# Latest papers in fluid mechanics

### Turbulence energetics in an axisymmetric impinging jet flow

Turbulence energetics is investigated in the impingement and wall jet regions of an axisymmetric impinging jet flow, by using the two-dimensional particle-image velocimetry measurement technique. The inlet-based Reynolds number is equal to 5200, and the height to the diameter ratio is equal to 5.95. This study shows that turbulence kinetic energy balances in outer, middle, and inner layers of the impingement region differ greatly from each other. The balances in near-field and far-field wall jet regions differ, as well. This study also provides various useful insights into the directional characteristics of the energy transports. For example, it has revealed that the turbulence diffusion process transports energy in the upstream direction in the jet core, but obliquely in the mixing layers. The balance terms are decomposed into physically meaningful spatial components, which, among various other insights, show that the negative production rate that is earlier reported in the stagnation region is caused by the negative work contributions of the radial and the tangential Reynolds stresses. This study, overall, lets us have a thorough understanding of the turbulence production, the convection, the turbulence diffusion, and the viscous diffusion processes, while the turbulence dissipation and the pressure diffusion terms are clubbed together and obtained as the residual of the energy balance equation. Information that is extracted from the residual has demonstrated the failure of Lumley’s model to estimate the pressure diffusion rate near the impingement surface.

### Dynamics and statistics of reorientations of large-scale circulation in turbulent rotating Rayleigh-Bénard convection

We present a direct numerical simulation to investigate the dynamics and statistics of reorientations of large-scale circulation (LSC) in turbulent rotating Rayleigh-Bénard convection for air (Pr = 0.7) contained in a cylindrical cell with unit aspect ratio. A wide range of rotation rates (0 ≤ Ro−1 ≤ 30) is considered for two different Rayleigh numbers Ra = 2 × 106 and 2 × 107. Using the Fourier mode analysis of time series data obtained from the different probes placed in the azimuthal direction of the container at the midplane, the orientation and associated dynamics of LSC are characterized. The amplitude of the first Fourier mode quantifies the strength of LSC, and its phase Φ1 gives the information on the azimuthal orientation of LSC. Based on the energy contained in the Fourier modes, different flow regimes are identified as the rotation rate is varied for a given Rayleigh number. The LSC structure is observed in the low rotation regime (Ro−1 ≲ 1), while the presence of other flow structures, namely, quadrupolar and sextupolar, is obtained at high rotation rates. In the LSC regime, a strong correlation between the orientation of LSC structure and the heat transfer and boundary layer dynamics is observed. At low rotation rates, the dissipation rates follow the log-normal behavior, while at higher rotation rates, a clear departure from log-normality is noted. Different types of reorientations, namely, rotation-led, cessation-led, partial, and complete reversal, are identified. The distribution of change in orientation of LSC follows a power law behavior as P(|ΔΦ1|) ∝|ΔΦ1|−m, with the exponent m ≈ 3.7. In addition, the statistics of time interval between successive reorientations follow a Poisson distribution. These observations are in good agreement with earlier experimental results.

### Azimuthal organization of large-scale motions in a turbulent minimal pipe flow

Direct numerical simulation data for turbulent minimal pipe flows with Reτ = 927, 1990, and 2916 are examined to explore the azimuthal (or spanwise) organization of their large-scale structures. We chose a streamwise-minimal unit with a streamwise domain length of [math], which is the characteristic streamwise length of near-wall streaks. The spanwise scales of most of the energetic motions and their contributions to the total energy are comparable with those of the streamwise long-domain simulation. In the azimuthal energy spectra of the streamwise velocity fluctuations (u), the large-scale energy increases with Reτ and three outer peaks (λθ = 0.7–0.8, π/2 and π) become evident when Reτ = 2916. The presence of the outer peaks at λθ = 0.7–0.8 and π/2 is consistent with the results of the long-domain simulation. The peak at λθ = 0.7–0.8 is associated with large-scale motions and the other two peaks are associated with very-large-scale motions (VLSMs). The maximum spanwise wavelength increases linearly with the wall-normal distance from the wall. A kz−1 region is evident in the range 0.3R < λz (=rλθ) < R, which indicates the presence of self-similar motions. The conditional two-point correlation with a cut-off wavelength of λz = 0.9R shows that there is a strong correlation between the enhanced energy in the outer region and the wall-attached structures, which were extracted from the time evolution of the streamwise-averaged u field (u2D). The spanwise sizes (lz) of the attached u2D structures scale with their height (ly) in the log region and their time scales (lt) follow ltuτ/lz = 2, which is consistent with the bursting time scale. Their spanwise sizes lie in the range R < lz < 3R, for which lt increases significantly, which indicates that these structures are associated with VLSMs and make the dominant contributions to the enhanced energy in the outer region. These structures penetrate to the wall region as a manifestation of the footprint and modulate the small-scale energy. The negative-u2D structures induce congregative motions in the near-wall region.

### Three-dimensional visualization of viscous fingering for non-Newtonian fluids with chemical reactions that change viscosity

Author(s): Sotheavuth Sin, Tetsuya Suekane, Yuichiro Nagatsu, and Anindityo Patmonoaji

Three-dimensional viscous fingering for miscible non-Newtonian fluids with and without chemical reactions were studied with a microfocus X-ray computed tomography scanner. We find that the area fraction of injected fluid in the reactive cases was lower than that in the nonreactive cases.

[Phys. Rev. Fluids 4, 054502] Published Fri May 24, 2019

### Convection pattern formation in a domain with a horizontal interface

For the classical constellation of a fluid heated from below and cooled at the top, convection patterns are examined, with the additional feature of a horizontal interface. The interface separates two subdomains of different types, which contain porous media with different properties. The case of a pure diffusive layer at the bottom and the case of a free fluid above a porous medium are considered also. It is outlined that the approach can also be valid for the case of haline convection. Using finite element modeling for the nondimensional formulation, 2-dimensional transient and steady state convection patterns are visualized and examined. The simulations show that the interface significantly changes the convection cells in the domain as well as the heat transfer through the system. In all cases, the emerging pattern on one side of the interface is related to the pattern on the other side. The results are relevant for the understanding of heat and mass flow through layered geological strata, at the bottom of water bodies and in technical devices, for example layered insulation systems.

### 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

### Time-of-flight of solitary waves in dry and wet chains of beads: Experimental results and phenomenological models

A highly nonlinear solitary wave is generated by impacting a dry chain of beads on one of its ends. Its speed depends on the speed [math] of the striker and the details of the contact force. The force on the bead at the site n = 7 and the end of the chain, as well as the time-of-flight (ToF) of both, the incident and reflected waves, is measured as a function of [math]. This study was performed on a chain of stainless steel beads in two general cases: the dry chain and wet chains having three different types of oil on and around the contact points between the beads. The ToF displays a complex dependence on the fluid’s rheological properties not seen in previous studies. Power-law dependencies of the ToF on [math] in both, dry and wet, cases were found. It turned out that the Hertz plus viscoelastic interactions are not enough to account for the measured data. Two phenomenological models providing a unified and accurate account of our results were developed.

### Hydrodynamics of a weakly curved channel

The underlying mechanism of curvature induced helicoidal flow in a weakly curved channel intrigues researchers. Here, we explore the hydrodynamics of weakly curved channels, defined by the limiting values of the curvature ratio (ratio of channel half-width to radius of curvature) and aspect ratio (ratio of channel half-width to average flow depth) as 0.1 and 10, respectively. The three-dimensional continuity and momentum equations are solved analytically, involving the appropriate boundary conditions and closing the system by means of the turbulence closure model and the indispensable fluid constitutive formulations. The skewed filament of the azimuthal velocity component, emanating from the effects of curvilinear streamlines, is introduced into the analysis, for the first time, to address the flow asymmetry across the flow cross section. The modification of the radial slope due to the presence of the stress term in the radial momentum balance is accomplished by a slope correction factor, which turns out to be a weak function of the reciprocal of the power-law exponent. The attenuation of the azimuthal shear stress component, resulting from the skewed velocity profile, is characterized by the damping function to provide a quantitative insight into the redistribution of the primary flow momentum. The velocity field reveals that the flow circulation (on the flow cross-sectional plane) about the azimuthal axis and the flow helicity strengthen with an increase in the curvature ratio. The variation of the radial free surface profile is more sensitive to the flow Froude number than to the curvature ratio. The evolutions of the stress field with several key parameters are also examined.

### Non-monotonic viscous dissipation of bouncing droplets undergoing off-center collision

The off-center collision of binary bouncing droplets of equal size was studied numerically by a volume-of-fluid method with two marker functions, which has been justified and validated by comparing with available experimental results. A nonmonotonic kinetic energy (KE) recovery with varying impact parameters was discovered. This can be explained by the prolonged entanglement time and the enhanced internal-flow-induced viscous dissipation for bouncing droplets at intermediate impact parameters, compared with those at smaller or larger impact parameters. The distribution of the local viscous dissipation rate (VDR) in the droplet interior shows two major concentration areas, and the competition between these two concentration areas accounts for the nonmonotonic viscous dissipation with varying impact parameters. The nonmonotonic KE recovery with varying impact parameters can also be attributed to the competition between the VDR induced by normal strains and shear strains. The nonmonotonicity was further numerically verified for wider ranges of parameters, and a practically useful formula was proposed to correlate the KE dissipation factor with the impact parameter for various Weber numbers and Ohnesorge numbers.

### Image processing for bubble morphology characteristics in diluted bubble swarms

The present investigation describes, in detail, a data processing strategy for characterizing bubble sizes and shapes properly from shadowgraph images in diluted bubble swarm conditions. A flat pseudo-two-dimensional bubble column is studied, where two different bubble types (ellipsoidal and spherical caps) can be injected through two different spargers. Various statistical equivalent diameters (D10, D20, D30, D32) are considered, and the morphology is characterized via the eccentricity (χ) as a function of the size. To further broaden the experimental conditions, several Newtonian liquids characterized by different viscosities and gas injection rates ranging from 50 to [math] are used. Additionally, an original method for verifying results, using control parameters such as orientation and solidity, is presented.

### 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.