# Latest papers in fluid mechanics

### Coupled triads in the dynamics of internal waves: Case study using a linearly stratified fluid

Author(s): Q. Pan, N. N. Peng, H. N. Chan, and K. W. Chow

Coupled triads (two sets of resonant triads with one member in common) can arise in linearly stratified fluids. Such coupling may induce modulation instabilities which are otherwise absent for component triads in isolation themselves. Long wavelength instabilities will imply the occurrence of internal rogue waves which may attain amplitudes much larger than their surface wave counterparts.

[Phys. Rev. Fluids 6, 024802] Published Mon Feb 22, 2021

### Marginal regeneration in a horizontal film: Instability growth law in the nonlinear regime

Author(s): Alice Gros, Adrien Bussonnière, Sanjiban Nath, and Isabelle Cantat

The marginal regeneration process responsible for foam film drainage is revisited. It is shown that a horizontal, micron thick, foam film in contact with a meniscus destabilizes and that patches of thinner film grow along the meniscus, forming a very regular pattern.

[Phys. Rev. Fluids 6, 024004] Published Fri Feb 19, 2021

### Subgrid-scale characterization and asymptotic behavior of multidimensional upwind schemes for the vorticity transport equations

Author(s): Daniel Foti and Karthik Duraisamy

We establish subgrid-scale (SGS) characteristics of a finite volume vorticity-transport-based approach for large-eddy simulations. Modified equation analysis indicates that dissipation can be controlled locally via nonlinear limiting of the gradient employed for the vorticity reconstruction. The enstrophy budget highlights the remarkable ability of the truncation terms to mimic the true SGS dissipation and diffusion. Numerical dissipation in under-resolved simulations can be characterized by diffusion terms discovered in the modified equation analysis.

[Phys. Rev. Fluids 6, 024606] Published Fri Feb 19, 2021

### Pore network model of drying with Kelvin effect

A pore network model of isothermal drying is presented. The model takes into account the capillary effects, the transport of vapor by diffusion, including Knudsen effect, in the gas phase, and the Kelvin effect. The model is seen as a first step toward the simulation of drying in mesoscopic porous materials involving pore sizes between 4 nm and 50 nm. The major issue addressed with the present model is the computation of the menisci mean curvature radius at the boundary of each liquid cluster in conjunction with the Kelvin effect. The impact of Kelvin effect on the drying process is investigated, varying the relative humidity in the ambient air outside the medium. The simulations indicate that the Kelvin effect has a significant impact on the liquid distribution during drying. The evaporation rate is found to fluctuate due to the menisci curvature variations during drying. The simulations also highlight a noticeable non-local equilibrium effect.

### Direct numerical simulation of bidisperse inertial particles settling in turbulent channel flow

The behavior of settling velocity and clustering of bidisperse inertial particles in a turbulent channel flow is investigated through direct numerical simulation. The particle-laden planar channel flow has a friction Reynolds number at Reτ = 180. Eulerian–Lagrangian method is used to study the dynamic properties of bidisperse and monodisperse inertial particles with 16 different simulation sets, which are distinguished by Stokes numbers ranging from St+ = 1.31 to 52.58 and particle number ratio from 1:1 to 1:8. Momentum exchange between fluid and particle phases is considered in the simulation as the chosen initial volume fraction at 5 × 10−5 is in the two-way coupling regime. The gravity is set at the direction normal to both the wall normal direction and the streamwise direction. We observe that in the bidisperse cases the turbophoresis effect of inertial particles with the smaller diameter is significant even though it is very weak in the corresponding monodisperse cases. We use radial distribution function (RDF) to investigate the degree of clustering and turbophoresis. The results indicate that RDF is larger in the bidisperse cases for both large and small particles and it is greatly affected by the bulk particle number ratio and the Stokes number ratio. Unlike clustering, the terminal settling velocities of inertial particles in the bidisperse cases are affected by the final volume fraction at the dynamic equilibrium state. When their final volume fractions are lower than those in the corresponding monodisperse cases, the settling velocity of either particle becomes reduced from the monodisperse value. We also investigate the relationship between settling velocity and vortex strength. The results show that the preferential sweeping mechanism is strengthened with Stokes number decreasing and the mechanism can be quantified by the slope of the curve of settling velocity variation with vortex strength.

### On the H-type transition to turbulence—Laboratory experiments and reduced-order modeling

A series of experiments were conducted to understand the sources of local, high-amplitude velocity fluctuations produced at the late stages of boundary-layer flow transition to turbulence. The laboratory experiments considered the controlled injection of Tollmien–Schlichting (TS) waves into a nearly zero pressure gradient, laminar boundary layer, resulting in H-type transition to turbulence. Proper orthogonal decomposition (POD) was used to extract the energetic coherent structures within the transitional flow field obtained with particle image velocimetry. The first three modes were observed to feature spatial mode shapes consistent with a cross-section of a canonical hairpin vortex structure and were associated with time-dependent amplitudes having consistent peak frequencies with the fundamental TS wave frequency. Higher-order modes exhibited a combination of sub- and super-harmonics of the TS wave frequency and were attributed to flow interactions produced by a hairpin packet. A conditional averaging method was used to establish a reduced-order model for the overshoot phenomena in Reynolds shear stress and turbulence kinetic energy observed at the late transition stage. The lower portion of the large-scale hairpin vortex structure was observed to be primarily responsible for the overshoot mechanisms, which was well captured in a reduced-order model of the velocity field. The first four POD modes were used to create this reduced-order model, which, while only consisting of ≈15% of the total turbulence kinetic energy of the original velocity field, was able to capture ≈85% of the peak Reynolds stress amplitude across the overshoot region.

### Theoretical analysis of quantum turbulence using the Onsager ideal turbulence theory

Author(s): Tomohiro Tanogami

We investigate three-dimensional quantum turbulence as described by the Gross-Pitaevskii model using the analytical method exploited in the Onsager “ideal turbulence” theory. We derive the scale independence of the scale-to-scale kinetic energy flux and establish a double-cascade scenario: At scales...

[Phys. Rev. E 103, 023106] Published Thu Feb 18, 2021

### 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.