# Latest papers in fluid mechanics

### The effects of upstream perturbations on large-scale field and the proliferation of λ2 vortices

The effects of upstream perturbations on large-scale field are analyzed using direct numerical simulation data of a channel flow of frictional Reynolds number, [math], 394. A set of three and five spanwise blowing jets are used to create the upstream perturbations. The premultiplied energy spectra show that upstream perturbations led to the increase in range of large-scale wavenumbers in contrast to the unperturbed channel flow. The energy of wavenumbers lower than inertial sub-range ([math] power law) shows an increase in energy due to the perturbations and sustained downstream up to x = 10D from jets. Two-point correlation based Gaussian filter is used to extract large-scale features of correlation length greater than 2h (where h is channel half-height). Premultiplied energy spectra of the Gaussian filtered large-scales demonstrate the importance of jet spacing and diameter in exciting large-scale wavenumbers. The λ2 vortices of large-scale features formed a strong ring-type vortices at [math]. Spectral turbulence kinetic energy (TKE) production depicts a secondary peak in TKE production at [math], which indicates the formation of a shear layer due to the upstream perturbations.

### Spatio-temporal evolution mechanism of cavitation vortex ropes in a swirling flow

Cavitation vortex rope widely occurs in hydraulic machinery, leading to the decrease in performance characteristic and increase in pressure fluctuation. The objective of this study was to explore the generation and transformation of cavitation vortex ropes in a swirling flow. A visual swirling-flow generator platform was designed to investigate their spatiotemporal evolution mechanism. A flow pattern observation system with a high-speed camera was built to capture the vortex rope forms, and pressure fluctuation experiments were carried out to present fluctuating characteristics of corresponding cavitation vortex ropes. Cavitation vortex rope forms and pressure fluctuation characteristic under different operating conditions were exhibited. Four types of stable cavitation vortex ropes (broken, dual, single, and subulate) were observed. Regional distribution of vortex ropes under different Reynolds and cavitation numbers was characterized, which showed that broken and subulate vortex ropes account in large Reynolds and cavitation ranges. Pressure fluctuation analyses revealed dominant characteristic frequencies were 2.13, 1.98, 1.74, and 1.93 times the rotational frequency of the runner for the broken, dual, single, and subulate cavitation vortex ropes, respectively. In addition, two unstable transitions were identified during the conversion process. One is an unstable transitional triple-vortex rope during from a dual- to single-vortex rope process, and the other is an unstable subulate-vortex rope between the occurrence of the single- and stable subulate-vortex ropes. The present study could give a deep understanding of the generation of cavitation vortex ropes and provide some references to improve the hydraulic instabilities induced by cavitation vortex ropes in hydraulic machinery.

### A well-posed multilayer model for granular avalanches with μ(I) rheology

The description of geophysical granular flows, like avalanches and debris flows, is a challenging open problem due to the high complexity of the granular dynamics, which is characterized by various momentum exchange mechanisms and is strongly coupled with the solid volume fraction field. In order to capture the rich variability of the granular dynamics along the avalanche depth, we present a well-posed multilayer model, where various layers, made of the same granular material, are advected in a dynamically coupled way. The stress and shear-rate tensors are related to each other by the μ(I) rheology. A variable volume fraction field is introduced through a relaxation argument and is governed by a dilatancy law depending on the inertial number, I. To avoid short-wave instabilities, which are a well-known issue of the conditionally hyperbolic multilayer models and also of three-dimensional models implementing the μ(I) rheology, a physically based viscous regularization using a sensible approximation of the in-plane stress gradients is proposed. Linear stability analyses in the short-wave limit show the suitability of the proposed regularization in ensuring the model well-posedness and also in providing a finite cutoff frequency for the short-wave instabilities, which is beneficial for the practical convergence of numerical simulations. The model is numerically integrated by a time-splitting finite volume scheme with a high-resolution lateralized Harten–Lax–van Leer (LHLL) solver. Numerical tests illustrate the main features and the robust numerical stability of the model.

### Evaluation of gas permeability in porous separators for polymer electrolyte fuel cells: Computational fluid dynamics simulation based on micro-x-ray computed tomography images

Author(s): Soichiro Shimotori, Toshihiro Kaneko, Yuta Yoshimoto, Ikuya Kinefuchi, Amer Alizadeh, Wei-Lun Hsu, and Hirofumi Daiguji

Pore structures and gas transport properties in porous separators for polymer electrolyte fuel cells are evaluated both experimentally and through simulations. In the experiments, the gas permeabilities of two porous samples, a conventional sample and one with low electrical resistivity, are measure...

[Phys. Rev. E 104, 045105] Published Mon Oct 18, 2021

### Self-amplifying hetons in vertically sheared geostrophic turbulence

This paper examines baroclinic turbulence in the local approximation using a quasi-geostrophic beta-plane numerical model with bottom friction. New coherent vortex structures are found to emerge and self-amplify in a horizontally homogeneous mean flow directed westward in the upper layer where the potential vorticity gradient (PVG) is negative. Opposite sign eddies shifted eastward are formed in the lower layer with positive PVG owing to the Rossby wave radiation. Such baroclinic structures can be viewed as self-amplifying hetons supported by the energy transfer from the mean flow. Their growth and saturation are controlled by the competition between vortex amplification associated with the crossflow drift and viscous decay enhanced by core deformations. The presented numerical simulations indicate that subtropical regions with westward flows in the upper layer favor eddy growth and long-distance propagation.

### Hypersonic transition over a heated wall

We investigate the transition in Mach 6 boundary layers over a heated wall by magenta using the Mach 6 wind tunnel at Peking University and using visualization, focused laser differential interferometry, infrared imaging, and numerical simulation. The model's wall-temperature ratio [math] (where [math] and T0 are the wall and total temperature, respectively) can be controlled to vary from 0.66 to 1.77. The results show that increasing [math] initially delays but then promotes the transition to turbulence with the reversal point near [math]. In contrast with the cooled-wall condition ([math]), for which the second mode is dominant, the first-mode-induced oblique breakdown dominates the transition over the heated wall ([math] 1). Ultrafast visualization and Lagrangian tracking indicate that wave packets play a dominant role in producing turbulence, which is similar to the soliton-like coherent structure detected in low-speed boundary layers.

### Phase diagram for nanodroplet impact on solid surfaces

The impact dynamics of water nanodroplets on flat solid surfaces was studied by molecular dynamics simulations over a wide range of Weber numbers (We) and surface wettability (θ0), where θ0 is the Young contact angle. A phase diagram in the parameter space of We vs θ0 was established accommodating eight impact outcomes noted in the final stage of impact, with three of them, holes rebound, partial-rebound splash, and rebound splash, for the first time being identified and reported. The eight impact outcomes were classified into three categories, i.e., non-bouncing, bouncing, and splash. The results show that the splash is triggered only when Wecr > 140. The boundaries separating bouncing from non-bouncing were determined based on the phase diagram. When θ0 > 160°, the boundary is described as Wecr = a ≪ 1; when 110° < θ0 < 160°, the boundary depends on both We and θ0, with a larger We required to trigger bouncing on a less hydrophobic surface, expressed as Wecr = b + ccosθ0; when θ0 < 110°, bouncing never takes place, and hence, the boundary is determined only by the critical contact angle, expressed as θ0,cr = 110°. Here, a, b, and c are constants.

### Lattice Boltzmann method for fluid–structure interaction in compressible flow

We present a two-way coupled fluid–structure interaction scheme for rigid bodies using a two-population lattice Boltzmann formulation for compressible flows. An arbitrary Lagrangian–Eulerian formulation of the discrete Boltzmann equation on body-fitted meshes is used in combination with polynomial blending functions. The blending function approach localizes mesh deformation and allows treating multiple moving bodies with a minimal computational overhead. We validate the model with several test cases of vortex induced vibrations of single and tandem cylinders and show that it can accurately describe dynamic behavior of these systems. Finally, in the compressible regime, we demonstrate that the proposed model accurately captures complex phenomena such as transonic flutter over an airfoil.

### Periodic Rayleigh streaming vortices and Eckart flow arising from traveling-wave-based diffractive acoustic fields

Author(s): Kirill Kolesnik, Pouya Hashemzadeh, Danli Peng, Melanie E. M. Stamp, Wei Tong, Vijay Rajagopal, Morteza Miansari, and David J. Collins

Recent studies have demonstrated that periodic time-averaged acoustic fields can be produced from traveling surface acoustic waves (SAWs) in microfluidic devices. This is caused by diffractive effects arising from a spatially limited transducer. This permits the generation of acoustic patterns evoca...

[Phys. Rev. E 104, 045104] Published Fri Oct 15, 2021

### Dynamics of three-dimensional turbulence from Navier-Stokes equations

Author(s): Katepalli R. Sreenivasan and Victor Yakhot

Turbulent flows contain occasional, well-separated sharp features, as illustrated in this picture by Bonn et al. (1993), reproduced with permission, surrounded mostly by low levels of activity. Both interacting structures contribute to the complexity of turbulence. A full theory requires the understanding of both, which is what our paper attempts to do. We predict quantitatively the multi-scaling exponents for these singular-like features of different strengths, while also showing that the background flow is Gaussian. The large spatial separation between the sharp structures enables one to treat them as a “weakly interacting gas”.

[Phys. Rev. Fluids 6, 104604] Published Fri Oct 15, 2021

### Surface tension and instability in the hydrodynamic white hole of a circular hydraulic jump

Author(s): Jayanta K. Bhattacharjee and Arnab K. Ray

A circular hydraulic jump is a discontinuous rise of the downstream height of a radially outflowing liquid (water). The discontinuous circular front, which can be easily seen in a kitchen sink, is a hydrodynamic white hole. When two such impenetrable white holes collide, rather than yielding any ground to each other, they force a wall of liquid to stand between themselves. We associate surface tension with this phenomenon.

[Phys. Rev. Fluids 6, 104801] Published Fri Oct 15, 2021

### Global well-posedness and decay for viscous water wave models

The motion of the free surface of an incompressible fluid is a very active research area. Most of these works examine the case of an inviscid fluid. However, in several practical applications, there are instances where the viscous damping needs to be considered. In this paper, we derive and study a new asymptotic model for the motion of unidirectional viscous water waves. In particular, we establish the global well-posedness in Sobolev spaces. Furthermore, we also establish the global well-posedness and decay of a fourth order partial differential equation modeling bidirectional water waves with viscosity moving in deep water with or without surface tension effects.

### Modeling solute transport and mixing in heterogeneous porous media under turbulent flow conditions

We develop and test a modeling approach to quantify turbulence-driven solute transport and mixing in porous media. Our approach addresses two key elements: (a) the spatial variability of the effective diffusion coefficient which is typically documented in the presence of a sediment–fluid interface and (b) the need to provide a model that can yield the complete distribution of the concentration probability density function, not being limited only to the mean concentration value and thus fully addressing solute mixing. Our work is motivated by the importance of solute transport processes in the hyporheic zone, which can have strong implications in natural attenuation of pollutants. Our approach combines Lagrangian schemes to address transport and mixing in the presence of spatial variability of effective diffusion. An exemplary scenario we consider targets a setup constituted by a homogeneous (fully saturated) porous medium underlying a clear water column where turbulent flow is generated. Solute concentration histories obtained through a model based solely on diffusive transport are benchmarked against an analytical solution. These are then compared against the results obtained by modeling the combined effects of diffusion and mixing. A rigorous sensitivity analysis is performed to evaluate the influence of model parameters on solute concentrations and mixing, the latter being quantified in terms of the scalar dissipation rate.

### Publisher's Note: “The life span and dynamics of immiscible viscous fingering in rectilinear displacements” [Phys. Fluids 33, 096608 (2021)]

### Real Schur flow computations, helicity fastening effects and Bagua-pattern cyclones

A semi-analytical algorithm is developed for simulating flows with the velocity gradient uniformly of the real Schur form. Computations for both decaying and driven cases are performed, exhibiting basic results for general conception and testing the specific notion of “helicity fastening flows,” and, creating the Jiu-Gong/Ba-Gua (ditetragonal/octagonal) pattern of cyclones resembling Jovian northern circumpolar cluster.

### Experimental investigation of immersed granular collapse in viscous and inertial regimes

This paper presents an experimental investigation of immersed granular collapse with an initially dense packing, mainly focusing on the collapse characteristics of different flow regimes and the influence of the initial aspect ratio. A novel experimental setup and imaging method are introduced to simultaneously observe the motion of the particles and the fluid. The collapse dynamics, including the collapse acceleration, steady propagation velocity, and collapse duration, are analyzed based on the front propagation. It is found that the collapse procedures in the inertial and viscous regimes differ significantly, with the transitional regime possessing some unique characteristics of both. The inertial regime exhibits a faster collapse process, sharper final deposition, and a depression near the right wall in the case of high columns. The viscous regime collapses from the upper-left corner, from where particles drop to the bottom and form the flow front in advance of the particles initially at the bottom, and exhibits a triangular final deposition. The inertial regime exhibits swirling fluid motion, which helps the granular transport, whereas the fluid flow in the viscous regime mainly follows the granular flow. The collapse regime characteristics are more pronounced in higher columns.

### Noise reduction of sinusoidal wavy cylinder in subcritical flow regime

The sinusoidal wavy cylinder of circular cross section is able to substantially reduce the fluid forces by effectively stabilizing the near wake in the subcritical flow regime. Based on the anechoic wind tunnel measurements and large eddy simulations (LESs), we investigate the capability of the sinusoidal wavy cylinder to reduce aeroacoustic noise as well as underlying flow physics. The wavy cylinder studied in this work covers a range of spanwise wavelength [math] = 1.8–6.0[math] and a range of wave amplitude [math] = 0.15–0.25[math], where [math] is the mean diameter of the wavy cylinder. The wind tunnel measurements are conducted at Reynolds number [math] = 2.9–8.0 × 104, while LESs are conducted at [math] = 3.0 × 104. It is observed that the wavy cylinder's configuration, determined by [math] and [math], has a profound impact on the far-field sound pressure level (SPL) of both tonal and broadband noise. Compared with the baseline smooth cylinder, the wavy cylinder with [math] = 1.8[math] and [math] = 0.25[math] can reduce the peak value of SPL at the tonal frequency by up to 36.7 dB. The reductions in the overall SPL of the tonal and broadband noise are also tremendous, by up to 31.0 and 7.5 dB, respectively, by the wavy cylinder with the optimum wavelength. Consistent with observations on noise reduction are the significantly weakened near-wake structures and largely attenuated spanwise coherence, as well as substantially suppressed pressure fluctuations in the near wake and over the cylinder surface, based on the LES results. Dependence of the noise reduction on Reynolds number is discussed as well.

### Oil column pinch-off controls the oil fraction of the oil-coated bubble

We study experimentally the formation of millimeter-sized oil-coated bubbles at a customized co-axial orifice system and the pinch-off dynamics of the oil column attached below the rising gas bubble. After the gas bubble detaches from the inner orifice, it rises under buoyancy and stretches the oil column to cause pinch-off, forming an oil-coated bubble, with the oil fraction set by the pinch-off location. We show that this pinch-off location is dominated by the size ratio of the gas bubble/oil tail to the outer orifice, and a theoretical model is proposed to predict the oil fraction, describing the experimental results well. Our findings provide potential guidelines for the controllable generation of compound multiphase bubbles using co-axial orifices.

### A kinetic approach to studying low-frequency molecular fluctuations in a one-dimensional shock

Low-frequency molecular fluctuations in the translational nonequilibrium zone of one-dimensional strong shock waves are characterized for the first time in a kinetic collisional framework in the Mach number range [math]. Our analysis draws upon the well-known bimodal nature of the probability density function (PDF) of gas particles in the shock, as opposed to their Maxwellian distribution in the freestream, the latter exhibiting two orders of magnitude higher dominant frequencies than the former. Inside the (finite-thickness) shock region, the strong correlation between perturbations in the bimodal PDF and fluctuations in the normal stress suggests introducing a novel two-bin model to describe the reduced-order dynamics of a large number of collision interactions of gas particles. Our model correctly predicts two orders of magnitude differences in fluctuation frequencies in the shock vs those in the freestream and is consistent with the small-amplitude fluctuations obtained from the highly resolved direct simulation Monte Carlo computations of the same configuration. The variation of low-frequency fluctuations with changes in the conditions upstream of the shock revealed that these fluctuations can be described by a Strouhal number, based on the bulk velocity upstream of the shock and the shock-thickness based on the maximum density gradient inside the shock, that remains practically independent of Mach number in the range examined.

### Numerical investigation of flow around a square cylinder in accelerated flow

To investigate the flow field evolution and resultant aerodynamic characteristics of a square cylinder during flow acceleration, large-eddy simulations were undertaken to simulate flow with a dimensionless acceleration rate ap of 0.0048. The adopted ap resembles that is likely to be experienced during a severe downburst wind storm. The tested incidence angle α ranges from 0° to 45° and the time-dependent Reynolds number Re [Re = U(t)D/v, where U(t) is the time-dependent inflow velocity and D and v are the cylinder length and the kinematic viscosity, respectively] varies from 0 to 5 × 104 throughout the simulation. Results revealed that the flow around a square cylinder in accelerated flow evolves through three distinct temporal flow phases: namely, Phase I (Ia and Ib) where no vortex shedding (the instantaneous lift force through this period is zero) is observed, Phase II, where periodic vortex shedding and associated lift force oscillations are initiated and enhanced, and Phase III where stable vortex shedding occurs. Phase I can be further broken down into Phase Ia, which is characterized by laminar shear layer separation and the existence of steady recirculation vortices in the near wake region, and Phase Ib (only present at α = 0° and 45°) which is distinguished by the presence of quasi-steady recirculation vortices behind the cylinder. Aside from the variation of flow patterns, the transient lift and drag coefficients and the wind pressure distributions, as well as the spatial evolution of three-dimensional flow structures and pressure distributions, are also elucidated in detail.