# New Papers in Fluid Mechanics

### Asymmetric time-cross-correlation of nonequilibrium concentration fluctuations in a ternary liquid mixture

Author(s): Doriano Brogioli, Fabrizio Croccolo, and Alberto Vailati

Equilibrium phenomena are characterized by time symmetry. Thermodynamic fluctuations are also time-symmetric at equilibrium. Conversely, diffusion of a solute in a liquid in the presence of a gradient is a nonequilibrium phenomenon, which gives rise to long-range fluctuations with amplitude much lar...

[Phys. Rev. E 99, 053115] Published Thu May 23, 2019

### Stability of arrays of bottom-heavy spherical squirmers

Author(s): D. R. Brumley and T. J. Pedley

A dense planar array of spherical microswimmers is studied analytically and numerically using pairwise lubrication interactions. Suspension dynamics are mediated through gravitational torques exerted on the cells and cell-cell repulsive forces, and they reveal stable, oscillatory, and chaotic states.

[Phys. Rev. Fluids 4, 053102] Published Wed May 22, 2019

### Vortex-dynamical interpretation of anti-phase and in-phase flickering of dual buoyant diffusion flames

Author(s): Tao Yang, Xi Xia, and Peng Zhang

A study finds that for two adjacent buoyant flames the flickering mode transition from in-phase to anti-phase is caused by a transition of the inner-side vortex pattern from symmetric to staggered. This mechanism is similar to the instability in the wake of a bluff body that initiates the Karman vortex street.

[Phys. Rev. Fluids 4, 053202] Published Wed May 22, 2019

### Shear-induced particle migration and size segregation in bidisperse suspension flowing through symmetric T-shaped channel

Transport of dense suspension in T-shape channels is encountered in many practical applications. We report numerical simulations of bidisperse suspension flowing through symmetric T-shape channels in converging as well as diverging flow conditions. The difference in the migration flux of the two species leads to size segregation, and this causes alteration of velocity and concentration profiles in the downstream locations of confluence or bifurcation. The velocity and concentration profiles for bidispersed suspension are compared with that of the monodisperse case. The effect of the particle size ratio and the concentration of individual species on the size segregation are investigated. Depending upon the particle size ratio and species concentration, one or both species enriched the channel center. For a suspension comprised of an equal concentration of both species, larger particles always enriched the channel center. On the other hand, the position of the concentration peak for smaller particles strongly depends on the size ratio. The segregation behavior in the different branches of the channel was observed to be influenced by the particle size ratio.

### Control of circular cylinder flow via bilateral splitter plates

We carry out wind tunnel investigations to study the flow of a circular cylinder modified with two rigid splitter plates hinged along its stagnation points. The equal-sized and symmetrically placed splitter plates are both parallel to the incoming airflow, and their single-sided length in the streamwise direction varies from 0 to 2.0D (where D is the cylinder diameter). The wind tunnel experiments are conducted at the Re of 3.33 × 104. In addition to bilaterally arranged plates, two other configurations of splitter plates, i.e., front-plate-only and rear-plate-only, are also investigated. By employing the sectional measurement of surface pressure in the midspan slice, we evaluate typical aerodynamic parameters, including pressure distribution, instantaneous drag and lift forces, frequency spectra of the unsteady lift forces, mean drag, and root-mean-square lift coefficients acting on the cylindrical test models. A particle image velocimetry (PIV) system is used to visualize and quantify the vortex shedding process and the dynamic interactions of the natural and modified cylinders. Experimental results of the surface pressure measurement and PIV measurement results are then combined to reveal the effects of rigid plates with different configurations (bilateral, front-only, and rear-only) on the circular cylinder flow.

### Artificial neural network approach to large-eddy simulation of compressible isotropic turbulence

Author(s): Chenyue Xie, Jianchun Wang, Ke Li, and Chao Ma

A subgrid-scale (SGS) model for large-eddy simulation (LES) of compressible isotropic turbulence is constructed by using a data-driven framework. An artificial neural network (ANN) based on local stencil geometry is employed to predict the unclosed SGS terms. The input features are based on the firs...

[Phys. Rev. E 99, 053113] Published Tue May 21, 2019

### Local estimates of Hölder exponents in turbulent vector fields

Author(s): F. Nguyen, J.-P. Laval, P. Kestener, A. Cheskidov, R. Shvydkoy, and B. Dubrulle

It is still not known whether solutions to the Navier-Stokes equation can develop singularities from regular initial conditions. In particular, a classical and unsolved problem is to prove that the velocity field is Hölder continuous with some exponent h<1 (i.e., not necessarily differentiable) a...

[Phys. Rev. E 99, 053114] Published Tue May 21, 2019

### Comparison of aerodynamic models for two-dimensional pitching foils with experimental data

Several semiempirical models for the thrust force and propulsion efficiency of pitching foils have been developed recently to derive simple scaling laws for aquatic locomotion. In this work, we compare two of these models with the theoretical results from linear potential theory and with available experimental data. Overall, the results from the corrected linear potential theory are shown to agree better with most of the available experimental data for small enough amplitudes, while one of the semiempirical models tested performs better for large amplitudes. More experimental data for large reduced frequencies would be desirable to test the different models.

### Wall-attached clusters for the logarithmic velocity law in turbulent pipe flow

The logarithmic law of the mean velocity is considered a fundamental feature of wall-bounded turbulent flows. The logarithmic velocity law is used widely to model the near-wall turbulence and to predict skin friction. Although classical scaling theory has been used to verify that the velocity profile in the overlap region follows the logarithmic behavior asymptotically, and thus recent experiments have attempted to assess the logarithmic law in large-scale facilities, there is a lack of understanding of the structural basis for the logarithmic law. Here, we show the logarithmic law by extracting the wall-attached structures of the streamwise velocity fluctuations through direct numerical simulation of turbulent pipe flow. The wall-attached structures exhibit self-similar behavior according to their height and have an inverse-scale population density, reminiscent of Townsend’s attached-eddy hypothesis. The wall-normal distributions of the streamwise velocity within the identified structures are conditionally averaged with respect to their height. The velocity profile is reconstructed by superimposing the velocity distributions of the objects that follow the inverse-scale population density. The indicator function of the resulting velocity profile shows a complete plateau for the high-speed structures due to their higher local Reynolds number. These findings provide strong evidence that the identified coherent structures are directly related to the logarithmic velocity law and serve as the structural basis for the inertial layer.

### Bouncing of a projectile impacting a dense potato-starch suspension layer

When a solid projectile is dropped onto a dense non-Brownian-particle suspension, the action of an extremely large resistance force on the projectile results in its drastic deceleration, followed by a rebound. In this study, we perform a set of simple experiments of dropping a solid-projectile impact onto a dense potato-starch suspension. From the kinematic data of the projectile motion, the restitution coefficient and time scale of the rebound are measured. By assuming linear viscoelasticity, the effective transient elasticity and viscosity can be estimated. We additionally estimate the Stokes viscosity on a longer time scale by measuring the slow sinking time of the projectile. The estimated elastic modulus and viscosity are consistent with separately measured previous results. In addition, the effect of mechanical vibration on the viscoelasticity is examined. As a result, we find that the viscoelasticity of the impacted dense suspension is not significantly affected by the mechanical vibration.

### Damped interfacial oscillation of a particle-embedded viscous drop

This article describes how a drop with an embedded particle exhibits interfacial waves with transient decay due to the interplay between capillary and viscous effects. To reveal the damped oscillation of the system properly, the deformation and pressure fields inside the domain are described in terms of complete sets of basis functions. Such representation leads to a matrix formulation which enforces no-slip condition at the solid-liquid interface and ensures correct discontinuity in normal stress due to surface tension at the drop periphery. The resulting characteristic equation involving the natural frequencies and the decay constants is solved numerically to determine these quantities. The matrix expression implies a block-diagonalized structure with two uncoupled blocks corresponding to two distinctly different dynamics. The first of these is related to pure rotational velocities on spherical surfaces which monotonically decay in time without any fluctuation in the absence of any peripheral deformation. By contrast, the second block is associated with the undulation in shape. Due to the restoring features of surface tension, the latter can exhibit underdamped oscillatory modes, if the capillary number Ca is below a critical value. However, even these waves would become overdamped if the critical number is exceeded. These values of Ca for a few most relevant modes are plotted in this paper as functions of particle-to-drop size ratio. Also, the natural frequencies for the underdamped cases as well as the damping constants for all considered modes are presented for different size ratios and capillary numbers. The findings are verified by matching the computed results to a novel boundary layer theory under low capillary number limit. Under the limiting condition, both sets of independent calculations yield the same decay constants and natural frequencies providing mutual validations.

### Study of the 3D Euler equations using Clebsch potentials: Dual mechanisms for geometric depletion

Publication year: 2018

Journal / Book title: Nonlinearity

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### Discontinuity in the sedimentation system with two particles having different densities in a vertical channel

Author(s): Deming Nie and Jianzhong Lin

The two-dimensional lattice Boltzmann method was used to numerically study a sedimentation system with two particles having different densities in a vertical channel for Galileo numbers in the range of 5≤Ga≤15 (resulting in a Reynolds number, based on the settling velocity, approximately ranging bet...

[Phys. Rev. E 99, 053112] Published Mon May 20, 2019

### Invariant manifolds in stratified turbulence

Author(s): N. E. Sujovolsky, G. B. Mindlin, and P. D. Mininni

A low dimensional model for stratified turbulence predicts the existence of invariant manifolds for the evolution of temperature and velocity gradients. Fluid elements evolve preferentially along these manifolds, associated with stable regions and with regions prone to develop local convection.

[Phys. Rev. Fluids 4, 052402(R)] Published Mon May 20, 2019

### Stabilization of unsteady flows by reduced-order control with optimally time-dependent modes

Author(s): Antoine Blanchard and Themistoklis P. Sapsis

The Optimally Time-Dependent (OTD) modes, a set of deformable orthonormal modes that track transient instabilities, are incorporated into a robust, inexpensive control algorithm that can steer any trajectory of a high-dimensional nonlinear system toward a fixed point of the governing equations.

[Phys. Rev. Fluids 4, 053902] Published Mon May 20, 2019

### Numerical investigation of highly unsteady accelerated/decelerated flows for blunt bodies experiencing impulsive motion

Scale-resolving simulations (SRSs) such as large-eddy simulation (LES) and hybrid LES/Reynolds-averaged Navier–Stokes are applied to analyze the unsteady characteristics of the drag and flow fields for blunt bodies subject to impulsive motion. These simulations reveal highly transient behaviors of the primary and secondary vortices triggered by inertial forces during impulsive motion. A distinctive characteristic of the transient drag, namely, the existence of a plateau region, induced by a circular cylinder during impulsive acceleration is also revealed. It is found that among the SRS methods, the LES one-equation eddy method is able to more precisely capture the intrinsic local pressure gradient arising from unsteadiness of the vortices together with the instantaneous vorticity magnitude. The secondary vortices created by inertial forces and shear stresses due to the impulsive motion and the interactions of these vortices with the primary vortices turn out to play a key role in the transient behaviors of the flow field and the drag. The mechanism causing the highly unsteady flow field and its relationship to the bluntness of the shape configuration are also explored using the LES one-equation eddy method. It is found from the range of retained local Cp values and the transient vorticity distribution along the cylinder surface that the mobility of the unsteady flow separation point depends on the bluntness of the configuration.

### Phase difference effect on collective locomotion of two tandem autopropelled flapping foils

Author(s): Xingjian Lin, Jie Wu, Tongwei Zhang, and Liming Yang

The collective locomotion of two tandem autopropelled flapping foils is greatly affected by the phase difference. Two distinct vortex interactions are observed—merging interaction and broken interaction—which respectively result in the highest efficiency for the follower and the leader.

[Phys. Rev. Fluids 4, 054101] Published Fri May 17, 2019

### Numerical simulation of flow over a parallel cantilevered flag in the vicinity of a rigid wall

Author(s): Li Wang and Fang-bao Tian

Flow over a parallel cantilevered flag in the vicinity of a rigid wall is numerically studied using an immersed boundary–lattice Boltzmann method (IB–LBM) in two-dimensional domain, where the dynamics of the fluid and structure are, respectively, solved by the LBM and a finite-element method (FEM), ...

[Phys. Rev. E 99, 053111] Published Thu May 16, 2019

### Numerical investigation of the flow characteristics of underexpanded methane jets

In the present work, numerical simulations are carried out to investigate underexpanded methane jets with phase separation effects. In order to predict the fuel injection and the mixture formation in the constant volume chamber, a hybrid, pressure-based solver is combined with a vapor-liquid equilibrium model and a moving mesh methodology. The thermodynamic models are based on the cubic equation of state of Soave, Redlich, and Kwong. A compressibility correction for the widely known kωSST turbulence model is implemented additionally. Application-relevant simulations with a total fuel pressure of 300 bars and five different chamber pressures ranging from 12 to 60 bars were defined. Furthermore, the influence of two fuel and chamber temperatures, 294 and 363 K, is analyzed. Depending on the chamber pressure, two different flow structures of the potential core can be distinguished: (1) A series of typical shock barrels for small pressure ratios and moderately underexpanded jets and (2) a shear layer consisting of a two-phase mixture which enfolds the potential core for high pressure ratios and highly underexpanded jets. Increasing the fuel temperature leads to less significant phase separations, while an increase in the chamber pressure does not affect the structure of the potential core. A comparison with experimental measurements shows a very good agreement of the simulated structure of the potential core, providing evidence that the underlying phenomena are predicted correctly and suggesting that a moving mesh strategy and consistent two-phase thermodynamics implementation are necessary for a physical representation of high-pressure injections.

### Effect of finite amplitude of bottom corrugations on Fabry-Perot resonance of water waves

Author(s): Jie Zhang and Michel Benoit

Recently, the mechanism of Fabry-Perot (F-P) resonance in optics was extended to monochromatic water waves propagating in a domain with two patches of sinusoidal corrugations on an otherwise flat bottom. Assuming small-amplitude surface waves, an asymptotic linear analytical solution (ALAS) was deri...

[Phys. Rev. E 99, 053109] Published Wed May 15, 2019