# Latest papers in fluid mechanics

### Molecular dynamics study of the translation and rotation of amphiphilic Janus nanoparticles at a vapor-liquid surface

Author(s): Joel Koplik and Charles Maldarelli

The equilibrium contact angle of a heterogeneous colloidal particle at a liquid/vapor interface varies with position and may have distinct local equilibria at different orientations. We show that the free energy determines a particle’s orientation as a function of orientation and immersion depth.

[Phys. Rev. Fluids 4, 044201] Published Wed Apr 10, 2019

### Effect of a bottom gap on the mean flow and turbulence structure past vertical solid and porous plates situated in the vicinity of a horizontal channel bed

Author(s): K. Basnet and G. Constantinescu

A study of the wake past a porous barrier situated some distance above the ground shows that the presence of the bottom surface modifies the wake structure and breaks the antisymmetry of the von Karman billows. The bleeding flow increases the distance at which the wake billows form.

[Phys. Rev. Fluids 4, 044604] Published Wed Apr 10, 2019

### Flow instability in weakly eccentric annuli

A temporal linear stability analysis of laminar flow in weakly eccentric annular channels has been performed. It has been shown that, even for eccentricities ε and Reynolds numbers that were much smaller than those considered in previous studies, flow instability occurred in the form of travelling waves having characteristics that are very different from those of Tollmien-Schlichting waves and which were triggered at mid-gap by an inviscid mechanism that is associated with the presence of inflection points in azimuthal profiles of the base velocity. The critical stability conditions have been determined for 0 ≤ ε ≤ 0.1 and for diameter ratios 0 < γ < 1. The critical Reynolds number Rec decreased with increasing γ for 0 < γ ≲ 0.13, reached a minimum at γ ≈ 0.13, and increased with further increase in γ. The lowest observed Rec was 529 and occurred for ε = 0.1 and γ ≈ 0.13. As ε → 0, Rec ∝ ε−2. The critical wave number and the critical frequency of the disturbances decreased with increasing γ and approached zero as γ → 1, whilst their ratio was nearly constant in the range of parameters considered in this study. The most unstable regions were found to be at roughly mid-gap on the two flanks of the annulus, and the phase speed of the disturbances was close to the base flow velocity at these regions.

### Eigenvector perturbation methodology for uncertainty quantification of turbulence models

Author(s): Roney L. Thompson, Aashwin Ananda Mishra, Gianluca Iaccarino, Wouter Edeling, and Luiz Sampaio

Establishing turbulence models as reliable tools for aerospace design requires quantification of uncertainties in model predictions. A methodology for turbulence model uncertainty estimation in complex flows using physics-based perturbation is introduce and validated.

[Phys. Rev. Fluids 4, 044603] Published Tue Apr 09, 2019

### Magnetic quenching of the inverse cascade in rapidly rotating convective turbulence

Author(s): Stefano Maffei, Michael A. Calkins, Keith Julien, and Philippe Marti

Numerical simulations of a simplified asymptotic model find that sufficiently strong magnetic fields prevent the formation of large-scale vortices and saturate the inverse cascade at a finite length-scale.

[Phys. Rev. Fluids 4, 041801(R)] Published Mon Apr 08, 2019

### Global linear instability of rotating-cone boundary layers in a quiescent medium

Author(s): Christian Thomas and Christopher Davies

Numerical simulations of disturbance development in the family of rotating-cone boundary layers illustrates that for sufficiently large azimuthal mode numbers, a form of global linear instability ensues that is characterized by a faster than exponential temporal growth.

[Phys. Rev. Fluids 4, 043902] Published Mon Apr 08, 2019

### Hydrodynamic interactions in polar liquid crystals on evolving surfaces

Author(s): Ingo Nitschke, Sebastian Reuther, and Axel Voigt

The flow of passive and active polar liquid crystals on evolving surfaces is considered. The models are derived as a thin-film limit, and a finite element method is used to study the effect of hydrodynamics on the interplay of topology, geometric properties, and defect dynamics.

[Phys. Rev. Fluids 4, 044002] Published Mon Apr 08, 2019

### Transition to chaos in an acoustically driven cavity flow

Author(s): Gaby Launay, Tristan Cambonie, Daniel Henry, Alban Pothérat, and Valéry Botton

We show that a cavity flow driven by acoustic streaming can sustain low-dimensional chaos. Frequency and nonlinear times series analyses reveal a novel path to chaos with a sequence of two-way transitions between nonchaotic and chaotic states with steps where the dynamics drastically simplifies.

[Phys. Rev. Fluids 4, 044401] Published Mon Apr 08, 2019

### Velocity fluctuations in a dilute suspension of viscous vortex rings

Author(s): Thomas A. Morrell, Saverio E. Spagnolie, and Jean-Luc Thiffeault

Velocity fluctuations in a fluid due to a dilute suspension of vortex rings, such as those generated by a population of small jellyfish, are explored. The slow diffusion of momentum leads to a different stable distribution than is found for velocity fluctuations caused by microswimmers.

[Phys. Rev. Fluids 4, 044501] Published Mon Apr 08, 2019

### Direct numerical simulation of a supersonic turbulent boundary layer subjected to a concave surface

Author(s): Xiaoshuai Wu, Jianhan Liang, and Yuxin Zhao

An investigation finds that a supersonic turbulent boundary layer is highly destabilized by a longitudinal concave surface. The intensification of vortical structures reflects the effect of turbulence amplification. Streaky turbulent motions suggest enhanced inner-outer interactions.

[Phys. Rev. Fluids 4, 044602] Published Mon Apr 08, 2019

### Analysis of rheological behaviors of two-dimensional emulsion globules with asymmetric internal structures in modest extensional flows

The rheological behaviors of complex emulsion globules (CEGs) and its three asymmetric daughter droplets (DDs) have been studied numerically in this paper. Unlike simple eccentric emulsion globules (SEEGs), two more DDs are added into the globules and the three DDs are located initially in an asymmetric distribution with a triangular shape. Through this investigation, an oriented shift and an inverse of CEGs are observed. Especially, the movement of CEGs under more conditions is still caused by the interaction of the asymmetric inner pressure distribution and the total outer drag force. Due to the asymmetric internal structure, the deformation of CEGs caused by the outer flow is asymmetric and so is the interfacial curvature which results in the oriented inner circulation. Compared to SEEGs, the addition of two extra DDs leads to the bigger deformation of CEGs, and more CEGs will shift to the left in the parameter range of our investigation. The increases of the parameters in the discussed ranges will promote CEGs to move to the right. In addition, DDs will move away from the original position and move away from or close to the interface of the mother droplet (MD), which may result in interface contact between DDs and MD. The results investigated in this paper further prove the mechanical mechanism of the oriented shift of the complex emulsions globules and are helpful to the controllable movement of soft globules driven by the asymmetric curvatures.

### Dynamic mode decomposition for the inspection of three-regime separated transitional boundary layers using a least squares method

Transitional boundary layers undergoing separated flow transition for different free stream turbulence intensity levels and Reynolds numbers have been inspected by applying dynamic mode decomposition (DMD) to time-resolved particle image velocimetry data. The identification of the unstable modes responsible for transition suffers from nonlinear effects if the whole dataset is considered for the construction of the snapshot matrix underlying the flow evolution. To overcome this limit, piecewise linear models aimed at the identification of the different regimes in the entire transition process are proposed. In particular, the flow is initially laminar (i.e., stable), it becomes unstable due to transition, and once transition is completed, the fully turbulent condition leads the boundary layer to a stable regime. The norm of the residuals resulting from the application of DMD on a variable streamwise extension of the dataset shows a trend that is associated with the variation of regime. This trend is analyzed by means of the least squares method, which allows identifying the change in the regime with stable, unstable, and turbulent behaviors. The validity of this procedure is proved by comparing it with previously published results. Moreover, since the DMD is applied to limited temporal snapshots, it provides a temporal resolution of growth rate and positions of switch between the boundary layer states. Such information is used to extract from the big dataset under analysis the time sequences characterized by the largest growth rate, hence quickly highlighting the flow physics driving transition.

### Scaling laws for the transient convective flow in a differentially and linearly heated rectangular cavity at Pr [math] 1

The convective flow in a differentially heated cavity, with linear temperature profiles at two sidewalls, is investigated in the present study by a scaling analysis and direct numerical simulations (DNS). Scales for the thermal boundary layer and the subsequent intrusion are obtained through the scaling analysis. The velocity scale reveals that the characteristic velocity of the thermal boundary layer depends on both the streamwise position and the time after the initiation of the flow, which suggests a two-dimensional growth at the start-up stage, rather than the well-known one-dimensional growth of the thermal boundary layer induced by a constant temperature boundary condition. Furthermore, unlike the typical transition of the thermal boundary layer to a two-dimensional and steady stage that is characterized by the dying out of a “temperature overshoot” phenomenon, the thermal boundary layer under consideration enters a two-dimensional and steady stage smoothly, without the occurrence of the temperature overshoot. It is also found that, with the passage of time, whilst the characteristic velocity of the thermal boundary layer depends on the streamwise position, the thickness of the thermal boundary layer is streamwise position independent due to infinitesimally small time. Four possible flow regimes and corresponding scales for the unsteady intrusion flow underneath the cavity ceiling are finally obtained, which are two types of viscous-buoyancy dominated regimes and two types of inertial-buoyancy dominated ones. The important scales obtained in the present study are validated by corresponding DNS results.

### Mathematical framework for analysis of internal energy dynamics and spectral distribution in compressible turbulent flows

Author(s): Ankita Mittal and Sharath S. Girimaji

A new variable φ ∼ √p is introduced to examine the dynamics of the internal energy, its mean and fluctuations, and then represent the exchange between kinetic and internal energy.

[Phys. Rev. Fluids 4, 042601(R)] Published Fri Apr 05, 2019

### Fluctuating hydrodynamics of electrolytes at electroneutral scales

Author(s): Aleksandar Donev, Andrew J. Nonaka, Changho Kim, Alejandro L. Garcia, and John B. Bell

Electrolytes are effectively electroneutral at mesoscopic scales and the stochastic Poisson-Nernst-Planck equations are too stiff to solve numerically. We formulate theory and algorithms for the fluctuating hydrodynamics equations of charged, reactive mixtures with an electroneutral constraint.

[Phys. Rev. Fluids 4, 043701] Published Fri Apr 05, 2019

### Hydrodynamically bound states of a pair of microrollers: A dynamical system insight

Author(s): Blaise Delmotte

Particles rotating above a floor, called microrollers, can pair together in a stable fashion. The physical conditions for such self-assembly are identified and provide a stepping stone towards understanding the formation of large motile clusters in microroller suspensions.

[Phys. Rev. Fluids 4, 044302] Published Fri Apr 05, 2019

### Experimental study of single-particle trapping mechanisms into microcavities using microfluidics

Single-particle trapping mechanisms into microcavities are still puzzling for size-based particle/cell sorting in microfluidics. Aiming to verify the prediction of particle-wall collision trapping mechanism, we explore the effects of the microcavity trailing wall on the single-particle trapping behaviors for various microcavity aspect ratios (λ = 0.5–5) and inlet Reynolds numbers (Re = 5–400), uncovering three new trapping phenomena, namely, contact trapping, collision trapping, and rapid trapping. We characterize the particle velocity variation during the trapping process. We also investigate the separatrix topology (streamlines between the microvortex and microchannel flow) and map the different particle trapping phenomena. The particle trapping results from the combined effects of the microcavity trailing wall, the separatrix topology, and the particle dynamics. The results provide new insight into the fundamental understanding of particle trapping mechanisms and could guide the applications of microcavity-based microfluidics.

### Uplift of an elastic membrane by a viscous flow

Author(s): Michael Berhanu, Adrien Guérin, Sylvain Courrech du Pont, Fiona Raoult, Rémi Perrier, and Chloé Michaut

Pumping a viscous fluid underneath an elastic sheet will cause the sheet to bulge upward. The liquid pressure is balanced by the sheet’s elasticity as well as gravity. The authors’ experiment shows reasonable agreement with two different theories, and may provide a model for the formation of magma intrusions between layers of rock.

[Phys. Rev. E 99, 043102] Published Thu Apr 04, 2019

### Stochastic modeling of fluid acceleration on residual scales and dynamics of suspended inertial particles in turbulence

Author(s): Vladimir Sabelnikov, Alexis Barge, and Mikhael Gorokhovski

In the underresolved particle laden turbulence, we assess the intermittency effects in the carrier fluid. The stochastic subgrid acceleration model accounts for the orientation of vortical structures and for the local Reynolds number. Our statistics are in agreement with DNS and experiments.

[Phys. Rev. Fluids 4, 044301] Published Thu Apr 04, 2019

### Coexistence of acoustic waves and turbulence in low Mach number compressible flows

In this work, direct numerical simulations of the compressible fluid equations in turbulent regimes are performed. The behavior of the flow is either dominated by purely turbulent phenomena or by the generation of sound waves in it. Previous studies suggest that three different types of turbulence may happen at the low Mach number limit in polytropic flows: Nearly incompressible, modally equipartitioned compressible, and compressible wave. The distinction between these types of turbulence is investigated here applying different kinds of forcing. Scaling of density fluctuations with Mach number, comparison of the ratio of transverse velocity fluctuations to longitudinal fluctuations, and spectral decomposition of fluctuations are used to distinguish the nature of these solutions. From the study of the spatio-temporal spectra and correlation times, we quantify the contribution of the waves to the total energy of the system. Also, in the dynamics of a compressible flow, three associated correlation times are considered: the non-linear time of local interaction between scales, the sweeping time or non-local time of large scales on small scales, and the time associated with acoustic waves (sound). We observed that different correlation times dominate depending on the wave number (k), the Mach number, and the type of forcing.