the effects of gravitactic focusing alone and double accumulation together. The variations of vertical distribution, overall drift, and effective dispersivity are characterized by changing the characteristic parameters of the microorganisms and the flow. Consisting of a swimming-induced part and an advection-induced part, the overall drift and effective dispersivity are coupled with the shape factor, flow Péclet number, and swimming Péclet number, which leads to nonmonotonic variations as functions of these parameters.

We experimentally study a buoyant jet flow where a heavy fluid is injected into a rectangular reservoir filled with a light ambient fluid. The reservoir dimensions are sufficiently large so that the ambient fluid can be considered as unbounded, over the time scale of our interest. The jet and ambient fluids are miscible and the jet direction is downward. We use nonintrusive experimental methods, such as high-speed camera, laser imaging, and ultrasound velocimetry techniques, to analyze the flow versus the Reynolds (Re), Froude (Fr), and Archimedes (Ar) numbers. These dimensionless parameters cover a wide range, i.e., $3\times {10}^2\le \text{Re}\le 15\times {10}^3$, $2\le \text{Fr}<2\times {10}^2$, and $0\le \text{Ar}\le 25\times {10}^4$, governing the flow via an interplay between inertia, viscosity, and buoyancy. We analyze the jet quasisteady characteristics, in particular the laminar length, which enables us to classify the flow into fully turbulent and semiturbulent regimes. Via evaluating the characteristic momentum-buoyant parameters, we also succeed in dividing the semiturbulent regime into momentum and buoyancy dominated subregimes. We quantify the regime transition boundaries and develop a correlation to predict the laminar length for each (sub-)regime. To have a global view of the buoyant jet flow, we also analyze other jet quasisteady characteristics, including the jet radius, spread angle, virtual origin, velocity profiles, and energy dissipation. Finally, we quantify the starting jet characteristics, including the penetration length and the tip velocity, by developing correlations for the short and long time behaviors, as well as the corresponding transition time.

Fish swim by undulating their body to ensure propulsion. In steady state, thrust is balanced by a total drag force, whose dominant terms depend on the Reynolds number and on the flow regime. If skin friction prevails on pressure drag in the laminar regime, and conversely in the turbulent regime, it is not clear how important is the contribution of the vortex-induced drag in both regimes. In this article, we tackle both flow regimes within the same numerical framework to address this question and the relevant scaling laws at play. In particular, we show in the turbulent regime that the combination of both the pressure and vortex-induced drags sets the Strouhal number between 0.2 and 0.4 following the thrust and drag balance, in very good agreement with natural swimmers. In the laminar regime, the vortex-induced drag can be neglected in most cases. If not, we rationalize the correction and show that our two-dimensional swimmer needs to account for a significant amplification of the drag force to match the biological data.

A rich variety of scaling laws for the evolution of convective buoyant thermals generated by an explosive release of energy has been established. Such events may correspond to a blast, spark, or volcano eruption. It was found that an occurrence of a particular scaling law depends on the interplay of many factors, viz., (1) amount of energy released in the environment, (2) time since the release, and (3) spatial scale of the release domain. The analytical treatment involves solutions of coupled equations for mass, momentum and buoyancy (heat) conservation in the Boussinesq and non-Boussinesq approximation. A model for the entrainment flow that accounts for a strong thermal flux has been proposed. For the limiting case of a weak thermal and the Boussinesq approximation (low density contrast between the buoyant thermal and the ambient environment) the celebrated Batchelor, Morton, and Turner scalings are recovered. Results have been favorably compared with limited data available in the literature.

We use high-speed imaging to study the effect of thixotropic aging in drop impact of yield-stress fluids on precoated substrates. Our results reveal that drop splashing is suppressed for “aged” compared to “unaged” samples, indicating that thixotropic breakdown timescales during impact are long enough to affect the dynamics. We propose and test several hypotheses for modifying the dimensionless group [ , Phys. Fluids 27, 043101 (2015), S. Sen et al., J. Fluid Mech. 891, A27 (2020)] to account for thixotropic aging. The main challenge is that the steady flow properties (Herschel-Bulkley model parameters) used in the current dimensionless group cannot be defined or measured for thixotropically aged samples because any deformation inherently rejuvenates and breaks down the microstructure. We find the most suitable hypothesis is to only increase the yield stress (${\sigma }_{\mathrm{y}}$, plastic component) based on the storage modulus of aged samples, while keeping the viscous parameters $(K \mathrm{or} {\eta }_{\infty })$ constant. The work reveals fundamental insight into rarely studied short-timescale flow conditions with thixotropic effects. These results are important for applications such as fire suppression or spray coating that involve complex fluids of varying degrees of thixotropic aging.

When a liquid drop is gently deposited on a wetting solid surface, it spreads due to capillary forces until it reaches a thermodynamical equilibrium set by the relative surface energies of the system. We investigate here experimentally the spreading ability of drops made of yield stress fluids, which flow only if the applied stress is above a finite value. We observe that in this case, after a spreading phase, the motion stops and a well-defined contact angle can be measured. This contact angle depends on the rheological properties of the fluid and in particular on its yield stress, on the drop radius and on the hydrodynamic boundary condition at the surface. These results are quantitatively compared to an analysis showing that, due to the yield stress of the fluid, a mechanical equilibrium is indeed reached which does not correspond to the thermodynamical equilibrium.

Detonation diffraction has been extensively studied because it is a very fundamental problem and has broad practical applications. In this study, two-dimensional simulations considering detailed chemistry and transport are conducted to investigate the weakly unstable detonation diffracting through an obstacle. The emphasis is placed on assessing the effects of obstacle size and shape on detonation diffraction. For a semicircular obstacle, the subcritical, critical, and supercritical regimes are identified by increasing the obstacle radius. The competition between the energy release rate and expansion rate is analyzed; it interprets the regime distribution. Increasing the radius of a semicircular obstacle can reduce the curvature and thereby the expansion rate. The energy release rate dominates over the loss due to expansion during the diffraction process with a large obstacle radius. For triangular and rectangular obstacles, the supercritical regime without detonation quenching is not observed in the present simulations. Furthermore, the critical regime for transverse detonation formation is investigated and the critical obstacle sizes are compared for different obstacle geometries. It is found that the semicircular obstacle has the smallest critical size while the rectangular obstacle has the largest critical size. Unlike the critical obstacle size, the wall reflection distance of transverse detonation is independent of the obstacle geometry and it varies in the range of 10–15 times the detonation cell width. The characteristics of transverse detonation are compared for two weakly unstable mixtures, hydrogen/air without and with nitrogen dilution. A pair of transverse detonations induced by local explosion is observed in hydrogen/air with nitrogen dilution, which is quite different from the single transverse detonation in hydrogen/air. The comparison of the three regimes’ distributions for these two mixtures shows that a larger obstacle size is required for transverse detonation formation in hydrogen/air with nitrogen dilution. However, the critical obstacle size normalized by the corresponding detonation induction length becomes closer for two mixtures. This indicates that the formation of transverse detonation is nearly independent of nitrogen dilution for weakly unstable mixtures.

Characteristics and material transport of a bubble-driven plume in stably stratified water with uniform crossflow are studied using an Eulerian-Eulerian large-eddy simulation model. Four laboratory-scale plume conditions with different bubble rise velocities ($w_r=3$, 6, 12, and $20\mathrm{cm}/\mathrm{s}$) are considered, and their characteristics under three weak crossflow conditions ($U_c=0.5$, 1, and $2\mathrm{cm}/\mathrm{s}$) are studied. The interaction between the rising bubbles and the stratified water generates a double-plume structure, consisting of a rising plume of bubble/water mixture and a falling plume of dense water peeled from the rising plume due to the stratification effect. The presence of crossflow forces the rising plume to incline and causes the falling plume to form on the downstream side (with respect to the crossflow direction) of the rising plume, resulting in reduced contact area between the two plumes. Consequently, the turbulent mixing of the vertical momentum between the rising and falling plumes is reduced, causing the magnitude of the vertical velocity in both plumes to increase when the crossflow velocity is increased. The material transport from the plume to the horizontal intrusion layer (traced using dye) also exhibits strong dependence on the crossflow velocity. Faster crossflow results in narrower lateral extension and wider vertical extension of the intrusion layer due to the interaction between the peeling process and the crossflow. For cases with the two smaller $w_r$ (3 and $6\mathrm{cm}/\mathrm{s}$), the plume can form a distinct peeling event that dominates the material transport process. As a result, the mean intrusion layer height $h_t$ shows only small variation for these two plume conditions when $U_c$ is increased. In contrast, the plumes with $w_r=12$ and $20\mathrm{cm}/\mathrm{s}$ exhibit noticeable decrease of $h_t$ ($9\%$ and $24\%$, respectively) when $U_c$ is increased from $0.5$ to $2\mathrm{cm}/\mathrm{s}$. Statistical analysis of the streamwise dye flux shows that the decrease of $h_t$ with increased $U_c$ for the cases with $w_r=12$ and $20\mathrm{cm}/\mathrm{s}$ is mainly due to the crossflow-enhanced mean flux of dye from the rising plume at the low elevation.

The macroscopic dynamics of a droplet impacting a solid is crucially determined by the intricate air dynamics occurring at the vanishingly small length scale between droplet and substrate prior to direct contact. Here we investigate the inverse problem, namely, the role of air for the impact of a horizontal flat disk onto a liquid surface, and find an equally significant effect. Using an in-house experimental technique, we measure the free surface deflections just before impact, with a precision of a few micrometers. Whereas stagnation pressure pushes down the surface in the center, we observe a liftup under the edge of the disk, which sets in at a later stage, and which we show to be consistent with a Kelvin-Helmholtz instability of the water-air interface.

When a droplet hits a surface fast enough, droplet splashing can occur: Smaller secondary droplets detach from the main droplet during impact. While droplet splashing on smooth surfaces is by now well understood, the surface roughness also affects at which impact velocity a droplet splashes. In this paper, the influence of the surface roughness on droplet splashing is investigated. By changing the root-mean-square roughness of the impacted surface, we show that the droplet splashing velocity is only affected when the droplet roughness is large enough to disrupt the spreading droplet lamella and change the droplet splashing mechanism from corona to prompt splashing. Finally, using Weber and Ohnesorge number scaling models, we also show that the measured splashing velocity for both water and ethanol on surfaces with different roughnesses and water-ethanol mixtures collapses onto a single curve, showing that the droplet splashing velocity on rough surfaces scales with the Ohnesorge number defined with the surface roughness length scale.

We report a linear scaling law for an electrical voltage as a function of the pressure drop in capillary pipes and ducts. This voltage is generated by a process which is termed spin hydrodynamic generation (SHDG), a result of the collective electron spin–coupling to the vorticity field in the laminar flow in combination with an inverse spin-Hall effect. We study this phenomenon in laminar duct flows with different width-to-height aspect ratios ranging from 1 (square ducts) to infinite (two dimensional channels). First, we analytically solve the governing Valet-Fert spin diffusion equations for the SHDG by means of the method of small parameters together with proper boundary conditions for the set of inhomogeneous elliptic partial differential equations. Second, the proposed linear scaling law is validated through a series of experiments using capillary tubes with rectangular and square cross sections. The experimental results show very good agreement to the analytically found scaling law. A subsequent substitution of the bulk velocity of the laminar wall-bounded flows by the pressure drop reveals a universal scaling law for the electrical voltage that incorporates all pipe and duct geometries which we could study in our experiments. Finally, the efficiency of the system is estimated for circular pipes, rectangular and square ducts. This study shows that the efficiency of a spin hydrodynamic generator is the same for a circular pipe and a square duct with the same diameter and height, respectively. Hence, due to the ease of manufacturing and the possibility to scale the experiments up to parallel settings in a compact form, micro-channels with a square cross section seem to be the optimum for a spin hydrodynamic generator.

The deformation of hemispherical bubbles under vertical static electric fields was studied using a plane capacitor. The deformation and the bubbles shape have been monitored according to the amplitude of the electric field and the initial volume of the bubbles. Two different substrates, a dry solid plate or a liquid pool, were used to inspect the influence of the pining of the contact line. The deformation of sessile (on dry solid plate) and floating (on a liquid pool) bubbles were compared. The deformation parameter has been rationalized using a simple model. More precisely, the number of interfaces has been found to be a relevant parameter that imposes the shape of the bubbles.

The purpose of the present experimental study is to get a better understanding of the dynamics of the vapor phase spatiotemporal repartition in a cavitating backward facing step flow. We provide a refined data base of the use of the void fraction transport equation to model such flows. The backward facing step flow provides a well-known test case to compare vortex dynamics between single and two-phase flow. To evidence the vapor phase dynamics, the flow is probed by high-speed x-ray attenuation techniques and by pressure fluctuation measurements at the walls. Long-time dynamics are also visualized using conventional high-speed imaging synchronized with pressure measurements. Large vortex structures, free shear layer instability, wall interaction and reverse flow are observed. The two-phase structures are studied at different cavitation levels corresponding void fractions ranging from 1% to 50%. The topology of the mean and fluctuating void fraction maps is performed, leading to the establishment of three specific areas in the flow. These areas are distinguished by the underlying mechanisms happening within them: vaporization, transport, and condensation. The statistical analysis underlines the existence of extreme events associated with high void fraction levels and wave propagations. While these events are associated with topological changes from a shear layer to a wake mode that also exist in the single-phase case, they are associated with much lower frequency at high cavitation levels.

We conduct experiments with force-free magnetically driven rigid helical swimmers in Newtonian and viscoelastic (Boger) fluids. By varying the sizes of the swimmer body and its helical tail, we show that the impact of viscoelasticity strongly depends on the swimmer geometry: it can lead to a significant increase of the swimming speed (up to a factor of 5), a similar decrease (also up to a factor of 5), or it can have approximately no impact. Using an analysis of our data along with theoretical modeling we suggest that the influence of viscoelasticity on helical propulsion is controlled by an asymmetry effect, previously reported for dumbbell swimmers, wherein the front-back size mismatch leads to a non-Newtonian elastic force that can either enhance or hinder locomotion.