# Physical Review Fluids

### Suppression of viscous fingering during perfect dielectric fluid displacement using transverse electric fields

Author(s): Jiachen Zhao, Zhongzheng Wang, and Emilie Sauret

This study numerically and theoretically investigates the control of viscous fingering using a transverse electric field. Viscous fingering can be delayed in the presence of an electric field due to the electrical force distribution along the fluid interface and completely suppressed when the electric field strength exceeds a certain value. A non-dimensional parameter ϕ is defined based on the force balance, which shows good capability for predicting the transition from an unstable viscous fingering to stable displacement under various fluid properties and flow conditions.

[Phys. Rev. Fluids 9, 033701] Published Tue Mar 26, 2024

### Flow kinematics model for universal Strouhal number in the separated flow past a bluff body

Author(s): A. Barrero-Gil and A. Velazquez

This letter revisits the problem of the existence of a universal Strouhal number in the separated flow past a stationary bluff body. Theoretical considerations grounded in flow kinetics yield a concise mathematical expression. The resultant model anticipates a universal Strouhal number equal to 1/2π≈0.159, aligning closely with experimental finding. Furthermore, the model has been expanded to forecast the Strouhal – Reynolds relationship in the supercritical regime, demonstrating a universal nature as it relies solely on critical Strouhal and Reynolds numbers. The circular, square, and triangular cross-section shapes have been used for validation purposes.

[Phys. Rev. Fluids 9, L032701] Published Tue Mar 26, 2024

### Equilibrium bridge solution from a sessile drop partially covered by another fluid

Author(s): P. D. Ravazzoli, A. G. González, and J. A. Diez

Liquid bridges are present in different four-phase systems, like the one studied here, which is formed by a liquid connecting a horizontal solid substrate with a gas phase while surrounded by another immiscible liquid. We obtain the equilibrium solutions by treating each interface as a simple curve with axial symmetry and constant curvature, and satisfying the boundary conditions given by Neumann’s and Young’s laws. Therefore, the final equilibrium solution is formed by a union of a spherical cap, a catenoid, and portions of onduloids or nodoids. We find that the γ-angle is the control parameter of the problem, as it defines the existence and shape of the final equilibrium solution.

[Phys. Rev. Fluids 9, 033601] Published Mon Mar 25, 2024

### Nonaxisymmetric modes of magnetorotational and possible hydrodynamical instabilities in the upcoming DRESDYN-MRI experiments: Linear and nonlinear dynamics

Author(s): Ashish Mishra, George Mamatsashvili, and Frank Stefani

Magnetorotational instability (MRI) is responsible for angular momentum transport in astrophysical disks. However, its definitive experimental confirmation is still missing. The upcoming DRESDYN-MRI experiments using a liquid sodium Taylor-Couette flow are a new effort to detect MRI. In preparation for this, here we study the dynamics of nonaxisymmetric MRI via simulations for the DRESDYN-MRI device. It is shown that nonaxisymmetric modes are important for large Re≳4×104 and relevant in these experiments with Re≳106. These modes are, however, of nonmagnetic nature, which grow and form a turbulent boundary layer near the cylinders, while axisymmetric MRI dominates in the bulk flow.

[Phys. Rev. Fluids 9, 033904] Published Mon Mar 25, 2024

### Model for the dynamics of the large-scale circulations in two-layer turbulent convection

Author(s): Yu Sun, Yi-Chao Xie, Jin-Xiao Xie, Jin-Qiang Zhong, Jianwei Zhang, and Ke-Qing Xia

A physically motivated low-dimensional model describes properly the interaction of two vertically-aligned large-scale circulations (LSC) in two-layer turbulent convection, and predicts their preferred flow states of thermal and viscous coupling. The model reveals that flow reversals can be achieved when turbulent fluctuations drive the LSC azimuthal diffusion into a flow state such that the two LSC planes are orthogonal to each other, the strength of the LSC in the high Rayleigh number fluid layer then reduces to zero deterministically. The model provides satisfactory interpretation for the high occurrence frequency of flow reversals observed in two-layer turbulent convection.

[Phys. Rev. Fluids 9, 033501] Published Fri Mar 22, 2024

### Turbulent thermal convection across a stable liquid-liquid interface

Author(s): Hailong Huang, Yin Wang, Wei Xu, Xiaozhou He, and Penger Tong

In this work, we conducted a systematic experimental study of turbulent two-layer convection in an upright cylinder, as illustrated. From the measured mean temperature and temperature variance profiles, we find a unique twin-boundary-layer structure across the liquid interface with one of the twin boundary layers (BLs) on each side of the interface. The functional form of the measured mean temperature and temperature variance profiles is well described by the equations for a BL attaching to a solid conducting plate, so long as a thermal slip length is introduced to account for the convective heat flux passing through the liquid interface.

[Phys. Rev. Fluids 9, 033502] Published Fri Mar 22, 2024

### Wake characteristics behind a tidal turbine with surface waves in turbulent flow analyzed with large-eddy simulation

Author(s): Pablo Ouro, Hannah Mullings, Aristos Christou, Samuel Draycott, and Tim Stallard

Understanding of the influence of waves on a tidal turbine wake in a turbulent channel flow is developed using large eddy simulations with modeling of the air-water interphase deformation. For wavelengths between two- and sixteen-times channel depth, the rate of wake recovery is faster than in the absence of waves with only small differences in turbine mean loading. The smallest wavelengths cause fastest wake recovery, and hence shortest wake length. This is due to enhanced vertical and transverse components of convection and turbulent transport of mean kinetic energy. Advection of helical tip vortices shed by the turbine blades is impacted by vertical and streamwise wave kinematics.

[Phys. Rev. Fluids 9, 034608] Published Fri Mar 22, 2024

### Unbounded two-dimensional wall turbulence induced by inverse cascade

Author(s): Xi Chen, Peng-Yu Duan, and Jianchao He

What would be the ultimate statistical invariance for wall turbulence? In 3D flows, whether turbulent fluctuations are bounded or unbounded for a series of quantities when the Reynolds number (Re) tends to infinity, is debated. Here, we focus on 2D wall turbulence and find that fluctuations in wall units such as root mean square of wall pressure, wall shear stress intensity, streamwise velocity fluctuation, etc., all exhibit a distinct Re1/3 scaling law. This scaling indicates an unbounded behavior for 2D flows due to the inverse energy cascade, which sheds light on the asymptotical behavior of 3D flows that fluctuations might be bounded because of the forward energy cascade.

[Phys. Rev. Fluids 9, 034609] Published Fri Mar 22, 2024

### Initial evolution of three-dimensional turbulence en route to the Kolmogorov state: Emergence and transformations of coherent structures, self-similarity, and instabilities

Author(s): Giorgio Krstulovic and Sergey Nazarenko

The development of singular structures and the path to turbulence in fluids is a fundamental problem that has puzzled researchers for a long time. In this work, we study numerically the evolution of a large-scale initial condition under the hyperviscous incompressible Navier-Stoke equations. Our observations revealed the emergence of shrinking vortex pancakes, which lead to vortex ribs and, eventually, vortex ropes, as depicted in the figure. Eventually, a fully developed turbulent state was achieved prior to its viscous decay.

[Phys. Rev. Fluids 9, 034610] Published Fri Mar 22, 2024

### Vortex dynamics: A variational approach using the principle of least action

Author(s): Nabil M. Khalifa and Haithem E. Taha

Vortices are found everywhere around us at every scale. Current models describing vortices are mainly kinematics-based, in which the resulting dynamics are limiting in their nature. Relying on these models, one can predict vortices response for a prescribed initial condition but cannot study their response under generic conditions and external disturbances. That is because current models are a well devised formulation. However, we propose a model from first-variational principles relying on the Principle of Least Action, and not only was it able to predict the vortices response in a generic sense, but also it can be extended to include varying strength vortices or any dynamical constraints.

[Phys. Rev. Fluids 9, 034701] Published Fri Mar 22, 2024

### Critical slope singularities in rotating and stratified fluids

Author(s): Stéphane Le Dizès

Gravito-inertial waves propagate in fixed directions and exhibit a critical slope singularity whenever one of these directions is tangent to a surface boundary. The nature of this singularity is analyzed. It is shown how it governs the scaling and the structure of the intense viscous beam that it generates.

[Phys. Rev. Fluids 9, 034803] Published Fri Mar 22, 2024

### Wake transition of an unconstrained self-propelled flexible flapping plate

Author(s): Kui Liu and Haibo Huang

This study numerically investigates the wake transition of an unconstrained self-propelled flexible flapping plate, which can move freely both longitudinally and laterally. Three distinct wake patterns, including symmetric, deflected, and chaotic, are identified quantitatively. The symmetry breaking will be triggered when the cruising and flapping Reynolds number as well as translational kinetic energy reach critical values, which follow some simple scaling laws. it is also revealed that passive lateral oscillation and bending deformation of the plate are two key mechanisms affecting wake symmetry properties.

[Phys. Rev. Fluids 9, 033102] Published Thu Mar 21, 2024

### Description of laminar-turbulent transition of an airfoil boundary layer measured by differential image thermography using directed percolation theory

Author(s): Tom T. B. Wester, J. Peinke, and G. Gülker

The laminar-turbulent transition still poses a challenging problem to fluid dynamic research. This study shows how differential image thermography can be utilized to capture the spatiotemporal aspects of this phenomenon along the curved surface of an airfoil. Further, an incredible agreement between the transition characteristics and the (1+1)D directed percolation theory is observed for a broad range of experimental parameters, namely angle of attack and inflow velocity.

[Phys. Rev. Fluids 9, 033903] Published Thu Mar 21, 2024

### Turbophoresis and preferential accumulation of inertial particles in compressible turbulent channel flow: Effect of Mach number

Author(s): Ping Wang, Bowen Zhou, and Xiaojing Zheng

This paper investigates the effects of the Mach number on turbophoresis and the preferential accumulation of particles. A particle relaxation time weighting transformation is proposed which collapses the concentration profiles not only for particles with small inertia, but also for turbulence with various compressibility at the studied low Reynolds number and in the inner region. Inertial particles in compressible wall turbulence tend to distribute in high-fluid-density and negative-fluid-dilatation regions. This is explained by the changes in turbulent structures at varying Mach number, which in turn also account for the varying scales of particle streaks.

[Phys. Rev. Fluids 9, 034305] Published Thu Mar 21, 2024

### On granular flows: From kinetic theory to inertial rheology and nonlocal constitutive models

Author(s): Diego Berzi

The case is made that the kinetic theory of granular gases provides the long-sought universal framework to predict the flow of realistic particles from dilute to very dense conditions. In so doing, the popular inertial rheology and its nonlocal extension to deal with heterogeneities based on the granular fluidity concept are derived as special limits of the kinetic theory.

[Phys. Rev. Fluids 9, 034304] Published Wed Mar 20, 2024

### Toroidal cavitation by a snapping popper

Author(s): Akihito Kiyama, Sharon Wang, Jisoo Yuk, and Sunghwan Jung

Our study demonstrates how a child’s rubber popper, when snapped underwater, creates fascinating cavitation bubble formations. By using high-speed imaging, we explore the fluid mechanics behind the formation and collapse of these cavitation bubbles due to pressure changes. Interestingly, the cavitation bubble forms a toroidal shape rather than a spherical one, with a lifespan shorter than that of a spherical bubble with the same outer radius. This research illuminates the intricate interplay between bubble dynamics within a thin gap and material elasticity.

[Phys. Rev. Fluids 9, 030501] Published Tue Mar 19, 2024

### Near-wall depletion and layering affect contact line friction of multicomponent liquids

Author(s): Michele Pellegrino and Berk Hess

Viscosity and contact line friction are the main channels of energy dissipation in wetting dynamics. Experiments and theoretical models haven’t singled out a universal scaling between the two. We perform molecular dynamics simulations of droplets spreading over hydrophilic surfaces, aiming to disentangle the effect of viscosity on friction. The viscosity of the fluid is tuned by changing the chemical composition of the liquid, mimicking real-world experiments. It is found that contact line friction does not scale linearly with viscosity. The trend is explained by accounting for molecular depletion in the near-wall region.

[Phys. Rev. Fluids 9, 034002] Published Tue Mar 19, 2024

### Stick-slip-to-stick transition of liquid oscillations in a U-shaped tube

Author(s): A. Bongarzone and F. Gallaire

In this work, we employ a physics-inspired mathematical model based on successive linear eigenmode projections to solve the relaxation dynamics of liquid oscillations in a U-shaped tube and subjected to a phenomenological nonlinear contact line model. Each projection induces a rapid loss of total energy in the motion and contributes to its nonlinear damping. The present approach not only describes well the transient stick-slip dynamics, but it also captures the global stick-slip-to-stick transition and the residual exponentially decaying bulk motion following the arrest of the contact line. This study offers a further contribution to rationalizing the impact of contact angle hysteresis.

[Phys. Rev. Fluids 9, 034401] Published Tue Mar 19, 2024

### Stagnation enthalpy effects on hypersonic turbulent compression corner flow at moderate Reynolds numbers

Author(s): M. Di Renzo, C. T. Williams, and S. Pirozzoli

This work investigates the interaction of turbulent hypersonic flows with a 15° compression corner using direct numerical simulations. Different values of stagnation enthalpy, ranging approximately from 600kJ to 4MJ, are considered. Vibrational excitation of the gas molecules is also included in the model for the higher stagnation enthalpy cases. The analysis presented in the manuscript illustrates the effects of the flow thermodynamic state on quantities that determine the main mechanical and thermal stresses generated on a hypersonic vehicle, namely the shear stress, heat flux, and pressure fluctuations at the wall.

[Phys. Rev. Fluids 9, 033401] Published Mon Mar 18, 2024

### Stresslet in a dilute suspension of rigid spheres in an Oldroyd-B fluid

Author(s): Boon Siong Neo and Eric S. G. Shaqfeh

The stresslet in a dilute suspension of rigid spheres in a viscoelastic (Oldroyd-B) fluid is studied under imposed shear and uniaxial extensional flow. We observe that, due to its hyperbolic nature, the polymer constitutive equation can be directly evaluated along streamlines of the flow. Specifically, evaluating along streamlines on the particle surface, in the limit of the Newtonian flow fields, produces an analytical scaling which we evaluate and test against numerical results. This approach also provides physical insight into the mechanism driving the observed trends.

[Phys. Rev. Fluids 9, 033301] Published Fri Mar 15, 2024