# Latest papers in fluid mechanics

### Wake topology and dynamics over a slender body at a high incidence and their relation to structural loading

The flow over a slender cylindrical body with a hemisphere end was studied experimentally using a combination of force balance and time-resolved particle image velocity measurements. The investigation was performed at a subcritical Reynolds number (Re = 11 000) over a range of high incidence angles from 30° to 90°. The results show that significant cross-flow loading occurs for a range of incidence angles from 50° to 70°, with maximum mean and fluctuating loads taking place at 60°. Within this range of incidence angles, the loading has a bimodal nature, with intermittent switching between two states associated with the positive and negative cross-flow loading direction. The analysis of simultaneous force and wake measurements reveals that the two loading regimes are produced by two distinct wake topologies defined by strongly asymmetric vortex dynamics near the tip of the model. The results provide insight into salient features of the wake development and vortex dynamics and show that transient changes in the cross-flow force direction progress through a consistent change in the wake structure between two bounding quasi-steady states.

### Surface density function evolution and the influence of strain rates during turbulent boundary layer flashback of hydrogen-rich premixed combustion

The statistical behavior of the magnitude of the reaction progress variable gradient [alternatively known as the surface density function (SDF)] and the strain rates, which govern the evolution of the SDF, have been analyzed for boundary layer flashback of a premixed hydrogen-air flame with an equivalence ratio of 1.5 in a fully developed turbulent channel flow. The non-reacting part of the channel flow is representative of the friction velocity based Reynolds number Reτ = 120. A skeletal chemical mechanism with nine chemical species and twenty reactions is employed to represent hydrogen-air combustion. Three definitions of the reaction progress variable (RPV) based on the mass fractions of H2, O2, and H2O have been considered to analyze the SDF statistics. It is found that the mean variations of the SDF and the displacement speed Sd depend on the choice of the RPV and the distance away from the wall. The preferential alignment of the RPV gradient with the most extensive principal strain rate strengthens with an increase in distance from the cold wall, which leads to changes in the behaviors of normal and tangential strain rates from the vicinity of the wall toward the middle of the channel. The differences in displacement speed statistics for different choices of the RPV and the wall distance affect the behaviors of the normal strain rate due to flame propagation and curvature stretch. The relative thickening/thinning of the reaction layers of the major species has been explained in terms of the statistics of the effective normal strain rate experienced by the progress variable isosurfaces for different wall distances and choices of RPVs.

### Effects of moving contact line on filament pinch-off dynamics of viscoelastic surfactant fluids

Author(s): Shijian Wu and Hadi Mohammadigoushki

Experiments illustrate that the moving fluid contact line can significantly affect the extensional rheology of viscoelastic surfactant solutions. A scaling analysis is provided to rationalize the effects of contact-line spreading on extensional rheology of viscoelastic fluids.

[Phys. Rev. Fluids 5, 053303] Published Fri May 29, 2020

### How pointed can magnetized ferrofluid tips be?

Author(s): Aaron Madden, Juan Fernandez de la Mora, Hadi Sabouri, Nguyen Pham, and Brian Hawkett

The typical magnetized ferrofluid tip radius is ~0.1 mm, where capillary stress balances magnetostatic stress. Here we confirm experimentally the controlling role of magnetic saturation in more general conditions, even for ferrofluid menisci in highly nonuniform magnetic fields created by supporting them at a ferrous needle tip facing a strong magnet. We use a wide range of ferrofluid tensions and solvent polarities. Substantial changes in saturation magnetization are achieved with solvent evaporation, and record tip radii to 9.5 mm demonstrated at high volume fractions of magnetic particles.

[Phys. Rev. Fluids 5, 053604] Published Fri May 29, 2020

### Theory of hydrodynamic interaction of two spheres in wall-bounded shear flow

Author(s): Itzhak Fouxon, Boris Rubinstein, Zhouyang Ge, Luca Brandt, and Alexander Leshansky

It is shown theoretically that the presence of a wall induces qualitative and quantitative changes in the hydrodynamic interaction between two particles in a shear flow. The phase portrait of particles’ relative motion is rather different from the classical Batchelor and Green’s theory corresponding to an unbounded shear flow. It has the same topology upon varying the distance between the particle pair and the wall and contains new, previously overlooked, regions of closed trajectories. The theory is able to explain the origin of open swapping trajectories found earlier in numerical simulations.

[Phys. Rev. Fluids 5, 054101] Published Fri May 29, 2020

### Active and finite-size particles in decaying quantum turbulence at low temperature

Author(s): Umberto Giuriato and Giorgio Krstulovic

Motivated by current experiments, quantum turbulence in the presence of active and finite size particles is investigated numerically. We show that particles do not affect the development of the Kolmogorov regime, and the large scale Lagrangian observables are also compatible with a classical picture. Particles stay trapped inside superfluid vortices with occasional detachment and recapture. At small scales, particle dynamics is dominated by a fast precession frequency from the Magnus effect. Moreover, we observe that particle acceleration decorrelates much faster than in classical turbulence.

[Phys. Rev. Fluids 5, 054608] Published Fri May 29, 2020

### Symmetry breaking phenomena in thermovibrationally driven particle accumulation structures

Following the recent discovery of new three-dimensional particle attractors driven by joint (fluid) thermovibrational and (particle) inertial effects in closed cavities with various shapes and symmetries [M. Lappa, Phys. Fluids 26(9), 093301 (2014); ibid. 31(7), 073303 (2019)], the present analysis continues this line of inquiry by probing influential factors hitherto not considered; among them, the role of the steady component of thermovibrational convection, i.e., the time-averaged velocity field that is developed by the fluid due to the non-linear nature of the overarching balance equations. It is shown how this apparently innocuous problem opens up a vast parameter space, which includes several variables, comprising (but not limited to) the frequency of vibrations, the so-called “Gershuni number,” the size of particles (Stokes number), and their relative density with respect to the surrounding fluid (density ratio). A variety of new particle structures (2D and 3D) are uncovered and a complete analysis of their morphology is presented. The results reveal an increase in the multiplicity of solutions brought in by the counter-intuitive triadic relationship among particle inertial effects and the instantaneous and time-averaged convective thermovibrational phenomena. Finally, a universal formula is provided that is able to predict correctly the time required for the formation of all the observed structures.

### Viscous Rayleigh-Taylor and Richtmyer-Meshkov instabilities in the presence of a horizontal magnetic field

Author(s): Y. B. Sun and C. Wang

We first derive the exact dispersion relation for viscous Rayleigh-Taylor instability in the presence of a horizontal magnetic field using a decomposition method, and we find that the horizontal magnetic field contributes to the generation of vorticity inside the flow, thereby further distorting the...

[Phys. Rev. E 101, 053110] Published Thu May 28, 2020

### Drag force in immersed granular materials

Author(s): Tanvir Hossain and Pierre Rognon

Objects buried in granular materials can move when subjected to a large enough force. Experiments show that their mobility response is strongly affected by the presence of interstitial water, as it then features a visco-elasto-plastic dynamics.

[Phys. Rev. Fluids 5, 054306] Published Thu May 28, 2020

### Dynamics of floating objects at high particulate Reynolds numbers

Author(s): H. Ghaffarian, D. Lopez, E. Mignot, H. Piegay, and N. Riviere

The dynamics of high Reynolds number floating objects in one- and two-dimensional free surface flows are studied theoretically and experimentally. The results can greatly simplify the analyses and computations of the motion of floating objects at high particulate Reynolds number, first by identifying a characteristic distance, scaling the length of the acceleration phase, and then by showing that once the flow velocity is reached the object is transported as a passive tracer.

[Phys. Rev. Fluids 5, 054307] Published Thu May 28, 2020

### Robust principal component analysis for modal decomposition of corrupt fluid flows

Author(s): Isabel Scherl, Benjamin Strom, Jessica K. Shang, Owen Williams, Brian L. Polagye, and Steven L. Brunton

Robust principal component analysis (RPCA) is a powerful technique from robust statistics that can be used to extract dominant coherent structures from flow fields corrupted with outliers and missing measurements. The effectiveness of RPCA on flows acquired experimentally and by simulation is demonstrated. In all cases, RPCA is able to de-noise these fields and vastly improve subsequent modal analysis, showing that RPCA can be used to robustly process particle image velocimetry flow fields.

[Phys. Rev. Fluids 5, 054401] Published Thu May 28, 2020

### Finite-time localized singularities as a mechanism for turbulent dissipation

Author(s): Christophe Josserand, Yves Pomeau, and Sergio Rica

Turbulence is one of the oldest unsolved problems of physics, with no satisfactory explanation based on the solutions of fluids equations. To overcome this difficulty, a scenario consisting of spatiotemporal singularities, à la Leray, is proposed, mediating dissipation in a simpler partial differential equation that shares many of the critical aspects of fluid turbulence.

[Phys. Rev. Fluids 5, 054607] Published Thu May 28, 2020

### Investigation of asymmetrically pitching airfoil at high reduced frequency

The expanding application in micro-air vehicles has encouraged many researchers to understand the unsteady flow around a flapping foil at a low Reynolds number. We numerically investigate an incompressible unsteady flow around a two-dimensional pitching airfoil (SD7003) at high reduced frequency (k ≥ 3) in the laminar regime. This study interrogates the effect of different unsteady parameters, namely, amplitude (A), reduced frequency (k), Reynolds number (Re), and asymmetry parameter (S) for pitching motion on the force coefficients. The inviscid theoretical model is utilized to calculate the lift coefficient for sinusoidal motion in the viscous regime, and a comparison is made with the numerical results. The theoretical analysis identifies the influence of the non-circulatory lift over circulatory lift at a high reduced frequency. Furthermore, the results indicate that the reduced frequency (k) and asymmetry parameter (S) have a significant impact on the instantaneous and time-averaged force coefficients as well as on the vortex structure in the wake. Finally, the fast Fourier transformation analysis is carried out over a simulated case with fixed amplitude and Reynolds number for distinct k and S values. The findings confirm that the dominant frequency in the flow (k*) has a direct correlation to the airfoil pitching frequency (k).

### Droplet deformation and breakup in shear flow of air

The deformation and breakup of droplets in airflows is important in many applications of spray and atomization processes. However, the shear effect of airflow has never been reported. In this study, the deformation and breakup of droplets in the shear flow of air is investigated experimentally using high-speed imaging, digital image processing, and particle image velocimetry. We identify a new breakup mode of droplets, i.e., the butterfly breakup, in which the strong aerodynamic pressure on the lower part of the droplet leads to the deflection of the droplet and then the formation of a butterfly-shaped bag. A regime map of the droplet breakup is produced, and the transitions between different modes are obtained based on scaling analysis. The elongation and the fragmentation of the droplet rim are analyzed, and the results show that they are significantly affected by the shear via the formation and the growth of nodes on the rim.

### Effect of suction on laminar-flow control in subsonic boundary layers with forward-/backward-facing steps

In a subsonic boundary layer, a forward-facing step (FFS) or a backward-facing step (BFS) usually destabilizes the oncoming Tollmien–Schlichting (T-S) waves, leading to a promotion of laminar–turbulent transition. This paper studies a laminar-flow control strategy by introducing wall suction immediately ahead of the FFS or behind the BFS. The impact of the step–suction combination on an oncoming T-S wave is quantified by a transmission coefficient, defined as the ratio of the asymptotic amplitude downstream of the step and suction to that upstream. In order to solve this problem, a local scattering theory based on the large-Reynolds number (large-R) asymptotic framework and a Harmonic linearized Navier–Stokes approach, that calculates the perturbation field at finite Reynolds numbers, are employed. The latter approach is confirmed to be accurate by comparing its results with direct numerical simulations, and the results given by the two approaches agree when the Reynolds number is asymptotically large. According to the large-R triple-deck formulism, a few control parameters, such as the Mach number, Reynolds number, and wall temperature, disappear, which makes a systematical parametric study possible. The destabilizing effect of a step increases with its height, while the stabilizing effect of suction increases with its flux. For a step with a moderate height, suction with a small flux is sufficient to compensate the destabilizing effect of the step.

### Physical topology of three-dimensional unsteady flows with spheroidal invariant surfaces

Author(s): P. S. Contreras, M. F. M. Speetjens, and H. J. H. Clercx

Scope is the response of Lagrangian flow topologies of three-dimensional time-periodic flows consisting of spheroidal invariant surfaces to perturbation. Such invariant surfaces generically accommodate nonintegrable Hamiltonian dynamics and, in consequence, intrasurface topologies composed of island...

[Phys. Rev. E 101, 053109] Published Wed May 27, 2020

### Quantized orbital-chasing liquid metal heterodimers directed by an integrated pilot-wave field

Author(s): Jianbo Tang, Xi Zhao, and Jing Liu

A liquid metal hydrodynamic pilot-wave system reveals fascinating droplet and bath dynamics. Both the bouncing droplets and the oscillating bath meniscus become harmonic wave emitters and the superposition of their waves forms an integrated pilot-wave field. Riding on the pilot waves, dissimilar liquid metal droplet pairs (heterodimers) show kaleidoscopic double-quantized, directional, in-orbit chasing motions.

[Phys. Rev. Fluids 5, 053603] Published Wed May 27, 2020

### Experimental and numerical study of effect of secondary surfaces fixed over rectangular vortex generator with an overview of dynamic mode decomposition

Addition of a vortex generator (VG) to the heated surface creates longitudinal vortices in the flow; however, it induces drag. Surface modification of the VG may play a role in the thermal performance of the system. Therefore, flow and thermal behavior are studied for a secondary surface (SS) attached to the primary surface of a rectangular VG, which is placed inside a rectangular channel using air at Re = 5000. The VG with the SS is compared with a conventional rectangular VG having volume constant. With the addition of SS, the flow behind the VG greatly shears the produced primary vortex (P), which results in stretching. Stretching increases the angular momentum of the vortex with the decrease in the span of the produced vortices. The interaction between the co-rotating vortices P and high pressure side horse-shoe vortex (Hp) shows that the higher strain field induced by the vortex P shears away the vortex Hp. The vortex P developed under the influence of SS induces a higher degree of tilting toward the heated surface with low propagation speed. Finally, the dynamic decomposition of the vortices in the channel reveals that the vortex P appears to be dominant.

### Analysis of flow characteristics downstream delta-winglet vortex generator using stereoscopic particle image velocimetry for laminar, transitional, and turbulent channel flow regimes

The evolution of flow structures downstream a single pair of delta-winglet vortex generators (VGs) is investigated experimentally using stereoscopic particle image velocimetry. In addition, the laser Doppler anemometer technique is performed to characterize the upstream flow. Experiments are conducted in a bounded channel flow (height H) for the Reynolds numbers (ReDH, based on the hydraulic diameter height) ranging from 400 to 12 000. The purpose of this study is to provide detail insight into the generation and the dissipation of longitudinal vortices over a wide flow regime range including the laminar–turbulent transition. With a focus on transverse sections, the flow field is detailed. For all flow regimes, the main flow topology shows that the two main counter-rotating vortices are generated at a certain streamwise distance downstream the VG and then are advected gradually toward the channel lateral-walls. A secondary vortex pair is induced closer to the wall. Our results show that close to the VGs, local regions (1 > z/H > −1) are strongly defined as the inception of the turbulence production. The intensity of this latter is shown to vanish beyond a certain distance far from the origin of the perturbation (when x/H is greater than 3). The instantaneous flow structure describes the mechanism of vortex generation, relying on the intermittence of the flow organization and the sweep and ejection event balance. Detailed analysis on the turbulence properties and wall shear stress has been assessed and revealed that the flow transition induced by the perturbation of the VG is achieved at a Reynolds number no greater than 1500.

### Stability of flow in a deformable channel with an unrestrained boundary

We report results from a linear stability analysis of Newtonian plane Poiseuille flow through a deformable linear elastic channel with an unrestrained boundary wherein the deformable wall is not rigidly bonded to a substrate and is free to undergo motion. The objective of this study is to address the experimental observations of instabilities for this configuration [S. S. Srinivas and V. Kumaran, “Transitions to different kinds of turbulence in a channel with soft walls,” J. Fluid Mech. 822, 267–306 (2017)]. We analyze the role of an unrestrained deformable boundary on the stability of channel flow using both asymptotic and numerical methods. Our results show that when the solid to fluid layer thickness ratio is O(1), both wall modes (whose critical Reynolds number Rec ∝ G3/4, with G being the shear modulus of the solid) and inviscid modes (whose Rec ∝ G1/2) are significantly destabilized by the presence of an unrestrained boundary when compared to channels with completely bonded deformable boundaries. In agreement with experimental observations, the eigenfunctions corresponding to both these unstable modes exhibit a pronounced asymmetric behavior, thereby highlighting the influence of the unrestrained deformable boundary on the stability of the flow. The asymptotic predictions for the wall mode instability are shown to be in excellent agreement with our numerical results. However, for the solid to fluid thickness ratio ∼7.7 (used in the aforementioned experiments), our results show that the reduction in the critical Reynolds number due to the unrestrained boundary is only moderate; we provide possible reasons for the same.