# Latest papers in fluid mechanics

### Inlet swirl decay and mixing in a laminar micro-pipe flow with wall slip

In this work, the decaying laminar inlet swirl flow in a straight circular micro-pipe with wall slip is solved analytically and the solution is verified numerically. Based on a fully developed parabolic axial velocity profile, the swirl velocity equation is solved by the separation of variables technique. The solution is expressed as a function of the flow Reynolds number, the axial distance within the circular micro-pipe from the inlet, the wall slip, and the inlet swirl velocity profile. The effects of the parameters on the swirl velocity distribution and the swirl decay are analyzed along the flow. The addition of swirling velocity to the flow of a fluid in a pipe is of great importance in the enhancement of transport characteristics. The current results offer analytical equations to estimate the swirl velocity distribution with slip at the walls for the design of swirl flow devices. Furthermore, to quantify mixing, the change in the average distance traveled by fluid particles from the inlet in a swirl flow is compared with the average distance traveled by the fluid particles in the case of no swirl. A clear enhancement of the average distance traveled is obtained for flows with the interaction of both swirl and slip effects. In our opinion, the present work is useful to researchers looking for the enhancement of transport characteristics in circular micro-pipes.

### Bicritical states in a vertical layer of fluid under two-frequency temperature modulation

Author(s): Jitender Singh, Puneet Kaur, and Renu Bajaj

In this paper, the effect of two-frequency modulation of boundary temperatures on the onset of natural convection in a layer of fluid (with Prandtl number <12.5) between two vertical parallel planes is considered. The ratio of the two forcing frequencies and the mixing angle for the amplitude of ...

[Phys. Rev. E 101, 023109] Published Wed Feb 26, 2020

### Local details versus effective medium approximation: A study of diffusion in microfluidic random networks made from Voronoi tessellations

Author(s): Washington Ponce and María Luisa Cordero

We measured the effective diffusion coefficient in regions of microfluidic networks of controlled geometry using the fluorescence recovery after photobleaching (FRAP) technique. The geometry of the networks was based on Voronoi tessellations, and had varying characteristic length scale and porosity....

[Phys. Rev. E 101, 023110] Published Wed Feb 26, 2020

### Experimental and theoretical investigation of cubic stabilization of instability of an interface in surface wave motion

Motivated by recent laboratory and field observations, this paper reports the first quantitative measurements of the stabilization phase of interfacial instability in a two-layer fluid in surface wave motion. The instability results from the formation of a resonant triad between the surface wave and noise-level sub-harmonic interfacial waves. To exclude the effects of interfacial mixing on the interaction, the experiments were carried out with immiscible fluids. Carrying out a resonant interaction analysis to the third order of nonlinearity using a Lagrangian formulation, we also show for the first time that the three-wave resonance is inherently accompanied by a harmonic four-wave resonant interaction among the interfacial waves. Omitting the four-wave resonant interaction terms from the analysis results in over-prediction of the final amplitude of the interfacial waves by a factor greater than 2. The theoretical predictions are well-supported by the experiments.

### Transitions near the onset of low Prandtl-number rotating convection in presence of horizontal magnetic field

We investigate the transitions near the onset of thermal convection in electrically conducting low Prandtl-number (Pr) fluids in the presence of rotation about a vertical axis and external horizontal magnetic field. Three-dimensional direct numerical simulations (DNSs) and low dimensional modeling are performed with the Rayleigh–Bénard convection system in the ranges 0 < Q ≤ 1000 and 0 < Ta ≤ 500 of the Chandrasekhar number (Q) and the Taylor number (Ta), respectively, for that purpose. For larger Q(≥32.7), DNSs show substantial enhancement of convective heat transport and only finite amplitude steady two dimensional roll patterns at the onset. On the other hand, for smaller Q(<32.7), very rich dynamics involving different stationary as well as time dependent patterns, including stationary two-dimensional rolls, cross rolls, and oscillatory cross rolls, are observed at the onset of convection. Our investigation uncovers the cause of enhancement of heat transport and the origin of different flow patterns at the onset. We establish that a first order transition to convection occurring at the onset is responsible for the enhancement of the heat transport there. Furthermore, as the Rayleigh number (Ra) is increased beyond the onset, subsequent transitions near it are also explored in detail for smaller Q, and these are found to be associated with a variety of bifurcations including subcritical/supercritical pitchfork, Hopf, imperfect pitchfork, imperfect gluing, and Neimark–Sacker.

### Large-eddy simulation study of Reynolds number effects on the flow around a wall-mounted hemisphere in a boundary layer

Large-eddy simulations were used to investigate unsteady flows around a wall-mounted hemisphere as the Reynolds number (Re, based on the diameter of the hemisphere D) increased from 7 × 104 to 7 × 105. The hemisphere was immersed in a low-turbulence-intensity boundary layer with a thickness of δ/D = 0.5. Strong Re dependence was confirmed to be present even for the flow around a wall-mounted obstacle after systematic examination of aerodynamic forces, local pressures, and flow structures. Drag and lift crises were observed simultaneously, with the critical Re noted at approximately 3 × 105. As with circular cylinders and spheres, a laminar-turbulent transition and induced flow separation delay were observed in the supercritical Re regime. Flow separation occurred on the sides of the body later than on the top, regardless of whether Re was subcritical or supercritical. The spatial and temporal features of flow structures at different scales were described in detail based on the present high-resolution simulations. The coexistence of lateral oscillations and arch-type vortex shedding occurred throughout the subcritical and supercritical Re range. However, both of these motions diminished in scale and strength at supercritical Re. Flow motion frequencies were also quantified. The frequency ratio of arch vortex shedding to lateral oscillation was approximately 4 at subcritical Re but decreased to 3 at supercritical Re.

### Coupling effects and thin-shell corrections for surface instabilities of cylindrical fluid shells

Author(s): Shuai Zhang, Hao Liu, Wei Kang, Zuoli Xiao, Jianjun Tao, Ping Zhang, Weiyan Zhang, and X. T. He

We show that when linear azimuthal perturbations on the surfaces of a fluid shell are regrouped according to αm, they can be divided into Bell model terms, coupling terms, and the newly identified thin-shell correction terms, where α is the ratio of Rout to Rin, and m is the mode number of a given u...

[Phys. Rev. E 101, 023108] Published Tue Feb 25, 2020

### Topology of the second-order constitutive model based on the Boltzmann–Curtiss kinetic equation for diatomic and polyatomic gases

The topological aspects of fluid flows have long been fascinating subjects in the study of the physics of fluids. In this study, the topology of the second-order Boltzmann–Curtiss constitutive model beyond the conventional Navier–Stokes–Fourier equations and Stokes’s hypothesis was investigated. In the case of velocity shear, the topology of the second-order constitutive model was shown to be governed by a simple algebraic form. The bulk viscosity ratio in diatomic and polyatomic gases was found to play an essential role in determining the type of topology: from an ellipse to a circle, to a parabola, and then finally to a hyperbola. The topology identified in the model has also been echoed in other branches of science, notably in the orbits of planets and comets and Dirac cones found in electronic band structures of two-dimensional materials. The ultimate origin of the existence of the topology was traced to the coupling of viscous stress and velocity gradient and its subtle interplay with the bulk viscosity ratio. In the case of compression and expansion, the topology of the second-order constitutive model was also found to be governed by a hyperbola. The trajectories of solutions of two representative flow problems—a force-driven Poiseuille gas flow and the inner structure of shock waves—were then plotted on the topology of the constitutive model, demonstrating the indispensable role of the topology of the constitutive model in fluid dynamics.

### Energy transformation on flow-induced motions of multiple cylindrical structures with various corner shapes

A comprehensive numerical study on flow-induced motions (FIMs) of a deep-draft semi-submersible, a typical multiple cylindrical structure in offshore engineering, was carried out to investigate the energy transformation of the vortex shedding process. In addition, the corner shape effect on the flow characteristics, the hydrodynamic forces, and the FIM responses are presented for a multiple cylindrical structure with various corner shapes (sharp, rounded, and chamfered) under 45° current incidence. Different energy transformations, hydrodynamic characteristics, and FIM responses were observed due to the slight variation of the corner shape. The galloping at 45° incidence for a square-section shape column was observed when the corner shape modified as a chamfered corner. A “re-attached vortex shedding” phenomenon is discovered when the “lock-in” happened for a chamfered corner design. Further insights of the fluid physics into the flow characteristics due to the difference of the corner shape are revealed. In addition, the energy transformation and the mechanism for reducing the hydrodynamic forces and the FIM responses are analyzed.

### Symmetries and turbulence modeling

This work applies new insights into turbulent statistics gained by Lie symmetry analysis to the closure problem of turbulence. Founded in the mathematics of partial differential equations, Lie symmetries have helped advances in many fields of modern physics. The main reason for this is their ability to encode important physical principles that are implicitly expressed by governing equations. Newly discovered symmetries of the multi-point correlation equations describing turbulent motion have been shown to encode two central effects of turbulent statistics: intermittency and non-Gaussianity. Moreover, these symmetries play a pivotal role in obtaining turbulent scaling laws such as the logarithmic law of the wall. Evidently, correctly preserving these symmetry properties in a turbulence model would render it capable of accurately predicting important effects of turbulent statistics and turbulent scaling. As these symmetry constraints have so far not been taken into account when devising turbulence models, we present a completely new modeling framework that can yield models fulfilling these conditions. In order to accomplish this, it turns out to be helpful, if not necessary, to introduce an entirely new symmetry-based modeling strategy that allows systematically constructing equations based on symmetry constraints imposed on them. From these considerations, it can be shown that in order to create meaningful turbulence models that fulfill these constraints, it is necessary to introduce a new velocity and pressure field. A possible skeleton of model equations for second moment closure is presented.

### Series expansion for normal stress differences in large-amplitude oscillatory shear flow from Oldroyd 8-constant framework

The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. In this paper, we focus on the normal stress difference responses to large-amplitude oscillatory shear (LAOS) flow. The nonlinearity of the polymeric liquids, triggered by LAOS, causes these responses at even multiples of the test frequency. We call responses at a frequency higher than twice the test frequency higher harmonics. The normal stress difference responses for the Oldroyd 8-constant framework has recently yielded to the exact analytical solution. However, in its closed form, Bessel functions appear 24 times, each within summations to infinity. In this paper, to simplify the exact solution, we expand it in a Taylor series. We truncate the series after its 17th power of the shear rate amplitude. Our main result reduces to the well-known expression for the special cases of the corotational Jeffreys and corotational Maxwell fluids. Whereas these special cases yielded to the Goddard integral expansion (GIE), the more general Oldroyd 8-constant framework does not. We use Ewoldt grids to show our main result to be highly accurate for the corotational Jeffreys and corotational Maxwell fluids. For these two special cases, our solutions agree closely with the exact solutions as long as [math]. We compare our main result, for the special case of the Johnson–Segalman fluid, with measurements on dissolved polyisobutylene in the isobutylene oligomer. For this, we use the Spriggs relations to generalize our main result to multimode, which then agrees closely with the measurements.

### Dynamics of phase separation of sheared inertialess binary mixtures

When a viscous binary mixture subject to an applied shear flow is rapidly quenched into the unstable region of its phase diagram, the resulting phase separation is influenced by two competing effects. On one hand, nuclei of the minority phase tend to grow with a constant growth rate, while, on the other hand, they are stretched along the flow direction, forming thinner and thinner layered domains that eventually break. We simulate the dynamics of this system with a thermodynamics-based diffuse interface model, accounting for the full interplay between hydrodynamics (i.e., the Navier–Stokes equations) and species conservation (i.e., the Cahn–Hilliard equation) coupled via the Korteweg body-force. We show that periodic steady-state configurations with stable droplets are obtained for low capillary numbers while phase separation takes place along bands oriented in the direction of the flow in the case of strong shear because, in the long term, diffusion in the cross-flow direction prevails on the convective flow field. The dynamics of phase separation is highly non-linear and diverse even for inertialess flow, featuring multiple coalescence and breakups: although some typical time scaling for the characteristic droplet size in the flow and cross-flow directions can be obtained, the full evolution cannot be characterized only by the capillary number. The wide range of droplet morphologies predicted by the model, from round and elongated shapes to bands and hollow droplets, suggests interesting applications for manufacturing of polymers and soft materials.

### Active matter in a viscoelastic environment

Author(s): Emmanuel L. C. VI M. Plan, Julia M. Yeomans, and Amin Doostmohammadi

A two-phase model of active nematic matter within a passive polymeric phase is shown to capture important cellular dynamics, such as cell division and motility, in viscoelastic fluids. The results show the suppressing effect of polymer relaxation and viscosity on the dynamics of active matter.

[Phys. Rev. Fluids 5, 023102] Published Mon Feb 24, 2020

### Symmetry breaking of azimuthal waves: Slow-flow dynamics on the Bloch sphere

Author(s): Abel Faure-Beaulieu and Nicolas Noiray

A low-order model is proposed to describe the slow-timescale dynamics of thermoacoustic limit cycles in an idealized annular combustion chamber. A quaternion ansatz for the acoustic pressure field enables a unified description of the impact of system asymmetries (nonuniform distribution of heat release rate or azimuthal mean flow), flame response delay, and stochastic forcing from turbulence upon the standing or spinning nature of the thermoacoustic modes.

[Phys. Rev. Fluids 5, 023201] Published Mon Feb 24, 2020

### Surface jets and internal mixing during the coalescence of impacting and sessile droplets

Author(s): Thomas C. Sykes, Alfonso A. Castrejón-Pita, J. Rafael Castrejón-Pita, David Harbottle, Zinedine Khatir, Harvey M. Thompson, and Mark C. T. Wilson

A surface jet during droplet coalescence is identified and studied using two color high-speed cameras with side and bottom views. By introducing a surface tension difference between the droplets, the internal dynamics can be modified, while the surface jet can either be enhanced or suppressed. A mechanism to control mixing is therefore established.

[Phys. Rev. Fluids 5, 023602] Published Mon Feb 24, 2020

### Dynamics and flow characterization of liquid fountains produced by light scattering

Author(s): Hugo Chesneau, Julien Petit, Hamza Chraïbi, and Jean-Pierre Delville

Light scattering in turbid liquids induces bulk flows. These flows are simulated and analyzed to show how they can deform flat interfaces up to instability and jetting. Numerical results are compared to experimental ones performed in near-critical phase-separated liquid mixtures. The comparison shows quantitative agreement for interface shapes and allows qualitative retrieval of the behavior of the produced fluid flow rates. These light-induced bulk flows and their contactless actuation of interfaces are well suited for microscale applications.

[Phys. Rev. Fluids 5, 024002] Published Mon Feb 24, 2020

### Study on preferential concentration of inertial particles in homogeneous isotropic turbulence via big-data techniques

Author(s): M. Obligado, A. Cartellier, A. Aliseda, T. Calmant, and N. de Palma

We present an experimental study on the preferential concentration of sub-Kolmogorov inertial particles in active-grid-generated homogeneous and isotropic turbulence. Big data techniques able to detect centers and compute Voronoï tessellations 10 times faster than standard algorithms are used. Since preferential concentration depends on multiple parameters we performed experiments varying all except one parameter: volume fraction, Reynolds number based on the Taylor length scale, and particle residence time interacting with turbulence.

[Phys. Rev. Fluids 5, 024303] Published Mon Feb 24, 2020

### Inertial waves in turbine rim seal flows

Author(s): Feng Gao (高锋), John W. Chew, and Olaf Marxen

Unsteady flow modes with intrinsic frequencies unrelated to that of the turbine blades are found to be dominated by inertial waves. In the presence of these waves, rim sealing is less efficient, and conventional Reynolds-averaged Navier-Stokes methods fail to predict the sealing effectiveness. The radial seal, which limits the radial flow motion and, in turn, the circumferential Coriolis force, can suppress inertial waves (unsteady flow modes).

[Phys. Rev. Fluids 5, 024802] Published Mon Feb 24, 2020

### Referee acknowledgment for 2019

### Microscopic Richtmyer–Meshkov instability under strong shock

The microscopic-scale Richtmyer–Meshkov instability (RMI) of a single-mode dense-gas interface is studied by the molecular dynamics approach. Physically realistic evolution processes involving the non-equilibrium effects such as diffusion, dissipation, and thermal conduction are examined for different shock strengths. Different dependence of the perturbation growth on the shock strength is found for the first time. Specifically, the amplitude growths for cases with relatively lower shock Mach numbers (Ma = 1.9, 2.4, 2.9) exhibit an evident discrepancy from a very early stage, whereas for cases with higher Mach numbers (Ma = 4.9, 9.0, 16.0), their amplitude variations with time match quite well during the whole simulation time. Such different behaviors are ascribed to the viscosity effect that plays a crucial role in the microscale RMI. The compressible linear theory of Yang et al. [“Small amplitude theory of Richtmyer–Meshkov instability,” Phys. Fluids 6(5), 1856–1873 (1994)] accounting for the viscosity dissipation provides a reasonable prediction of the simulated linear growth rate. Furthermore, a modified compressible nonlinear model [Q. Zhang et al., “Quantitative theory for the growth rate and amplitude of the compressible Richtmyer–Meshkov instability at all density ratios,” Phys. Rev. Lett. 121, 174502 (2018)] considering both the viscosity effect and the corrected linear growth rate is proposed, which gives an excellent forecast of the linear and nonlinear growths of the present microscale RMI.