Particle image velocimetry (PIV) measurements are performed to examine the structural organization inside a turbulent boundary layer under the influence of free-stream turbulence (FST). In particular, streamwise-wall-normal plane PIV measurements are presented for two cases at two different turbulent intensity levels (about 13% and 8%). The free-stream turbulence is generated using an active grid in a wind tunnel. The statistical information of the flow regarding the wall-normal velocity and Reynolds shear stress are presented. The effect of increasing the turbulence level in the free stream for these flows has been found to have similarities with increasing Reynolds number for high-Reynolds-number canonical flows. Quadrant analysis is performed to determine the contributions of different Reynolds-stress-producing events. In this regard, the distribution of momentum transport events shows some similarity with channel flows, which can be justified by comparison of similar intermittency characteristics of both flows. In addition, the coherent structures found inside the boundary layer have inclined features that are consistent with the previous studies for canonical flows. The fact that the external disturbance, such as FST in this study, does not alter the organization of the structures inside the boundary layer supports the growing evidence for a universal structure for wall-bounded flows.

The route to turbulence in the boundary layer on a rotating broad cone is investigated using hot-wire anemometry measuring the azimuthal velocity. The stationary fundamental mode is triggered by 24 deterministic small roughness elements distributed evenly at a specific distance from the cone apex. The stationary vortices, having a wave number of 24, correspond to the fundamental mode and these are initially the dominant disturbance-energy carrying structures. This mode is found to saturate and is followed by rapid growth of the nonstationary primary mode as well as the stationary and nonstationary first harmonics, leading to transition to turbulence. The amplitudes of these are plotted in a way to highlight the continued growth after saturation of the fundamental stationary mode.

The present study evaluates the capabilities of a low-order flow model based on the resolvent analysis of McKeon and Sharma [B. J. McKeon and A. S. Sharma, J. Fluid Mech. 658, 336 (2010)] for the purpose of controller design for drag reduction in wall-bounded turbulent flows. To this end, we first show that the model is able to approximate the change in mean wall shear stress, which is commonly used as measure for drag reduction. We also derive an analytical expression that decomposes the drag reduction in internal flows into terms that can be predicted directly by the model and terms that allow for quantification of model error if high-fidelity data are available. We then show by example of varying-phase opposition control in a low-Reynolds-number turbulent channel flow that the drag reduction predicted by the resolvent model captures the trend observed in direct numerical simulation (DNS) over a wide range of controller parameters. The DNS results confirm the resolvent model prediction that the attainable drag reduction strongly depends on the relative phase between sensor measurement and actuator response, which raises interesting flow physics questions for future studies. The good agreement between the resolvent model and DNS further reveals that resolvent analysis, which at its heart is a linear technique, is able to approximate the response of the full nonlinear system to control. We also show that in order to make accurate predictions the model only needs to resolve a small subset of the DNS wave numbers and that the controlled resolvent modes obey the Reynolds-number scaling laws of the uncontrolled resolvent operator derived by Moarref et al. [R. Moarref et al., J. Fluid Mech. 734, 275 (2013)]. As a consequence, our results suggest that resolvent analysis can provide a suitable flow model to design feedback flow control schemes for the purpose of drag reduction in incompressible wall-bounded turbulent flows even at technologically relevant Reynolds numbers.

The growth of the average size of liquid droplets suspended in a turbulent air flow is of paramount importance in several natural and engineering systems. Here we present an experimental study of the effects of air flow turbulent intensity on the size growth of water droplets in a polydisperse droplet field. For a given initial distribution of droplets in the size range of 0–120 $\mu \mathrm{m}$ diameter, we identify an optimum air turbulent intensity that maximizes the rate at which the average droplet diameter increases with time. The observed trend is understood in terms of droplet collision rate statistics, droplet clustering, and the existence of a crossover diameter, below and above which the number of droplets decreases and increases in time, respectively. We show that the onset of clustering suppresses the intuitive effect of an increase in droplet collision rate with air turbulent intensity, resulting in the existence of an optimum air turbulent intensity that maximizes the average droplet size growth rate due to droplet coalescence. Our results bear consequences for the understanding of warm rain initiation from clouds and the design of engines with improved combustion characteristics.

We present laboratory experiments of surface wave turbulence excited by paddles in the deep water regime. The free surface is seeded with buoyant particles that are advected and dispersed by the flow. Positions and velocities of the floaters are measured using particle tracking velocimetry. We study the statistics of velocity and acceleration of the particles, mean vertical displacements, single-particle horizontal dispersion, and the phenomenon of preferential concentration. Using a simple model together with the experimental data, we show that the time evolution of the particles has three characteristic processes that dominate the dynamics at different times: drag by surface waves at early times, trapping by short-lived horizontal eddies at intermediate times, and advection by a large-scale mean circulation at late times.

We propose a method to measure the drag force due to synthetic polymers in flowing fluids by using a scanning probe microscope (SPM). Methoxy polyethyleneglycol thiol (mPEG-SH) was attached to the cantilever probe of the SPM, which was further immersed in flows of glycerol and polyethyleneglycol (PEG) solutions. The mPEG-SH-bonded cantilever detects the extra force due to polymer-polymer and polymer-fluids interaction in flowing fluids. The conformation of the mPEG-SH polymer bonded to the probe of the cantilever was predicted as having a stem and ellipsoidal-flower shape, and the drag force due to the deformed mPEG-SH was calculated. The forces detected by experiments using the SPM and the forces obtained by model calculations were compared and found to be reasonably close.

We advance a method to estimate the carrier-flow dissipation ${\varepsilon }_p$ in the presence of inertial sub-Kolmogorov particles at moderate ${\text{Re}}_{\lambda }$. Its foundations rely on the unladen flow dissipation calculation using the Rice theorem, and the density of zero crossings of the longitudinal velocity fluctuation $u^{\prime }\left(x\right)$ coming from a laser Doppler anemometry device. Our experimental results provide strong evidence regarding the non-negligible effect that sub-Kolmogorov particles have on the carrier-flow energy cascade at ${\varphi }_v=O\left({10}^{-5}\right)$, and ${\text{Re}}_{\lambda }\in [200–600]$.

The impacts of the interaction with grid turbulence of a turbulent Mach number in the range $0.6\times {10}^{-2}$ to $2.4\times {10}^{-2}$ (representative value) on a planar shock wave with a shock Mach number of about 1.04 were experimentally investigated. Using the counter-driver shock tube with a 120 mm × 120 mm square cross section, the turbulent Mach number level and the interaction length at the observation section were varied independently. Within resolvable experimental data, the shock Mach number became a decreasing function of the interaction length. The thickness of the shock front side-view profile increased as the turbulent Mach number and the interaction length increased. With a turbulent Mach number of $2.4\times {10}^{-2}$ (representative value) and an interaction length longer than 200 mm, the shock front profile became fragmented. The condition for the fragmentation is consistent with the “broken shock” criterion proposed by numerical studies.

We consider the Basset-Boussinesq (history) force experienced by a spherical drop. We seek to determine the kernel of the Basset-Boussinesq force when internal circulation of the fluid occurs. We first characterize the slip at a fluid-sphere interface. Under both steady and unsteady conditions, the corresponding slip length is remarkably uniform along the fluid-sphere interface and is directly related to the viscosity ratio. Combining the analytical expression of the Basset-Boussinesq kernel obtained for a solid sphere with the interface slip and the obtained description of the slip at the fluid-fluid interface, we are able to describe the Basset-Boussinesq history force acting on a spherical drop. This expression is valid whatever the viscosity ratio from bubbles to viscous drops.

The Reynolds-number-dependence of wall shear stress (${\tau }_w$) in fully developed, high-aspect-ratio turbulent channel flow is experimentally studied over the range of $230\le {\text{Re}}_{\tau }\le 950$. The principal conclusion of the present work is that beyond ${\text{Re}}_{\tau }\sim 600$, the wall shear stress evolves to an asymptotic state in which the statistical moments, probability density function, and power spectra of ${\tau }_w$ become independent of Reynolds number. In this state, the turbulent intensity, skewness and kurtosis of the wall shear stress take on values that are slightly larger than those previously measured, because prior estimates of these quantities did not resolve the full range of wall shear stress fluctuations, which extended beyond 10 standard deviations above the mean. For ${\text{Re}}_{\tau }\gtrsim 600$, the spectra of ${\tau }_w$ were found to collapse very well when using a wall-unit-based normalization, providing further evidence of an asymptotic state of the wall shear stress at large Reynolds numbers.

This paper investigates the scaling properties of the mean momentum balance (MMB) equation and the mean thermal energy balance (MHB) equation for buoyancy-driven turbulent flow and heat transfer in a differentially heated vertical channel (DHVC). Based on the characteristics of force balance, a three-layer structure is developed for the mean momentum balance equation. In Layer I, a viscous inner layer adjacent to the wall, the force balance is between the viscous force and the buoyancy force. In Layer III, the outer layer, the force balance is between the Reynolds shear force and the buoyancy force. A multiscaling analysis of the MMB equation is developed for the inner and outer layers. In the outer layer, a proper length scale is the channel half width $\delta$, a proper velocity scale is the maximum mean streamwise velocity $U_{\max }$, and a proper scale for the Reynolds shear stress is $u_{\tau }{U}_{\max }$ where $u_{\tau }$ is the friction velocity. In the viscous inner layer, a proper length scale is found to be $\frac{\nu }{u_{\tau }}\frac{U_{\max }}{u_{\tau }}$, where $\nu$ is the kinematic viscosity. The structure for the MHB equation can also be divided into three layers based on the characteristics of the diffusional and turbulent heat flux. The thickness of thermal inner layer is found to be $O\left(\frac{k}{u_{\tau }}\sqrt{\frac{U_{\max }}{u_{\tau }}}\right)$, where $k$ is the thermal diffusivity. A multiscaling analysis of the MHB equation is developed for the inner and outer layers. The outer-scaling of the MHB equation in a DHVC is similar to passive scalar transport in forced convection, where the channel half width $\delta$ is a proper length scale, friction temperature ${\theta }_{\tau }$ is a proper temperature scale, and $u_{\tau }{\theta }_{\tau }$ is a proper scale for turbulent heat flux. The inner-scaling for the thermal inner layer in a DHVC, however, is distinctly different from that in forced convection. The thermal inner length scale in a DHVC is found to be $\frac{k}{u_{\tau }}\sqrt{\frac{U_{\max }}{u_{\tau }}}$. The multiscaling analysis of the MMB and MHB equations agree well with direct numerical simulation data of DHVC.

We perform a priori and a posteriori analyses of the equilibrium wall model for high-speed wall-bounded turbulent flows. The time-averaged flow from various direct numerical simulation (DNS) databases is used as input to the wall model and the accuracy of the predictions in terms of wall shear stress and wall temperature (or heat flux for isothermal wall boundary conditions) are assessed. Two different mixing-length-based eddy-viscosity models and various damping functions are tested in this study. Both mixing-length models involve two adjustable parameters: (i) the von Kármán constant $\kappa$, which varies in the literature from 0.37 to 0.44, and (ii) a viscous damping constant $A^{+}$ (for the van Driest damping function). Also, for compressible flows, multiple scalings can be used for the viscous wall-normal spacing in the damping function. The sensitivity of the results to these model parameters is reported and it is found that the predictions of skin friction and wall temperature (or heat flux) are sensitive to the constants used, damping function scaling, and the wall-model exchange location. Wall-modeled large-eddy simulation (WMLES) is performed for (i) supersonic channel flow with a cold wall and (ii) an axisymmetric supersonic boundary layer for the adiabatic wall condition, to verify the a priori trends observed with respect to the damping functions. A posteriori WMLES results are consistent with the trends observed in the a priori analysis of DNS data, thus indicating the usefulness of the a priori analysis. We introduce a damping function scaling, which works well over a range of Mach numbers and thermal wall conditions.

Nearly all geophysical flows entrain, transport, and deposit sediment, and many studies have sought to define how the presence of suspended sediment can affect flow dynamics of the carrier fluid. Yet the mechanisms of turbulence modulation by suspended sediment remain poorly understood. Experiments were conducted in a mixing box to evaluate the effects of suspended sand on the turbulent flow generated by an oscillating grid placed near the bottom of the box. Two-phase particle image velocimetry was used to obtain velocity characteristics of the sediment and fluid phases separately. Boundary conditions included a clear-water flow and six sediment-laden flows for comparative purposes. A strong secondary circulation was observed within the mixing box due to the position of the grid and stroke length. As sediment loading increased, the depth affected by the secondary circulation, the mean and turbulent kinetic energy, and the total suspended-sediment concentration decreased while turbulent length scales increased. These features coincided with the formation of a stratified layer where high suspended-sediment concentration occurred. Key length scales related to the vertical extent of secondary circulation regions, vertical mixing, and maxima of suspended-sediment concentrations were defined and used to identify and explain the formation of this stratified layer and the modulation of flow. The results presented here demonstrate the marked effects that suspended sediment and the formation of a stratified layer have on turbulent flow dynamics within a mixing box, and these results are expected to have broader implications for the study and interpretation of a wide range of sediment-laden geophysical flows.

Water droplet icing on solid surfaces has been intensively studied in recent years but still with many mechanisms unrevealed. Here, we report a bubble formation phenomenon that always occurs in freezing droplets, from millimeter-sized sessile droplets to microscale condensed droplets, during icing and condensation frosting. In the second stage of icing (the first stage is nucleation and recalescence), air dissolved in liquid water is separated out in the ice front, forming many isolated bubbles. Coupled with the droplet icing physics, a theoretical model was proposed to predict the bubble formation and elucidate its influencing factors. Due to the bubble formation, the final ice droplet is actually a porous medium, rather than a complete solid ice. These results bring new insight into icing physics, helping modify icing models and improve anti-icing and deicing techniques.

Lubricant infused in micropatterned substrates will drain in the presence of an external, immiscible shear flow, but this drainage can be retarded by using the substrate geometry to exploit capillary effects at the interface. Recent work [Wexler et al., Phys. Rev. Lett. 114, 168301 (2015)] produced general geometric guidelines for the design of substrates to oppose this shear drainage in rectangular grooves with uniform cross section in the streamwise direction of the external flow. In this study, we generalize the fluid-retention predictions for lubricant-infused grooves with slowly varying cross section and interfacial geometries. Accounting for interfacial deformation is found to reduce the predicted lubricant retention in geometrically uniform grooves, albeit differently from past predictions. Streamwise nonuniformity in groove cross section is shown to provide little benefit to lubricant retention but may potentially cause significant reductions in retention, and thus should be considered carefully when establishing substrate manufacturing tolerances. An optimal groove shape for maximal lubricant-retention length is derived, although its practical use appears limited by its small surface area coverage compared to uniform grooves.

Heat and momentum transfer in wall-bounded turbulent flow, coupled with the effects of wall roughness, is one of the outstanding questions in turbulence research. In the standard Rayleigh-Bénard problem for natural thermal convection, it is notoriously difficult to reach the so-called ultimate regime in which the near-wall boundary layers are turbulent. Following the analyses proposed by Kraichnan [Phys. Fluids 5, 1374 (1962)] and Grossmann and Lohse [Phys. Fluids 23, 045108 (2011)], we instead utilize recent direct numerical simulations of forced convection over a rough wall in a minimal channel [MacDonald et al., J. Fluid Mech. 861, 138 (2019)] to directly study these turbulent boundary layers. We focus on the heat transport (in dimensionless form, the Nusselt number Nu) or equivalently the heat transfer coefficient (the Stanton number $C_h$). Extending the analyses of Kraichnan and Grossmann and Lohse, we assume logarithmic temperature profiles with a roughness-induced shift to predict an effective scaling of $\text{Nu}\sim {\text{Ra}}^{0.42}$, where Ra is the dimensionless temperature difference, corresponding to $C_h\sim {\text{Re}}^{-0.16}$, where Re is the centerline Reynolds number. This is pronouncedly different from the skin-friction coefficient $C_f$, which in the fully rough turbulent regime is independent of Re, due to the dominant pressure drag. In rough-wall turbulence, the absence of the analog to pressure drag in the temperature advection equation is the origin for the very different scaling properties of the heat transfer as compared to the momentum transfer. This analysis suggests that, unlike momentum transfer, the asymptotic ultimate regime, where $\text{Nu}\sim {\text{Ra}}^{1/2}$, will never be reached for heat transfer at finite Rayleigh number.

We present a mesoscale representation of near-contact interactions between colliding droplets which permits one to reach up to the scale of full microfluidic devices, where such droplets are produced. The method is demonstrated for the case of colliding droplets and the formation of soft flowing crystals in flow-focusing microfluidic devices. This model may open up the possibility of multiscale simulation of microfluidic devices for the production of new droplet and bubble-based mesoscale porous materials.

We present quantitative measurements of a dilute micellar solution past a falling sphere. The dilute micellar solution that consists cetyltrimethylammonium bromide and 5-methyl salicylate (CTAB/5mS) in deionized water exhibits shear-thickening behavior beyond a critical shear rate of $\dot{{\gamma }_c}\approx 0.4$ (1/s). Previous experiments have demonstrated that this micellar solution forms unentangled rodlike micelles at equilibrium [Davies et al., J. Am. Chem. Soc. 128, 6669 (2006)]. At a vanishingly small Reynolds number $\mathrm{Re}=0.03$, the drag coefficient for the falling sphere is similar to that of a Newtonian fluid. However, surprisingly, for conditions that correspond to $0.09\le \text{Re}\le 9.86$, falling spheres experience a significant drag reduction. Moreover, an unusually extended wake which spans over a long distance $>80a$ downstream of the sphere is detected by particle image velocimetry. These unusual results could be rationalized by invoking the phenomenon of flow-induced structure formation. We hypothesize that strong shear and/or extensional flows around the falling sphere could trigger aggregation of rodlike micelles into giant wormlike structures. Such wormlike micelles may induce significant sphere drag reduction and extended elastic wakes in the rear of sphere. This interpretation is consistent with the steady shear and transient extensional experiments, whereby a strong shear and elongational thickening have been recovered.

In Coriolis-centrifugal convection (${\mathrm{C}}^3$), buoyancy effects not only drive convective motions in the vertical direction due to the gravitational acceleration but also in the radial direction due to the centrifugal acceleration [Horn and Aurnou, Phys. Rev. Lett. 120, 204502 (2018)]. Here, we use the flexibility of numerical simulations to vary the gravitational Rossby number ${\text{Ro}}_{\parallel }$ and the rotational Froude number Fr independently and thereby study ${\mathrm{C}}^3$ over the broadest available parameter space. Based on our simulation results we give predictions for laboratory experiments of rotating convection, which inevitably include centrifugal effects. We especially focus on the spatial distribution of the temperature field. Unlike idealized Coriolis convection in which centrifugal buoyancy is neglected, the vertical temperature profiles become strongly radially dependent and exhibit a top-bottom asymmetry with increasing Froude number. In the quasicyclostrophic regime the temperature in the center of the fluid volume shows a strong enhancement, reaching values close to the bottom boundary temperature, whereas the temperatures at the sidewall are well below the arithmetic mean. We find further that the axisymmetric, linear model of Hart and Ohlsen [Phys. Fluids 11, 2101 (1999)] cannot be used to accurately predict the measured center temperatures, and provide an alternative empirical function based on our fully three-dimensional simulation results. Suggestions are given for the optimal local thermal measurement positions in laboratory experiments to estimate the global heat transfer and the vertical mean-temperature profiles in centrifugally affected rotating convection cases.

The flow of two immiscible liquids or fluids in bounded systems where confinement geometry varies can lead to drop or bubble formation. This phenomenon has been reported in the context of oil recovery and named snap-off, or exploited for making emulsions, and then foams, by using microfluidic systems, namely, microchannel emulsification or step emulsification. We report a comprehensive experimental investigation of such an emulsification process occurring at the end of a glass rectangular tube filled with oil and immersed in a water bath. This allows us to clearly visualize the breakup event of the dispersed phase liquid finger at the capillary's end. Below a critical flow rate, the drop size varies slowly with the flow rate and it is linked to the pinching time of the dispersed phase. A semiempirical law that gives the resulting drop size as a function of fluid and geometrical properties is proposed. However, this feature is altered for an aspect ratio of the rectangular tube below 2.5 where the forming drop hinders the counterflow of the continuous phase leading to larger drops. Then, above a critical flow rate, or capillary number that weakly depends on the viscosity ratio of the two liquids, the neck adopts a quasistatic shape well accounted for by a model based on a Hele-Shaw flow. In that case, drop formation is driven by gravity and a transition from a dripping regime to a jetting regime is observed at higher flow rates. Monodisperse foam can also be formed by injecting air. While the overall dynamics of bubble formation shares similarities with an incompressible fluid, the bubble size and the critical capillary number do not follow the same scaling laws.