# Latest papers in fluid mechanics

### Energy transfer mechanisms and resolvent analysis in the cylinder wake

Author(s): Bo Jin, Sean Symon, and Simon J. Illingworth

We investigate discrepancies between the two-dimensional cylinder flow and a quasilinear model (i.e.~resolvent analysis) from an energy transfer perspective at Re=100. The energy balances achieved by the true flow are characterized and compared to predictions from resolvent analysis. The impact of the neglected nonlinear energy transfer on the resolvent mode shapes is clarified by analyzing the spatial distribution of the energy transfer mechanisms. This provides insights into the extent to which resolvent analysis correctly models energy transfer mechanisms, which is essential for understanding the limitations of quasilinear approximations and improving the modeling of nonlinear flows.

[Phys. Rev. Fluids 6, 024702] Published Thu Feb 18, 2021

### Wavelet analysis of shearless turbulent mixing layer

The intermittency and scaling exponents of structure functions are experimentally studied in a shearless turbulent mixing layer. Motivated by previous studies on the anomalous scaling in homogeneous/inhomogeneous turbulent flows, this study aims to investigate the effect of strong intermittency caused by turbulent kinetic energy diffusion without energy production by mean shear. We applied an orthonormal wavelet transformation to time series data of streamwise velocity fluctuations measured by hot-wire anemometry. Intermittent fluctuations are extracted by a conditional method with the local intermittency measure, and the scaling exponents of strong and weak intermittent fluctuations are calculated based on the extended self-similarity. The results show that the intermittency is stronger in the mixing layer region than in the quasi-homogeneous isotropic turbulent regions, especially at small scales. The deviation of higher-order scaling exponents from Kolmogorov's self-similarity hypothesis is significant in the mixing layer region, and the large deviation is caused by strong, intermittent fluctuations even without mean shear. The total intermittent energy ratio is also different in the mixing layer region, suggesting that the total intermittent energy ratio is not universal but depends on turbulent flows. The scaling exponents of weak fluctuations with a wavelet coefficient flatness corresponding to the Gaussian distribution value of 3 follow the Kolmogorov theory up to fifth order. However, the sixth order scaling exponent is still affected by these weak fluctuations.

### The dynamics of parallel-plate and cone–plate flows

Rotational rheometers are the most commonly used devices to investigate the rheological behavior of liquids in shear flows. These devices are used to measure rheological properties of both Newtonian and non-Newtonian, or complex, fluids. Two of the most widely used geometries are flow between parallel plates and flow between a cone and a plate. A time-dependent rotation of the plate or cone is often used to study the time-dependent response of the fluid. In practice, the time dependence of the flow field is ignored, that is, a steady-state velocity field is assumed to exist throughout the measurement. In this study, we examine the dynamics of the velocity field for parallel-plate and cone–plate flows of Newtonian fluids by finding analytical solutions of the Navier–Stokes equation in the creeping flow limit. The time-dependent solution for parallel-plate flow is relatively simple as it requires the velocity to have a linear dependence on radial position. Interestingly, the time-dependent solution for cone–plate flow does not allow the velocity to have a linear dependence on radial position, which it must have at the steady state. Here, we examine the time-dependent velocity fields for these two flows, and we present results showing the time dependence of the torque exerted on both the stationary and rotating fixtures. We also examine the time dependence of spatial non-homogeneities of the strain rate. Finally, we speculate on the possible implications of our results in the context of shear banding, which is often observed in parallel-plate and cone–plate flows of complex fluids.

### Nature of trapping forces in optically induced electrothermal vortex based tweezers

Author(s): Avanish Mishra, Kshitiz Gupta, and Steven T. Wereley

Precise manipulation of micro and nanosized particles has enabled investigations into various applications ranging from mechanobiology of biomolecules and cells to self-assembly of two-dimensional colloids. This work is focussed on studying the nature of a noninvasive electrothermal vortex based micro-manipulation tool called rapid electrokinetic patterning (REP). Using the equipartition method, we show that a REP trap is Hookean in nature and has an ultralow trap stiffness on the order of femtonewtons/μm. The dynamic tunability of an optically induced REP trap makes it a versatile tool for various biophysical applications.

[Phys. Rev. Fluids 6, 023701] Published Wed Feb 17, 2021

### Referee acknowledgment for 2020

### A comparison of bioinspired slippery and superhydrophobic surfaces: Micro-droplet impact

Slippery lubricant impregnated surfaces (SLIPSs/LISs) exhibit remarkable features of repellency and droplet mobility to a broad range of complex fluids. Their performance in micro-droplet repellency has received less attention. In this study, the anti-wetting performance of SLIPSs in comparison to superhydrophobic surfaces (SHSs) is investigated for the micro-droplet impact on different textured surfaces. Different series of square-pillar arrays are modeled to consider the effect of surface morphology on droplet hydrodynamics. A multiphase numerical model in conjunction with an accurate contact angle method has been implemented to analyze details of three immiscible phases during the droplet impact on the SLIPS. Our findings revealed that on the SLIPS with a low-density micro-textured surface where the effect of lubricant is more significant, droplet repellency and mobility are improved compared to SHSs. It was illustrated that on the SLIPS, droplet pinning decreased significantly and in low Weber number cases where the effect of lubricant is more noticeable, partial bouncing occurred. It was also observed that slippery surfaces with a low-density of micro-pillars exhibit bouncing behavior, which indicated the repellency effect of lubricant in droplet hydrodynamics. Although micro-droplets failed to recoil at a higher Weber number ([math]) on both the SHS and the SLIPS, droplet penetration within the micro-structured surface was considerably smaller on the SLIPS.

### Flow and thermal characteristics of three-dimensional turbulent wall jet

In the present work, a three-dimensional turbulent wall jet is simulated using large-eddy simulation to characterize its flow and thermal characteristics. The solver is first validated for streamwise velocity decay, wall-normal and spanwise spread rates, and mean and second-order flow statistics using reference experimental data from the literature. The mean vorticity transport equation for the streamwise component is analyzed to identify the dominant terms that contribute to the large spanwise spread of the jet. The terms that contain Reynolds normal stresses are identified as major contributors to a large mean streamwise component of vorticity. The mean streamwise and wall-normal components of vorticity are studied for their evolution and contribution to the spanwise spread. It was found that both these components together aid in the large spanwise spread of the jet. The heat transfer characteristics are studied for the jet flow on a heated isothermal wall. The profiles of mean and fluctuating temperatures, the evolution of the Nusselt number, and turbulent heat flux characteristics are studied. The streamwise evolution of Nusselt number behavior is explained using instantaneous vortical structures. A significant drop in heat transfer is observed in the potential core region. Further, the turbulent heat flux contours show that the transport of heat in the streamwise direction is different from that of the plane wall jet. A peculiar turbulent heat transport was found in the analysis of the spanwise heat flux. The heat transfer characteristics noted for the three-dimensional wall jet may help in the design and analysis of film-cooling applications.

### Capillary transport from barrel to clamshell droplets on conical fibers

Author(s): J. Van Hulle, F. Weyer, S. Dorbolo, and N. Vandewalle

Droplets spontaneously move when they are placed at the tip of a cone surface. Using three-dimensionally-printed structures, an experimental exploration of a large panel of configurations regarding the aperture angle of the cone finds evidence for a change of the droplet geometry while moving along the conical fiber—from barrel to clamshell shape. The position of this geometrical transition is estimated and two models are proposed to describe the motion of the barrel and the clamshell droplets.

[Phys. Rev. Fluids 6, 024501] Published Tue Feb 16, 2021

### Transition from steady to oscillating convection rolls in Rayleigh-Bénard convection under the influence of a horizontal magnetic field

Author(s): J. C. Yang, T. Vogt, and S. Eckert

The effect of a horizontal magnetic field on the oscillatory instability of convection rolls in a finite liquid-metal layer is investigated. The flow measurements reveal that the first developing oscillations are of a two-dimensional nature. In particular, a mutual increase and decrease in the size of adjacent convection rolls is observed where the periodicity of the “breathing” convection rolls can be related to standing inertial waves. With gradual reduction of the magnetic-field strength, the oscillating convection rolls are increasingly affected by three-dimensional disturbances.

[Phys. Rev. Fluids 6, 023502] Published Mon Feb 15, 2021

### Large impact velocities suppress the splashing of micron-sized droplets

Author(s): Masashi Usawa, Yuta Fujita, Yoshiyuki Tagawa, Guillaume Riboux, and José Manuel Gordillo

An investigation shows that, counterintuitively, the splash of drops impacting with velocities of a few tens of meters per second is suppressed because the aerodynamic lift force that would cause the liquid film to separate from the substrate and to break into much finer droplets is inhibited. This occurs as a consequence of the fact that the thickness of the lamella becomes similar to the mean-free path of gas molecules.

[Phys. Rev. Fluids 6, 023605] Published Mon Feb 15, 2021

### Symmetry breaking in a turbulent environment

Author(s): Alexandros Alexakis, François Pétrélis, Santiago J. Benavides, and Kannabiran Seshasayanan

Symmetry breaking in laminar flows is well known in the transition to turbulence scenario. Here we consider the breaking of a remaining symmetry in an already turbulent flow, as in the transition from a two-dimensional turbulent flow shown in the figure to a three-dimensional turbulent flow. We show that such cases have critical exponents that differ from the mean-field predictions and our results indicate the possible existence of a new class of out-of-equilibrium phase transition controlled by the multiplicative turbulent noise.

[Phys. Rev. Fluids 6, 024605] Published Mon Feb 15, 2021

### The continuous eddy simulation capability of velocity and scalar probability density function equations for turbulent flows

There is a well developed spectrum of computational methods for turbulent flows: modeling methods such as Reynolds-averaged Navier–Stokes (RANS) and probability density function (PDF) methods, and resolving methods such as large eddy simulation (LES) and filtered density function (FDF) methods. However, the applicability of RANS/PDF methods is limited to flows that do not essentially require the inclusion of resolved motion, and LES/FDF methods are well applicable if resolution criteria can be satisfied [which is often infeasible for very high Reynolds number (Re) wall-bounded turbulent flows]. A highly attractive approach to overcome these problems is the design of hybrid RANS–LES methods, which can be used with varying amounts of resolved and modeled motions. However, this approach faces the problem to ensure communication and balancing of resolved and modeled motions. A well working solution to this problem was presented recently for non-homogeneous flows with respect to velocity two-equation eddy viscosity turbulence models. Exact analytical results regarding the extension of these methods to velocity and passive scalar PDF/FDF methods and their implied RANS/LES equations are presented here. The latter matters with respect to the justification of the theoretical basis of new hybrid methods (realizability) and the availability of a hierarchy of simple and advanced simulation methods (including passive scalar transport). Based on the continuous mode redistribution mechanism, the new simulation methods are capable of providing reliable predictions of very high Re turbulent flows, which cannot be accomplished by using existing techniques.

### Non-linear ultrasonic and viscoelastic properties of gelatine investigated in the temperature range of 30 °C–60 °C

Analysis based on the determination of the multifactorial non-linearity parameter (β) is a promising non-destructive investigation and testing technique. The contribution of temperature variations on the non-linear coefficient is known to be lower than that of hydrostatic pressure changes. We investigated the effect of temperature on the non-linearity parameter in the range 30 °C–60 °C for a viscous, gelatinous compound, resulting from controlled hydrolysis of the collagen protein. Considerable thermal effects are realized and are related to changes in viscous and elastic properties. Remarkable changes in the non-linearity coefficient at temperatures corresponding to the transition temperature of gelatine of 60 °C indicate a signature while no outspoken hysteresis effects were realized with cyclic temperature sweeps. Despite the non-Newtonian nature of the gel, our experiments show comparability to water within the examined range of temperature, which corresponds to a wavelength shift of about 40 μm.

### Aspect ratio affects iceberg melting

Author(s): Eric W. Hester, Craig D. McConnochie, Claudia Cenedese, Louis-Alexandre Couston, and Geoffrey Vasil

How iceberg shape affects melting is investigated in a combined experimental and numerical study of ice melting in warm salt water. Experiments show that, in contrast to previous models, melting is highly nonuniform—side melt rates can be up to 3 times larger than bottom melt rates, and melt rates vary significantly within each face. Numerical simulations reveal that vortices accelerate melting at high flow speeds, and double diffusive effects matter at low flow speeds. Improved parameterizations to incorporate nonuniform iceberg melting are proposed.

[Phys. Rev. Fluids 6, 023802] Published Fri Feb 12, 2021

### Multimodal distributions of agricultural-like sprays: A statistical analysis of drop population from a pressure-atomized spray

Author(s): Romain Vallon, Malek Abid, and Fabien Anselmet

Jets in the second wind induced atomization regime are challenging to investigate experimentally and theoretically. Using droplet tracking velocimetry measurements performed far from the nozzle, this study shows the bimodal nature of the size and velocity distributions of droplets generated by such jets, at a distance of between 400 and 800 nozzle diameters. Developments from turbulence and combustion applications are used to obtain satisfying models not only for the distribution of the size and the velocity but also for their joint distribution.

[Phys. Rev. Fluids 6, 023604] Published Thu Feb 11, 2021

### Three-dimensional flow structure in an axisymmetric separated/reattaching supersonic flow

Author(s): Branden M. Kirchner, Gregory S. Elliott, and J. Craig Dutton

The turbulence structure in massively separated supersonic flows is highly complex and dominated by three-dimensional turbulence mechanisms. Analysis of large ensembles of tomographic particle image velocimetry measurements acquired in the near-wake of a Mach 2.49 blunt-based cylinder wake reveals multiple coherent high-energy turbulence mechanisms. These mechanisms have strong contributions to the turbulent kinetic energy, and several of them appear consistent with past computational simulations of this flow.

[Phys. Rev. Fluids 6, 024604] Published Thu Feb 11, 2021

### Scaling of the translational velocity of vortex rings behind conical objects

Author(s): Guillaume de Guyon and Karen Mulleners

The study of vortex rings formed behind accelerating bluff bodies is necessary to reduce their harmful effects or harvest their potential. The scaling of the vortex growth is usually performed by comparing the vortex circulation with the body size and velocity. This study investigates various kinematics and conical body geometries to propose a more robust scaling based on the vortex circulation, energy, and self-induced velocity.

[Phys. Rev. Fluids 6, 024701] Published Thu Feb 11, 2021

### Magnetic separation of rare-earth ions: Transport processes and pattern formation

Author(s): Zhe Lei, Barbara Fritzsche, and Kerstin Eckert

The effective body force associated with the application of a magnetic field to a solution containing rare earth ions produces convection and a time varying flow field that enables separation of the ions from solution.

[Phys. Rev. Fluids 6, L021901] Published Thu Feb 11, 2021

### Solute induced jittery motion of self-propelled droplets

The intriguing role of the presence of solutes in the activity of a self-propelling droplet is investigated. A system of self-propelling micrometer-sized 4-Cyano-4′-pentylbiphenyl (5CB) droplets in an aqueous solution of tetradecyltrimethylammonium bromide (TTAB) as the surfactant is considered. It is shown that the addition of glycerol causes the active 5CB droplet to exhibit a transition from smooth to jittery motion. The motion is found to be independent of the droplet size and the nematic state of 5CB. Analogous experiments with Polyacrylamide (PAAm), Polyvinylpyrrolidone (PVP), and Polyvinyl Alcohol (PVA), as solutes, confirm that such a transition cannot merely be explained solely based on the viscosity or Peclet number of the system. We propose that the specific nature of physicochemical interactions between the solute and the droplet interface is at the root of this transition. The experiments show that the timescales associated with the influx and redistribution of surfactants at the interface are altered in the presence of solutes. Glycerol and PVP significantly enhance the rate of solubilization of the 5CB droplets resulting in a quicker re-distribution of the adsorbed TTAB molecules on the interface, causing the droplet to momentarily stop and then restart in an independent direction. On the other hand, low solubilization rates in the presence of PAAm and PVA lead to smooth trajectories. Our hypothesis is supported by the time evolution of droplet size and interfacial velocity measurements in the presence and absence of solute. Overall, our results provide fundamental insights into the complex interactions emerging due to the presence of solutes.

### A K–L model with improved realizability for turbulent mixing

Turbulent mixing, induced by Rayleigh–Taylor (RT), Richtmyer–Meshkov (RM), and Kelvin–Helmholtz (KH) instabilities, broadly occurs in both practical astrophysics and inertial confined fusion problems. The Reynolds-averaged Navier–Stokes models remain the most viable approach for the solution of these practical flows. The commonly used mixing models based on the standard eddy viscosity formulation are shown to be capable of accurately predicting the global mixing zone width. However, we find that this approach will become non-realizable for local flow characteristics in the case of a large mean strain rate, including yielding the negative normal stress and the unphysically large turbulence kinetic energy (TKE) in the presence of shocks. This can affect the numerical robustness in calculating turbulent statistics and give rise to highly inaccurate predictions for complex mixings. To overcome this problem, a realizable K–L mixing model is developed, extended from the standard K–L model given by our recent works. A new eddy viscosity formulation is used and modified from the work by Shih et al. to reproduce the growth rate of the KH mixing. This new model yields similar results as the standard model for canonical RT, RM, and KH mixings. However, for complex mixing problems, the present model gives a significant improvement in physically capturing the turbulence characteristics, e.g., predicting the non-negative normal stress for RT mixing with the initial tilted interface and the appropriate TKE when shock interacts with the mixing zone for spherical implosion.