# Latest papers in fluid mechanics

### Lagrangian analysis for turbulent transport in variable-density turbulence

Author(s): G. S. Sidharth and J. R. Ristorcelli

It is shown that the basis functions of gradient transport theory are different when there is an additional materially conserved variable. The turbulent fluxes now depend on the mean density gradient indicating the possibility of counter gradient transport from first principles as seen in some laboratory experiments. It is shown that arguments by analogy from constant density transport for the Favre fluxes are not consistent with the Lagrangian results.

[Phys. Rev. Fluids 6, 023202] Published Thu Feb 25, 2021

### Modeling the nonlinear aeroacoustic response of a harmonically forced side branch aperture under turbulent grazing flow

Author(s): Tiemo Pedergnana, Claire Bourquard, Abel Faure-Beaulieu, and Nicolas Noiray

The response of a side branch aperture to harmonic forcing is a key element of the feedback loop describing flow-induced aeroacoustic instability in deep cavities. We derive and validate two physics-based models which, after calibration at a given condition, predict the influence of frequency, mean flow speed, and acoustic pressure amplitude on the response. Notably, these low-order models enable robust analytical amplitude predictions of self-sustained oscillations in deep cavities under turbulent grazing flow

[Phys. Rev. Fluids 6, 023903] Published Thu Feb 25, 2021

### Vorticity transfer in a leading-edge vortex due to controlled spanwise bending

Author(s): Kun Jia, Tyler Scofield, Mingjun Wei, and Samik Bhattacharya

The effect of dynamic spanwise bending on the vortex dynamics of an accelerating flat plate is studied with experiments and numerical simulations. A flat plate, held at an angle of attack of 30 degrees, is accelerated from rest to Reynolds number 2400. It was bent dynamically along the span in a controlled manner with a bending ratio of 0.65. We find that a dynamic spanwise bending induces a change in the effective shear layer velocity along the span’s bent part and creates spanwise vorticity convection. As a result, the growth of circulation in the leading-edge-vortex gets delayed along the bent part, and the final circulation is smaller than the no bending case.

[Phys. Rev. Fluids 6, 024703] Published Thu Feb 25, 2021

### Robust propagation of internal coastal Kelvin waves in complex domains

Author(s): Chenyang Ren, Xianping Fan, Yiling Xia, Tiancheng Chen, Liu Yang, Jin-Qiang Zhong, and H. P. Zhang

Internal coastal Kelvin waves were experimentally generated in a two-layer fluid system on a rotating table. Waves are exponentially localized near the tank boundary and propagate in the same direction as the table rotation along boundaries of complex geometries without being scattered. Our experiments suggest a connection between these unusual wave characteristics and topological properties of the underlying governing equations.

[Phys. Rev. Fluids 6, L022801] Published Thu Feb 25, 2021

### Numerical study of the influence of wall roughness on laminar boundary layer flashback

Author(s): Shuyu Ding, Kai Huang, Yifan Han, and Damir Valiev

Boundary layer flame flashback is a phenomenon that may constitute a key challenge for efficient combustion of novel fuels at gas turbine conditions. In the present work, the effect of wall roughness on the laminar boundary layer flashback is studied systematically using numerical simulation. The results indicate that the wall roughness can attenuate flashback speed due to enhanced heat loss in case of low thermal resistance of the wall. The critical velocity gradient of the oncoming flow is shown to decrease with wall roughness level and increase with gas thermal expansion ratio.

[Phys. Rev. Fluids 6, 023201] Published Wed Feb 24, 2021

### Flow in a weakly curved square duct: Assessment and extension of Dean's model

Author(s): Leonardo Rigo, Damien Biau, and Xavier Gloerfelt

The laminar flow in a weakly bent pipe exhibits very rich dynamical properties. The flow is stationary, periodic or chaotic depending on one control parameter. A very practical simplification inspired by Dean is capable of reproducing this behavior with remarkable accuracy.

[Phys. Rev. Fluids 6, 024101] Published Wed Feb 24, 2021

### Effect of stratification on the mixing and reaction yield in a T-shaped micro-mixer

Author(s): A. Mariotti, C. Galletti, R. Mauri, M. V. Salvetti, and E. Brunazzi

Experiments, i.e. micro-PIV and flow visualization, and direct numerical simulations, are used jointly to investigate how stratification affects mixing and chemical reaction in a T-shaped microreactor fed with two miscible liquids exhibiting a small density difference. The work analyzes the dependence of the degree of mixing on the Reynolds number and correlates the reaction yield with the Damköhler number to help to devise strategies for the practical operation of microreactors with fluids of practical interest.

[Phys. Rev. Fluids 6, 024202] Published Wed Feb 24, 2021

### General method for determining the boundary layer thickness in nonequilibrium flows

Author(s): Kevin Patrick Griffin, Lin Fu, and Parviz Moin

In this work, a new method for computing the boundary layer thickness is proposed by reconstructing an approximate inviscid solution based on the Bernoulli equation. The viscous streamwise velocity profile U[y] agrees with this inviscid reconstruction UI[y] outside the boundary layer, and the solutions diverge from each other at the boundary layer edge. The boundary layer thickness is readily determined by examining the discrepancy between these profiles. Extensive validation suggests that the present method is more robust and more widely applicable than existing methods.

[Phys. Rev. Fluids 6, 024608] Published Wed Feb 24, 2021

### Dynamics of bubbles under stochastic pressure forcing

Author(s): Riccardo Vesipa, Eleonora Paissoni, Costantino Manes, and Luca Ridolfi

Several studies have investigated the dynamics of a single spherical bubble at rest under a nonstationary pressure forcing. However, attention has almost always been focused on periodic pressure oscillations, neglecting the case of stochastic forcing. This fact is quite surprising, as random pressur...

[Phys. Rev. E 103, 023108] Published Tue Feb 23, 2021

### Weakly nonlinear Holmboe waves

Author(s): Joshua Cudby and Adrien Lefauve

Holmboe waves are long-lived traveling waves commonly found in environmental stratified shear flows. Here we study their finite-amplitude properties in the nonlinear but nonturbulent regime, with a weakly nonlinear temporal stability analysis. Using a versatile amplitude expansion method, we analyze supercritical bifurcation diagrams both in Reynolds number and Richardson number, transient phase portraits, and the vertical structures of all components modes up to third order. We believe these results provide a basis for a future fully nonlinear analysis of the Holmboe dynamical system.

[Phys. Rev. Fluids 6, 024803] Published Tue Feb 23, 2021

### Stability analysis of a thinning electrified jet under nonisothermal conditions

Author(s): Dharmansh Deshawar and Paresh Chokshi

The linear stability of a jet propagating under an electric field is analyzed under nonisothermal conditions. The electrified jet of a Newtonian fluid is modeled as a slender filament, and the leaky dielectric model is used to account for the Maxwell stresses within the fluid. The convective heat tr...

[Phys. Rev. E 103, 023107] Published Mon Feb 22, 2021

### Wet to dry self-transitions in dense emulsions: From order to disorder and back

Author(s): Andrea Montessori, Adriano Tiribocchi, Marco Lauricella, Fabio Bonaccorso, and Sauro Succi

Computer simulations show the self-transition between ordered and disordered emulsions in divergent microfluidic channels. The transition is driven by the nonlinear competition between viscous dissipation and surface tension forces as controlled by the device geometry. An unexpected route back to order is observed in the regime of large opening angles where a trend towards increasing disorder would be intuitively expected.

[Phys. Rev. Fluids 6, 023606] Published Mon Feb 22, 2021

### Physical invariance in neural networks for subgrid-scale scalar flux modeling

Author(s): Hugo Frezat, Guillaume Balarac, Julien Le Sommer, Ronan Fablet, and Redouane Lguensat

A physics informed approach is applied to neural networks for subgrid-scale scalar flux modeling. We show that several invariances of the scalar transport equation are not enforced by existing parametric models, which reduce their interpretability and question their application. A new architecture embedding these invariances as hard and soft constraints is proposed. Through different flow configurations, we show that the proposed constraints increase both the performances and the generalization capabilities of the model.

[Phys. Rev. Fluids 6, 024607] Published Mon Feb 22, 2021

### Coupled triads in the dynamics of internal waves: Case study using a linearly stratified fluid

Author(s): Q. Pan, N. N. Peng, H. N. Chan, and K. W. Chow

Coupled triads (two sets of resonant triads with one member in common) can arise in linearly stratified fluids. Such coupling may induce modulation instabilities which are otherwise absent for component triads in isolation themselves. Long wavelength instabilities will imply the occurrence of internal rogue waves which may attain amplitudes much larger than their surface wave counterparts.

[Phys. Rev. Fluids 6, 024802] Published Mon Feb 22, 2021

### Marginal regeneration in a horizontal film: Instability growth law in the nonlinear regime

Author(s): Alice Gros, Adrien Bussonnière, Sanjiban Nath, and Isabelle Cantat

The marginal regeneration process responsible for foam film drainage is revisited. It is shown that a horizontal, micron thick, foam film in contact with a meniscus destabilizes and that patches of thinner film grow along the meniscus, forming a very regular pattern.

[Phys. Rev. Fluids 6, 024004] Published Fri Feb 19, 2021

### Subgrid-scale characterization and asymptotic behavior of multidimensional upwind schemes for the vorticity transport equations

Author(s): Daniel Foti and Karthik Duraisamy

We establish subgrid-scale (SGS) characteristics of a finite volume vorticity-transport-based approach for large-eddy simulations. Modified equation analysis indicates that dissipation can be controlled locally via nonlinear limiting of the gradient employed for the vorticity reconstruction. The enstrophy budget highlights the remarkable ability of the truncation terms to mimic the true SGS dissipation and diffusion. Numerical dissipation in under-resolved simulations can be characterized by diffusion terms discovered in the modified equation analysis.

[Phys. Rev. Fluids 6, 024606] Published Fri Feb 19, 2021

### Pore network model of drying with Kelvin effect

A pore network model of isothermal drying is presented. The model takes into account the capillary effects, the transport of vapor by diffusion, including Knudsen effect, in the gas phase, and the Kelvin effect. The model is seen as a first step toward the simulation of drying in mesoscopic porous materials involving pore sizes between 4 nm and 50 nm. The major issue addressed with the present model is the computation of the menisci mean curvature radius at the boundary of each liquid cluster in conjunction with the Kelvin effect. The impact of Kelvin effect on the drying process is investigated, varying the relative humidity in the ambient air outside the medium. The simulations indicate that the Kelvin effect has a significant impact on the liquid distribution during drying. The evaporation rate is found to fluctuate due to the menisci curvature variations during drying. The simulations also highlight a noticeable non-local equilibrium effect.

### Direct numerical simulation of bidisperse inertial particles settling in turbulent channel flow

The behavior of settling velocity and clustering of bidisperse inertial particles in a turbulent channel flow is investigated through direct numerical simulation. The particle-laden planar channel flow has a friction Reynolds number at Reτ = 180. Eulerian–Lagrangian method is used to study the dynamic properties of bidisperse and monodisperse inertial particles with 16 different simulation sets, which are distinguished by Stokes numbers ranging from St+ = 1.31 to 52.58 and particle number ratio from 1:1 to 1:8. Momentum exchange between fluid and particle phases is considered in the simulation as the chosen initial volume fraction at 5 × 10−5 is in the two-way coupling regime. The gravity is set at the direction normal to both the wall normal direction and the streamwise direction. We observe that in the bidisperse cases the turbophoresis effect of inertial particles with the smaller diameter is significant even though it is very weak in the corresponding monodisperse cases. We use radial distribution function (RDF) to investigate the degree of clustering and turbophoresis. The results indicate that RDF is larger in the bidisperse cases for both large and small particles and it is greatly affected by the bulk particle number ratio and the Stokes number ratio. Unlike clustering, the terminal settling velocities of inertial particles in the bidisperse cases are affected by the final volume fraction at the dynamic equilibrium state. When their final volume fractions are lower than those in the corresponding monodisperse cases, the settling velocity of either particle becomes reduced from the monodisperse value. We also investigate the relationship between settling velocity and vortex strength. The results show that the preferential sweeping mechanism is strengthened with Stokes number decreasing and the mechanism can be quantified by the slope of the curve of settling velocity variation with vortex strength.

### On the H-type transition to turbulence—Laboratory experiments and reduced-order modeling

A series of experiments were conducted to understand the sources of local, high-amplitude velocity fluctuations produced at the late stages of boundary-layer flow transition to turbulence. The laboratory experiments considered the controlled injection of Tollmien–Schlichting (TS) waves into a nearly zero pressure gradient, laminar boundary layer, resulting in H-type transition to turbulence. Proper orthogonal decomposition (POD) was used to extract the energetic coherent structures within the transitional flow field obtained with particle image velocimetry. The first three modes were observed to feature spatial mode shapes consistent with a cross-section of a canonical hairpin vortex structure and were associated with time-dependent amplitudes having consistent peak frequencies with the fundamental TS wave frequency. Higher-order modes exhibited a combination of sub- and super-harmonics of the TS wave frequency and were attributed to flow interactions produced by a hairpin packet. A conditional averaging method was used to establish a reduced-order model for the overshoot phenomena in Reynolds shear stress and turbulence kinetic energy observed at the late transition stage. The lower portion of the large-scale hairpin vortex structure was observed to be primarily responsible for the overshoot mechanisms, which was well captured in a reduced-order model of the velocity field. The first four POD modes were used to create this reduced-order model, which, while only consisting of ≈15% of the total turbulence kinetic energy of the original velocity field, was able to capture ≈85% of the peak Reynolds stress amplitude across the overshoot region.

### Theoretical analysis of quantum turbulence using the Onsager ideal turbulence theory

Author(s): Tomohiro Tanogami

We investigate three-dimensional quantum turbulence as described by the Gross-Pitaevskii model using the analytical method exploited in the Onsager “ideal turbulence” theory. We derive the scale independence of the scale-to-scale kinetic energy flux and establish a double-cascade scenario: At scales...

[Phys. Rev. E 103, 023106] Published Thu Feb 18, 2021