# Latest papers in fluid mechanics

### Acoustic microstreaming produced by nonspherical oscillations of a gas bubble. I. Case of modes 0 and $m$

Author(s): Alexander A. Doinikov, Sarah Cleve, Gabriel Regnault, Cyril Mauger, and Claude Inserra

A theory is developed that allows one to model the velocity field of acoustic microstreaming produced by nonspherical oscillations of an acoustically driven gas bubble. It is assumed that some of the bubble oscillation modes are excited parametrically and hence can oscillate at frequencies different...

[Phys. Rev. E 100, 033104] Published Tue Sep 10, 2019

### Acoustic microstreaming produced by nonspherical oscillations of a gas bubble. II. Case of modes 1 and $m$

Author(s): Alexander A. Doinikov, Sarah Cleve, Gabriel Regnault, Cyril Mauger, and Claude Inserra

This paper continues a study that was started in our previous paper [A. A. Doinikov *et al.*, Phys. Rev. E **100**, 033104 (2019)]. The overall aim of the study is to develop a theory for modeling the velocity field of acoustic microstreaming produced by nonspherical oscillations of an acoustically driven...

[Phys. Rev. E 100, 033105] Published Tue Sep 10, 2019

### Dynamics of groups of magnetically driven artificial microswimmers

Author(s): Jake Buzhardt and Phanindra Tallapragada

Magnetically driven artificial microswimmers have the potential to revolutionize many biomedical technologies, such as minimally invasive microsurgery, microparticle manipulation, and localized drug delivery. However, many of these applications will require the controlled dynamics of teams of these ...

[Phys. Rev. E 100, 033106] Published Tue Sep 10, 2019

### Transition to time-dependent flow in highly viscous horizontal convection

Author(s): Lennart Ramme and Ulrich Hansen

It is shown that horizontal convection at an infinite Prandtl number will become time-dependent at sufficiently high Rayleigh numbers. The point of the transition is dependent on the heating configuration, and the scaling laws of heat flux and circulation strength are subsequently changed.

[Phys. Rev. Fluids 4, 093501] Published Tue Sep 10, 2019

### Stochastic model for filtration by porous materials

Author(s): Filippo Miele, Pietro de Anna, and Marco Dentz

Transport and filtration of colloids through permeable materials is controlled by the underlying heterogeneous structure of the host medium. A stochastic model is proposed that takes into account pore-scale heterogeneity, which controls the macroscopic deposition.

[Phys. Rev. Fluids 4, 094101] Published Tue Sep 10, 2019

### A phase-field-based lattice Boltzmann modeling of two-phase electro-hydrodynamic flows

In this paper, a simple and accurate lattice Boltzmann (LB) model based on phase-field theory is developed to study the two-phase electro-hydrodynamics flows. In this model, three LB equations are utilized to solve the Allen-Cahn equation for the phase field, the Poisson equation for the electric potential, and the Navier-Stokes equation for the flow field. To test the proposed model, the deformation of a single droplet under a uniform electric field is considered. It is found that under a small deformation, the results are in good agreement with the previous work. For a large deformation, however, the theoretical results would give a large deviation, while the present results are close to the available numerical work.

### Solitary wave slamming induced by an asymmetric wedge through three degrees of freedom free motions

A time-domain higher-order boundary element method with fully nonlinear boundary conditions is developed to simulate the slamming of an asymmetric wedge entering freely and obliquely into a solitary wave in three degrees of freedom (3DOF). A third order analytical solution based on the Korteweg-de Vries equation is used to simulate the solitary wave incident boundary conditions. In the numerical model of slamming, a stretched coordinate system is applied to maintain numerical accuracy and stability at the initial stage. The thin long jet layer is generated along the wedge surface by assuming linear variation of the jet layer potential. A rotation scheme of the stretched coordinate system is adopted to avoid fluid particle leaving or entering the wedge surface. Some auxiliary functions are employed to decouple the intercoupling motions in 3DOF. The present model is verified by comparing with the published numerical results. Various parametric studies are carried out. Detailed results through the free surface, pressure distribution, accelerations, and velocities are provided to show the slamming effects, and their physical implications are discussed.

### An explicit expression for the calculation of the Rortex vector

Recently, a vector called Rortex was proposed and successfully applied to identify the local fluid rotation with both the rotation axis and strength. The first implementation relies on the real Schur decomposition of the velocity gradient tensor, resulting in a relatively long computational time. Subsequently, a mathematically equivalent eigenvector-based definition of Rortex was introduced with an improved implementation. Unfortunately, this definition still tends to be an algorithmic description rather than an explicit one and involves two successive cumbersome coordinate rotations. In this paper, a simple and explicit expression for the calculation of the Rortex vector, which is based on a special (transposed) Schur form of the velocity gradient tensor, is presented. The explicit expression is consistent with the previous definition but avoids the explicit calculation of the coordinate rotation, and thus can significantly simplify the implementation. According to the explicit expression, a new implementation is proposed and validated by a large eddy simulation of the flow transition around a NACA0012 airfoil and a direct numerical simulation of the boundary layer transition on a flat plate.

### Numerical simulation of the production of three-dimensional sediment dunes

Knowledge of the relationship between sediment motion and flow conditions is fundamental to our understanding of three-dimensional sediment dune development in river and coastal environments. In this study, numerical simulations were performed on a mobile flat sand bed. The simulation results provide important insights into the coupling between migrating bedforms and turbulent stratified flow in the open channel. The formation of micro sand waves can be divided into three stages. First, the initial defects appear on the bed at the beginning of the process and are closely correlated with the instantaneous flow velocity just before the bed is destabilized. Second, the defects in areas of high instantaneous flow velocity are washed away, while the defects in areas of low instantaneous flow velocity grow in length and height due to sediment deposition. Finally, a constant wake zone where sediment continues to accumulate forms downstream of the micro sand wave. Despite the formation of micro waves, the near-bed flow velocity and turbulent structures play important roles as sand passes from upstream dune crests to downstream ones. The high flow velocity breaks O-shaped dune crests and drives excess sand to the downstream dune crests. The near-bed vortices usually occur at the stoss sides of the dunes, and most are elongated in the spanwise direction.

### Extensional rheology of a dilute particle-laden viscoelastic solution

Author(s): Anika Jain, Jonas Einarsson, and Eric S. G. Shaqfeh

Numerical simulations of viscoelastic flow around an isolated particle find that, while the particle contribution to bulk elongational viscosity of a suspension increases at small strains, at larger strains the particle is shielded by stretched polymers, leading to a decrease in relative viscosity.

[Phys. Rev. Fluids 4, 091301(R)] Published Mon Sep 09, 2019

### Experimental study of coherent structures of finite-size particles in thermocapillary liquid bridges

Author(s): Masakazu Gotoda, Aro Toyama, Misa Ishimura, Tomoaki Sano, Mizuki Suzuki, Toshihiro Kaneko, and Ichiro Ueno

We experimentally investigate the formation of coherent structures by finite-size particles in thermocapillary liquid bridges. Special attention is paid to particle accumulation structures in which suspended particles gather to form a solid-like-structure in the rotating frame of reference.

[Phys. Rev. Fluids 4, 094301] Published Mon Sep 09, 2019

### Reducing the skin-friction drag of a turbulent boundary-layer flow with low-amplitude wall-normal blowing within a Bayesian optimization framework

Author(s): O. A. Mahfoze, A. Moody, A. Wynn, R. D. Whalley, and S. Laizet

A Bayesian optimization framework is developed to optimize low-amplitude wall-normal blowing control of a turbulent boundary-layer flow in order to generate net energy savings.

[Phys. Rev. Fluids 4, 094601] Published Mon Sep 09, 2019

### Flapping dynamics of a flexible plate with Navier slip

Seaweed and fish have slippery outer surfaces because of the secretion of a layer of mucus. Navier slip arises when the component of the tangential velocity at a wall is proportional to the strain. The hydrodynamics of a three-dimensional flexible plate with Navier slip was explored by using the immersed boundary method in an effort to scrutinize the effects on plate hydrodynamics of a slip boundary mimicking the mucus layers of seaweed and fish. For comparison, simulations with the no-slip condition were also performed. Two cases were chosen for simulation: a flexible plate with a fixed leading edge and a flexible plate with a heaving leading edge in a uniform flow. For the fixed plate, the velocity gradient and the total drag were determined to examine the influence of the slip surface. Drag was significantly reduced by the slip. The slip surface lessens the velocity gradient near the wall and suppresses the flapping motion. The drag reduction process was characterized by using the distributions of vorticity and pressure. The hydrodynamics of the heaving flexible plate with Navier slip was explored in terms of thrust generation. The flapping motion was mainly governed by the input heaving condition and a large form drag was exerted on the flexible plate. The net thrust, input power, and Froude efficiency were determined as a function of the bending rigidity. A large net thrust for the heaving plate was generated by the slip. The velocity ratio was employed to interpret the correlation between the slip velocity and the flapping motion.

### Numerical study of the stress singularity in stick-slip flow of the Phan-Thien Tanner and Giesekus fluids

Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien–Tanner (PTT) and Giesekus fluids, investigating the polymer stress behavior around the stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. [“Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity,” Phys. Fluids 29, 1–33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and natural stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The natural stress formulation gives improved convergence results both temporally and spatially near to the singularity while maintaining the same global flow characteristics as the Cartesian.

### Interfacial flows in sessile evaporating droplets of mineral water

Author(s): Massimiliano Rossi, Alvaro Marin, and Christian J. Kähler

Liquid flow in sessile evaporating droplets of ultrapure water typically results from two main contributions: a capillary flow *pushing* the liquid toward the contact line from the bulk and a thermal Marangoni flow *pulling* the drop free surface toward the summit. Current analytical and numerical model...

[Phys. Rev. E 100, 033103] Published Fri Sep 06, 2019

### Pairwise hydrodynamic interactions of synchronized spermatozoa

Author(s): Benjamin J. Walker, Kenta Ishimoto, and Eamonn A. Gaffney

Simulations of synchronized spermatozoa reveal stable pairwise swimming, with swimmers speeding up as they approach each other from above. However, swimming side-by-side proves unstable, highlighting anisotropy in planar-beating flagellates that is not captured by simple singularity representations.

[Phys. Rev. Fluids 4, 093101] Published Fri Sep 06, 2019

### Controlled gliding and perching through deep-reinforcement-learning

Author(s): Guido Novati, L. Mahadevan, and Petros Koumoutsakos

Gliding is an energetically efficient mode of transportation. It is shown that reinforcement learning identifies gliding strategies with minimum energy expenditure and fastest time of arrival, with better performance than model-based optimal control, while being robust to perturbations.

[Phys. Rev. Fluids 4, 093902] Published Fri Sep 06, 2019

### Performance and mechanism analysis of nanosecond pulsed surface dielectric barrier discharge based plasma deicer

Ice accretion on aircraft surfaces, especially on wings, may do harm to the aerodynamic performance and safety of an aircraft. In this work, de-icing experiments on an NACA0012 airfoil model were conducted in an icing wind tunnel using nanosecond pulsed surface dielectric barrier discharge (nSDBD) actuator under typical glaze icing conditions. The spatial-temporal distribution of the temperature and the dynamic process of de-icing on the surface of the airfoil were obtained and analyzed. Accreted ice with an average thickness of 3 mm can be removed within 4 s by nSDBD, and then the ice never appeared again on the plasma-protected zone. In the whole de-icing process, the ice on the plasma-protected zone was “cut” and the adhesion force between the ice layer and airfoil surface was reduced by the heat generated by the plasma actuator. The “cut” ice layer was blown downstream by aerodynamic force of the incoming flow. It can be concluded that both the thermal effects of the nSDBD actuator and the aerodynamic force of the incoming flow contribute to the de-icing performance.

### Active control of vortex-induced vibration of a circular cylinder using machine learning

We demonstrate the use of high-fidelity computational fluid dynamics simulations in machine-learning based active flow control. More specifically, for the first time, we adopt the genetic programming (GP) to select explicit control laws, in a data-driven and unsupervised manner, for the suppression of vortex-induced vibration (VIV) of a circular cylinder in a low-Reynolds-number flow (Re = 100), using blowing/suction at fixed locations. A cost function that balances both VIV suppression and energy consumption for the control is carefully chosen according to the knowledge obtained from pure blowing/suction open-loop controls. By implementing reasonable constraints to VIV amplitude and actuation strength during the GP evolution, the GP-selected best ten control laws all point to suction-type actuation. The best control law suggests that the suction strength should be nonzero when the cylinder is at its equilibrium position and should increase nonlinearly with the cylinder’s transverse displacement. Applying this control law suppresses 94.2% of the VIV amplitude and achieves 21.4% better overall performance than the best open-loop controls. Furthermore, it is found that the GP-selected control law is robust, being effective in flows ranging from Re = 100 to 400. On the contrary, although the P-control can achieve similar performance as the GP-selected control at Re = 100, it deteriorates in higher Reynolds number flows. Although for demonstration purpose the chosen control problem is relatively simple, the training experience and insights obtained from this study can shed some light on future GP-based control of more complicated problems.

### Building a Maxey–Riley framework for surface ocean inertial particle dynamics

A framework for the study of surface ocean inertial particle motion is built from the Maxey–Riley set. A new set is obtained by vertically averaging each term of the original set, adapted to account for Earth’s rotation effects, across the extent of a sufficiently small spherical particle that floats at an assumed unperturbed air–sea interface with unsteady nonuniform winds and ocean currents above and below, respectively. The inertial particle velocity is shown to exponentially decay in time to a velocity that lies close to an average of seawater and air velocities, weighted by a function of the seawater-to-particle density ratio. Such a weighted average velocity turns out to fortuitously be of the type commonly discussed in the search-and-rescue literature, which alone cannot explain the observed role of anticyclonic mesoscale eddies as traps for marine debris or the formation of great garbage patches in the subtropical gyres, phenomena dominated by finite-size effects. A heuristic extension of the theory is proposed to describe the motion of nonspherical particles by means of a simple shape factor correction, and recommendations are made for incorporating wave-induced Stokes drift and allowing for inhomogeneities of the carrying fluid density. The new Maxey–Riley set outperforms an ocean adaptation that ignored wind drag effects and the first reported adaption that attempted to incorporate them.