# Latest papers in fluid mechanics

### Fluid dynamics of millefiori: Mixing ferrofluid with watercolor

Author(s): Azar Eslam-Panah, Cooper Kovar, Lisa Panczner, and Heidi Reuter

This paper is associated with a poster winner of a 2019 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.20...

[Phys. Rev. Fluids 5, 110510] Published Thu Nov 12, 2020

### Blooming flowers from drying drops

Author(s): Paul Lilin, Philippe Bourrianne, Guillaume Sintès, and Irmgard Bischofberger

This paper is associated with a video winner of a 2019 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2019...

[Phys. Rev. Fluids 5, 110511] Published Thu Nov 12, 2020

### Hydrodynamic tweezing: Using water waves to push and pull

Author(s): Ahmed Sherif and Leif Ristroph

This paper is associated with a poster winner of a 2019 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/AP...

[Phys. Rev. Fluids 5, 110512] Published Thu Nov 12, 2020

### Phoretic self-propulsion of Janus disks in the fast-reaction limit

Author(s): Ehud Yariv and Darren Crowdy

Using a combination of singular perturbation analysis and conformal mapping techniques, the self-propulsion velocity is found in the limit of fast reaction for a Janus particle with half of the boundary active and the other half inert.

[Phys. Rev. Fluids 5, 112001(R)] Published Thu Nov 12, 2020

### Effect of gusty inflow on the jet-switching characteristics of a plunging foil

The effect of stochastic inflow fluctuations on the jet-switching characteristics of a harmonically plunging elliptic foil at a low Reynolds number regime has been analyzed in the present study. The inflow fluctuations are generated by simulating an Ornstein–Uhlenbeck process—a stationary Gauss–Markov process—with a chosen correlation function. In the absence of fluctuations, quasi-periodic movement of the wake vortices plays a key role in bringing out jet-switching at κh ≥ 1.5. However, fluctuating inflow alters the organized arrangement of the vortex street even at a lower κh (κh = 1.0), giving way to an advanced jet-switching onset. More frequent switching with a larger deflection angle is also observed at κh = 1.5 as compared to the no fluctuation case. Effects of inflow timescales on the deflection angle and switching frequency of the wake are investigated by varying the input correlation-lengths. The underlying flow physics are investigated through a qualitative study of the near-field interactions as well as various quantitative measures derived from the unsteady flow-field.

### Synthetic capsule breakup in simple shear flow

Synthetic capsules in which a thin membrane encloses some biological or chemical ingredients are used in diverse industrial and biomedical applications. In extreme flow environments, the hydrodynamic loading acting on the membrane of the capsule may cause large deformation and structural failure. Although previous experimental studies have focused on the rheological behavior of capsules immersed in different types of flow, the mechanical characteristics of capsules under high shear rate and their breakup mechanism remain unclear. To investigate the breakup process in a simple shear flow, capsules based on human serum albumin are fabricated and used in experiments with a Couette flow rheoscope. The deformation of a tank-treading capsule is examined with the tension distribution on the membrane estimated by a simple analytical model, and the effects of membrane pre-stress on tension distribution and deformation are analyzed using non-inflated and inflated capsules. A non-inflated capsule without pre-stress continues to elongate with increasing shear rate until breakup, while an inflated capsule with pre-stress exhibits a plateau in the deformation under a high shear rate. Furthermore, based on the measurement of the time scale of breakup, we suggest that the breakup of a capsule may occur as a result of membrane fatigue. Given sufficiently high shear rate, the rupture of a membrane segment is induced by large-amplitude cyclic stress, which leads to the tear-up of the capsule along its meridional plane and finally the formation of two daughter lumps.

### The role of the “monopole” instability in the evolution of two-dimensional turbulent free shear layers

The role of instability in the growth of a two-dimensional, temporally evolving, “turbulent” free shear layer is analyzed using vortex-gas simulations that condense all dynamics into the kinematics of the Biot–Savart relation. The initial evolution of perturbations in a constant vorticity layer is found to be in accurate agreement with the linear stability theory of Rayleigh. There is then a stage of non-universal evolution of coherent structures that is closely approximated not by Rayleigh stability theory, but by the Karman–Rubach–Lamb linear instability of monopoles, until the neighboring coherent structures merge. After several mergers, the layer evolves eventually to a self-preserving reverse cascade, characterized by a universal spread rate found by Suryanarayanan, Narasimha, and Hari Dass [“Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics,” Phys. Rev. E 89, 013009 (2014)] and a universal value of the ratio of dominant spacing of structures (Λf) to the layer thickness (δω). In this universal, self-preserving state, the local amplification of perturbation amplitudes is accurately predicted by Rayleigh theory for the locally existing “base” flow. The model of Morris, Giridharan, and Lilley [“On the turbulent mixing of compressible free shear layers,” Proc. R. Soc. London, Ser. A 431, 219–243 (1990)], which computes the growth of the layer by balancing the energy lost by the mean flow with the energy gain of the perturbation modes (computed from an application of Rayleigh theory), is shown, however, to provide a non-universal asymptotic state with initial condition dependent spread rate and spectra. The reason is that the predictions of the Rayleigh instability, for a flow regime with coherent structures, are valid only at the special value of Λf/δω achieved in the universal self-preserving state.

### Effect of charge convection on gravitational settling of drop in uniform electric field

Dynamics of droplets in an electrified medium is largely dictated by an intricate interplay between interfacial charge convection and Ohmic conduction within the bulk. The extent of this interaction is quantified by the electric Reynolds number, ReE, delineating their relative strengths. The reported asymptotic theories consider vanishingly low values of ReE, i.e., negligible surface charge convection as compared to the bulk Ohmic conduction, which, in turn, enables decoupling of the contributions of drop deformation and charge convection. This, however, is grossly inaccurate toward establishing an appropriate inter-connection between surface charge convection and morpho-dynamic evolution of the drop beyond such limiting conditions. Circumventing these limits, here we present a theoretical approach that is capable of bringing out the underlying physics beyond low ReE limits. We realize this by incorporating nonlinear charge-convection effects in the leading-order and first-order problem. The present analytical model not only predicts the drop speed accurately but also shows noticeable improvement over the predictive capabilities of the existing asymptotic models. Our results demonstrate that convection of charges can lead to a substantial increase or decrease in gravitational settling speed, depending on the relative electrical properties of the droplet and the carrier. In sharp contrast to previously reported findings, we show that sufficiently strong charge convection can overwhelm the effect of deformation and hence can reverse the trends in the settling speed reported earlier. Comparison with results from full-scale numerical simulations justifies the accuracy of our analytical approach up to a fair level of high asymmetric deformation.

### Nonlocal shear-thinning effects substantially enhance helical propulsion

Author(s): Ebru Demir, Noah Lordi, Yang Ding, and On Shun Pak

Theoretical and computational analyses show that a shear-thinning viscosity alone can cause a substantial enhancement to the propulsion of helical microswimmers.

[Phys. Rev. Fluids 5, 111301(R)] Published Wed Nov 11, 2020

### State-resolved transport collision integrals for the $\mathrm{O}+{\mathrm{O}}_{2}$ system

Author(s): Sharanya Subramaniam, Richard L. Jaffe, and Kelly A. Stephani

A technique to compute vibrationally resolved transport collision integrals for atom-diatom systems directly from *ab inito* potential energy surfaces (PES) is presented. These calculations are performed for the oxygen systems employing the Varga *et al.* set of PES, and Guyta-Yos style fits to the data are provided. It is found that simple empirical models are often unable to capture the dependence of these collision integrals on the vibrational state of the molecule. Differences of up to 80% are observed between the model predictions and the values computed directly from the PES.

[Phys. Rev. Fluids 5, 113402] Published Wed Nov 11, 2020

### Modal and nonmodal stability of a stably stratified boundary layer flow

Author(s): E. Parente, J. C. Robinet, P. De Palma, and S. Cherubini

We investigate the modal and nonmodal linear stability of a stably stratified Blasius boundary-layer flow, composed of a velocity and a thermal boundary layer. The nonmodal analysis, based on optimization of a weighted sum of the kinetic and potential energies, provides oblique optimal structures close to the wall at short target times and spanwise-homogeneous rolls at the freestream for long target times. The latter disappear when variation of stratification strength with height is accurately accounted for in the norm definition, underlining the importance of the choice of a meaningful norm for thermal boundary layer optimization.

[Phys. Rev. Fluids 5, 113901] Published Wed Nov 11, 2020

### Stabilizing water films using surface acoustic waves

Author(s): Amihai Horesh, Anna Zigelman, and Ofer Manor

MHz-frequency surface acoustic waves (SAWs) in a solid substrate will stabilize neighboring micron- and submicron-thick liquid films against film breakup and substrate de-wetting at large ratios of acoustic to capillary stresses in the films. Low such ratios actively de-stabilize oil films, yet continue to stabilize water films. The difference in the response of water and oil films to the SAW appears to be connected to the presence of excess pressure from the electrical double layer force in water films.

[Phys. Rev. Fluids 5, 114002] Published Wed Nov 11, 2020

### Effect of inertial migration of particles on flow transitions of a suspension Taylor-Couette flow

Author(s): Lina Baroudi, Madhu V. Majji, and Jeffrey F. Morris

Uniformly distributed particles in inertial flows migrate across the streamlines to form nonuniform distributions in the flow cross sections. Here, an experimental study of the influence of inertial migration of particles on flow transitions of a suspension in Taylor-Couette geometry is presented. It is shown that, relative to uniform concentration, the particle distribution following inertial migration either stabilizes or destabilizes the flow depending on the underlying flow structure and flow Reynolds number.

[Phys. Rev. Fluids 5, 114303] Published Wed Nov 11, 2020

### Settling of inertial particles in turbulent Rayleigh-Bénard convection

Author(s): Vojtěch Patočka, Enrico Calzavarini, and Nicola Tosi

Settling of inertial particles in basally heated fluids is a topic of great significance in nature and, in particular, for the study of how magma cools and solidifies. The residence time of particles in Rayleigh-Bénard convection is computed for a broad range of flow and particle parameters, and a general analytic formula is designed that captures the results. It is found that particles tend to settle rapidly compared with the characteristic solidification timescale of magmatic systems. In addition, the horizontal distribution of settling events shows a surprising pattern: Heavy particles settle preferentially below clusters of upwelling plumes.

[Phys. Rev. Fluids 5, 114304] Published Wed Nov 11, 2020

### Deep learning for <i>in situ</i> data compression of large turbulent flow simulations

Author(s): Andrew Glaws, Ryan King, and Michael Sprague

Large turbulent flow simulations can lead to information bottlenecks as data is generated faster than it can be processed and saved. Innovative in-situ data compression techniques are needed. Here we examine a deep learning approach to in-situ compression using a novel autoencoder architecture customized for three-dimensional turbulent flows. We compare it to a randomized single-pass singular value decomposition method and demonstrate improved compression and reconstruction, particularly with respect to important statistical quantities such as turbulent kinetic energy, enstrophy, and Reynolds stresses, at lower computational cost.

[Phys. Rev. Fluids 5, 114602] Published Wed Nov 11, 2020

### Study of the energy convergence of the Karhunen-Loeve decomposition applied to the large-eddy simulation of a high-Reynolds-number pressure-driven boundary layer

Author(s): Pieter Bauweraerts and Johan Meyers

The convergence of the Karunen-Loève (KL) decomposition in high-Reynolds-number boundary layers is investigated using large-eddy simulations. It is found that the KL dimension, namely, the number of KL modes necessary to represent 90% of the turbulent kinetic energy, is up to 3 orders of magnitude higher than values commonly reported in earlier studies. This indicates that more caution should be exercised when considering the convergence of a proper orthogonal decomposition basis in high-Reynolds-number boundary layers, and it illustrates once more the challenges associated with representing turbulence in a low-dimensional basis.

[Phys. Rev. Fluids 5, 114603] Published Wed Nov 11, 2020

### Modeling the pressure-Hessian tensor using deep neural networks

Author(s): Nishant Parashar, Balaji Srinivasan, and Sawan S. Sinha

The pressure-Hessian tensor (PHT) is an important factor governing the Lagrangian evolution of velocity gradients in turbulent flows. To help develop a physically consistent model for PHT, we train a tensor basis neural network (TBNN) using velocity gradient information as input. Our trained model is found to be superior to existing models, not just in terms of root-mean-squared error, but also for capturing PHT physical attributes. Our model retrieves almost identical alignment statistics between the pressure-Hessian and the strain-rate eigenvectors when compared with well established direct numerical simulation (DNS) datasets.

[Phys. Rev. Fluids 5, 114604] Published Wed Nov 11, 2020

### Signature and energetics of internal gravity waves in stratified turbulence

Author(s): Andrea Maffioli, Alexandre Delache, and Fabien S. Godeferd

Internal gravity waves in stratified turbulence are searched for using spatiotemporal Fourier transforms of the 3D velocity and density perturbation fields obtained from direct numerical simulation. Waves at high frequency up to ω=N are uncovered and the Doppler shift imparted on them by the horizontal mean flow is used to develop a method for estimating their energy content. The results highlight a variation of the wave energy with buoyancy Reynolds number. The wave signal is concentrated at the largest scales and is much less discernible over the majority of other scales, containing low-frequency nonlinear and anisotropic motions.

[Phys. Rev. Fluids 5, 114802] Published Wed Nov 11, 2020

### Dynamics of a reactive spherical particle falling in a linearly stratified fluid

Author(s): Ludovic Huguet, Victor Barge-Zwick, and Michael Le Bars

The behavior of a melting sphere, sinking in a linearly stratified fluid, is carefully investigated using an experimental setup. The melting of a sphere induces a large enhancement of the drag coefficient. A stratification drag enhancement for high Reynolds numbers is also observed. Internal gravity waves generated by wake turbulence redistribute the kinetic energy into the stratified fluid over a long period.

[Phys. Rev. Fluids 5, 114803] Published Wed Nov 11, 2020

### Surface wave characteristics of a volume source horizontally translating in a stratified fluid

The present work aims to investigate the free surface wave system of a volume source translating in a stratified fluid. In this paper, a modified model is established with linearized governing equations and the free surface condition. This modified model can describe both the internal and surface waves excited by a volume source with arbitrary density profiles. The wave characteristics that are analyzed include the half-wedge angle, crestlines, the maximum amplitude, and the apparent angle. The results show that the entire wave system is complex and composed by an infinite number of single wave modes. The different modes can be divided into surface modes (mode number n = 0) and internal modes (n ≥ 1). It is found that internal modes have many similarities to each other but are quite different from surface modes. In the subcritical area [[math], where the Froude number is [math] and the critical Froude number of mode n is [math]], the wave structure of the nth mode contains divergent and transverse waves, and the half-wedge angle of surface mode waves increases from the Kelvin-wave angle of 19°28′ to 90°, while the half-wedge angle of internal mode waves increases from 0° to 90°. In the supercritical domain (Fr ≥ Frn), there are only divergent waves, and the half-wedge angle of all mode waves decays as sin−1(Frn/Fr). The amplitude of waves is related to the velocity of the source, the location of the source, the depth of the fluid, the Brunt–Väisälä frequency, the thickness of the pycnocline, and the center location of the pycnocline. The effects of these factors have been discussed in this paper. The apparent angle, which indicates the highest peak of waves, is also discussed. The results show that the apparent angle of all mode waves scales like Fr−1 at large Froude numbers.