# Latest papers in fluid mechanics

### Solidification of the Lennard-Jones fluid near a wall in thermohydrodynamic lubrication

Author(s): Kouki Nakamura, Ryo Ookawa, and Shugo Yasuda

We investigate the thermohydrodynamic lubrication of the Lennard-Jones (LJ) fluid in plain wall channels by using a molecular-dynamics simulation. It is found that the LJ fluid solidifies near the wall when the viscous heating of the LJ fluid in the bulk regime is sufficiently large. The thickness o...

[Phys. Rev. E 100, 033109] Published Mon Sep 16, 2019

### Closed-loop adaptive control of extreme events in a turbulent flow

Author(s): Mohammad Farazmand and Themistoklis P. Sapsis

Extreme events that arise spontaneously in chaotic dynamical systems often have an adverse impact on the system or the surrounding environment. As such, their mitigation is highly desirable. Here, we introduce a control strategy for mitigating extreme events in a turbulent shear flow. The controller...

[Phys. Rev. E 100, 033110] Published Mon Sep 16, 2019

### Compressibility effects of supersonic Batchelor vortices

Author(s): Toshihiko Hiejima

Compressibility effects mean that fluctuation growth related to turbulence is suppressed as Mach number increases. An investigation that clarifies compressibility effects of the Batchelor vortex is presented. The findings indicate that entropy fluctuation in the vortex is strongly related to intrinsic compressibility.

[Phys. Rev. Fluids 4, 093903] Published Mon Sep 16, 2019

### Turbulent drag reduction by rotating rings and wall-distributed actuation

Author(s): Paolo Olivucci, Pierre Ricco, and Sohrab Khosh Aghdam

We use direct numerical simulations of turbulent channel flows to model skin-friction drag reduction with wall rotating rings combined with hydrophobic surfaces or opposition control. We find rotating rings reduce drag 20%. Combining with opposition control adds 7.4% and hydrophobic surfaces 6.5%.

[Phys. Rev. Fluids 4, 093904] Published Mon Sep 16, 2019

### Wave generation through the interaction of a mode-2 internal solitary wave and a broad, isolated ridge

Author(s): David Deepwell, Marek Stastna, Magda Carr, and Peter A. Davies

An investigation of a mode-2 internal solitary wave passing over a broad ridge finds that it is gradually adjusted into multiple waves of different form. The leading wave remains intact but is reduced in amplitude and energy. Incident amplitude, speed, and ridge height determine the strength of the resultant waves.

[Phys. Rev. Fluids 4, 094802] Published Mon Sep 16, 2019

### Drag reduction in turbulent flow along a cylinder by circumferential oscillating Lorentz force

Direct numerical simulations are performed to study the drag reduction effect in turbulent flow along a cylinder by the circumferential oscillating Lorentz force at the Reynolds number Reτ = 272 based on the reference friction velocity and the thickness of the boundary layer. The maximum drag reduction rate obtained in the present work is 42.6%. The intensity, penetration thickness, distribution (idealized or realistic), and oscillation period of the Lorentz force are all crucial in determining the drag reduction rate. As the Lorentz force is intensified or its penetration thickness and oscillation period increase, the wall friction drag will prominently decrease as long as the circumferential flow is stable. The Stokes layer, introduced by the circumferential oscillating Lorentz force, effectively manipulated the near-wall coherent structures, leading to the decrease of the wall friction drag. However, the occurrence of the force-induced vortices in the near-wall region can also lead to significant drag increase by enhancing the radial momentum transportation due to centrifugal instability. By estimating the energy consumption rate, it is clear that the extra power to implement the Lorentz force is far more than the power saved due to drag reduction, which is the result of the low conductivity of the fluid media. Taking the coupling between the electromagnetic field and the flow field into consideration, the wall friction drag is nearly zero and the turbulence intensity in the near-wall region is very low when the induced Lorentz force is high. But the induced Lorentz drag is greatly increased and the turbulence fluctuations are enhanced in the outer region.

### Surfactant-laden droplet behavior on wetting solid wall with non-Newtonian fluid rheology

We develop a coupled lattice-Boltzmann with finite-difference (LB-FD) method to simulate surfactant-laden droplet behaviors on wetting solid wall with non-Newtonian fluid rheology. The effects of the power-law exponent, wettability, force direction, and viscosity ratio on the droplet movement under the shear flow or body force are investigated. It is found that the surfactant-laden droplet moves faster and breaks up more easily than the clean droplet owing to the decreased local interfacial tension. During the initial period of the droplet movement, with the decrease of the power-law exponent of the matrix fluid, the unbalanced Young’s force plays a significant role in prompting droplet spreading along the hydrophilic wall whereas making the droplet recoil along the hydrophobic wall. Under the influence of the shear force, the droplet deformation is strengthened in the shear thickening matrix fluid due to high viscous stress from the external flow. However, under the influence of the body force, droplet deformation is strengthened in the shear thinning matrix fluid because the reduction of the matrix fluid apparent viscosity generates less viscous drag force. Furthermore, the shear thickening pendent droplet is more elongated and shows more flexible behavior than the shear thinning droplet during its falling in the Newtonian matrix fluid. The decrease of the viscosity ratio causes the shear thickening droplet to form the shape of a spherical cap, compared with the shear thinning droplet behaving like a rigid object. The present work not only demonstrates the capacity of the coupled LB-FD method but also sheds light on the mechanism of surfactant-laden droplet dynamics on wetting solid wall where non-Newtonian rheology is considered.

### Reactive-infiltration instability in radial geometry: From dissolution fingers to star patterns

Author(s): Piotr Grodzki and Piotr Szymczak

We consider the process of chemical erosion of a porous medium infiltrated by a reactive fluid in a thin-front limit, in which the width of the reactive front is negligible with respect to the diffusive length. We show that in the radial geometry the advancing front becomes unstable only if the flow...

[Phys. Rev. E 100, 033108] Published Fri Sep 13, 2019

### Pair dispersion in inhomogeneous turbulent thermal convection

Author(s): Olivier Liot, David Martin-Calle, Amélie Gay, Julien Salort, Francesca Chillà, and Mickaël Bourgoin

An experimental study of the pair separation of particles in turbulent thermal convection reveals the dramatic impact of the inhomogeneous large-scale flow on pair dispersion, without affecting the small-scale turbulent statistics. The Richardson-Obukhov regime is also revisited.

[Phys. Rev. Fluids 4, 094603] Published Fri Sep 13, 2019

### Vortex dynamics in low- and high-extent polymer drag reduction regimes revealed by vortex tracking and conformation analysis

Turbulent flow profiles are known to change between low- (LDR) and high-extent drag reduction (HDR) regimes. It is however not until recently that the LDR-HDR transition is recognized as a fundamental change between two DR mechanisms. Although the onset of DR, which initiates the LDR stage, is explainable by a general argument of polymers suppressing vortices, the occurrence of HDR where flow statistics are qualitatively different and DR effects are observed across a much broader range of wall regions remains unexplained. Recent development of the vortex axis tracking by iterative propagation algorithm allows the detection and extraction of vortex axis-lines with various orientations and curvatures. This new tool is used in this study to analyze the vortex conformation and dynamics across the LDR-HDR transition. Polymer effects are shown to concentrate on vortices that are partially or completely attached to the wall. At LDR, this effect is an across-the-board weakening of vortices which lowers their intensity without shifting their distribution patterns. At HDR, polymers start to suppress the lift-up of streamwise vortices in the buffer layer and prevent their downstream heads from rising into the log-law layer and forming hairpins and other curved vortices. This interrupts the turbulent momentum transfer between the buffer and log-law layers, which offers a clear pathway for explaining the distinct mean flow profiles at HDR. The study depicts the first clear physical picture regarding the changing vortex dynamics between LDR and HDR, which is based on direct evidence from objective statistical analysis of vortex conformation and distribution.

### Coupling effect on shocked double-gas cylinder evolution

Interaction of a weak planar shock wave with double heavy gas cylinders has been investigated, focusing on coupling effect on the post-shock flow. In experiments, the ideal two-dimensional discontinuous double heavy gas cylinders with controllable initial conditions are generated by soap film technique, and the shocked flow is captured by a high-speed schlieren photography. Two different initial center spacings of cylinders are considered to highlight the coupling effect. As the center spacing reduces, the coupling effect occurs earlier and becomes more prominent. The coupling effect greatly promotes the inner vortex motions near the symmetry axis relative to the outer ones, resulting in the formation of the mushroom and twisted jets. The fusion of the inner vortices completely differs from the observation in previous experimental work in which the inner vortices separate from each other. Quantitatively, the motion of the upstream interface in streamwise direction is obtained, and can be predicted by a nonlinear model considering the coupling effect. Besides, a vortex model is proposed based on the induction equation of point vortex, and the effect of the mutual interferences among vortices on the vortex motions can be well evaluated.

### Origin of localized snakes-and-ladders solutions of plane Couette flow

Author(s): Matthew Salewski, John F. Gibson, and Tobias M. Schneider

Spatially localized invariant solutions of plane Couette flow are organized in a snakes-and-ladders structure strikingly similar to that observed for simpler pattern-forming partial differential equations [Schneider, Gibson, and Burke, Phys. Rev. Lett. **104**, 104501 (2010)]. We demonstrate the mechani...

[Phys. Rev. E 100, 031102(R)] Published Thu Sep 12, 2019

### Reframing droplet coalescence: Identifying the distinctive dynamics of nanofilm evolution

Author(s): Jhoan Toro-Mendoza, Oscar Paredes-Altuve, Miguel A. Velasquez, and Dimiter N. Petsev

A new analysis reveals distinctive features of the modeled evolution of the fluid nanofilm formed between two coalescing droplets: an attractor-type phase space, a non-Fickean behavior of the growing film, and a complexity measure larger than that expected for fractional Brownian motion.

[Phys. Rev. Fluids 4, 093604] Published Thu Sep 12, 2019

### Trailing-edge noise from the scattering of spanwise-coherent structures

Author(s): Alex Sano, Leandra I. Abreu, André V. G. Cavalieri, and William R. Wolf

Using signal processing of a large-eddy simulation based on flow-acoustic correlations and spectral proper orthogonal decomposition, we identify regions and mechanisms effective at generating sound in a turbulent flow around a NACA 0012 airfoil with zero angle of attack and Mach number of 0.115.

[Phys. Rev. Fluids 4, 094602] Published Thu Sep 12, 2019

### Modulation of sound waves for flow past a rotary oscillating cylinder in a non-synchronous region

Modulation of sound waves for the laminar flow past a rotary oscillating circular cylinder has been studied for a free-stream Reynolds number Re = 150 and Mach number M = 0.2. Modulation of sound waves has been observed if the combination of applied rotary oscillation frequency and amplitude belongs to the nonsynchronous region where the hydrodynamic and acoustic quantities vary with the vortex shedding frequency as well as the applied forcing frequency. Two-dimensional direct numerical simulations (DNS) are carried out on a highly refined grid using high resolution physical dispersion relation preserving schemes for a nondimensional forcing frequency-ratio range 0.1 ≤ fr ≤ 2.0 at a nondimensional surface speed A1 = 0.1. Both the synchronous and the nonsynchronous zones are identified based on the time-varying fluctuations in the lift and the drag coefficients. In the nonsynchronous zone, modulation phenomena of the lift and the drag coefficients are explained by plotting the stream-function contours over multiple vortex shedding cycles. The modulation periods associated with the fluctuating lift and the drag coefficients are different for some cases. This particular observation is in contrast with the observation expressed in the previous studies investigating similar problems. Disturbance pressure fields obtained from the present DNS data are used to analyze the characteristics of radiated sound fields, especially in the nonsynchronous zone. Information related to aerodynamic sound sources has been obtained using approximated Lighthill’s stress tensor, and it is shown that the aerodynamic sound sources also display the modulation phenomenon similar to that observed in the vortex shedding process. Sound fields related to the nonsynchronous zone also exhibit the modulation phenomenon and are governed by the shedding frequency, the forcing frequency, and their linear combinations. Radiated sound field characteristics are further related to the time-varying fluctuations of the lift and the drag coefficients using Curle’s acoustic analogy. Modulated sound waves observed along the upstream and the transverse directions have similar time variation as that of the drag and the lift coefficients, respectively. The phenomenon of beat formation has been observed for the ranges 0.9 ≤ fr ≤ 0.99 and 1.2 ≤ fr ≤ 1.4. Although the observed modulation of sound waves varies significantly with the forcing frequency-ratio, the net radiated sound power has almost remained constant in the nonbeating, nonsynchronous zone. Furthermore, it is confirmed that the dominant sound modes obtained during the proper orthogonal decomposition of disturbance pressure fields in the nonsynchronous zone are related to the shedding frequency-ratio, the forcing frequency-ratio, and their linear combinations.

### An embedded boundary approach for efficient simulations of viscoplastic fluids in three dimensions

We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modeled by generalized Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelizable computations on block-structured grids. In this context, geometric features are handled by the embedded boundary approach, which requires specialized treatment only in cells intersecting or adjacent to the boundary. This constitutes the first published implementation of an embedded boundary algorithm for simulating flow of viscoplastic fluids on structured grids. The underlying algorithm employs a two-stage Runge-Kutta method for temporal discretization, in which viscous terms are treated semi-implicitly and projection methods are utilized to enforce the incompressibility constraint. We augment the embedded boundary algorithm to deal with the variable apparent viscosity of the fluids. Since the viscosity depends strongly on the strain rate tensor, special care has been taken to approximate the components of the velocity gradients robustly near boundary cells, both for viscous wall fluxes in cut cells and for updates of apparent viscosity in cells adjacent to them. After performing convergence analysis and validating the code against standard test cases, we present the first ever fully three-dimensional simulations of creeping flow of Bingham plastics around translating objects. Our results shed new light on the flow fields around these objects.

### Modes and break periods of electrowetting liquid bridge

Author(s): Mohsen Torabi, Ahmed A. Hemeda, James W. Palko, Yu Feng, Yong Cao, and Yanbao Ma

In this paper, we propose a microscale liquid oscillator using electrowetting-on-dielectric (EWOD). Specifically, a mesoscale liquid bridge (LB) between two horizontal surfaces with EWOD is considered. When EWOD is applied, the solid surface becomes more hydrophilic, and hence the contact angle (CA)...

[Phys. Rev. E 100, 033102] Published Wed Sep 11, 2019

### Analytic solution for the zero-order postshock profiles when an incident planar shock hits a planar contact surface

Author(s): F. Cobos-Campos and J. G. Wouchuk

An explicit analytical solution to calculate the profiles after the shock collision with a planar contact surface is presented. The case when a shock is reflected after the incident shock refraction is considered. The goal of this work is to present explicit formulas to obtain the quantities behind ...

[Phys. Rev. E 100, 033107] Published Wed Sep 11, 2019

### Collective diffusivity in a sheared viscous emulsion: Effects of viscosity ratio

Author(s): Abhilash Reddy Malipeddi and Kausik Sarkar

Shear-induced gradient diffusivity in an emulsion of viscous drops is determined from direct numerical simulations of the system using a dynamic structure factor approach. A nonmonotonic variation of the gradient diffusivity with viscosity ratio and capillary number is observed.

[Phys. Rev. Fluids 4, 093603] Published Wed Sep 11, 2019

### Internal waves in a shear background current: Transition from solitary-wave regime to dispersive-wave regime

Author(s): Chengzhu Xu and Marek Stastna

For a given stratification, the presence of a shear background current may significantly alter the wave form of internal waves. Depending on the direction and strength of background shear, it could prevent the formation of solitary waves but enable the formation of a dispersive wave train.

[Phys. Rev. Fluids 4, 094801] Published Wed Sep 11, 2019