# Latest papers in fluid mechanics

### A new linear forcing method for isotropic turbulence with controlled integral length scale

Turbulence is a common feature to all flows that surround us. Despite its ubiquity, particularly in industrial flows, it is very difficult to provide a mathematical framework for the generation of turbulent eddies. Several methods have been proposed which are able to reproduce realistic features for velocity fluctuations, exhibiting proper space- and time-correlations. Focusing on physical space forcing, these methods are usually first evaluated upon sustained homogeneous isotropic turbulence by introducing a body force to the Navier–Stokes equations. Since the pioneering work of Lundgren, these techniques usually experience difficulties in predicting the integral length scale. The present study provides a forcing through a reconstruction approach which consists in building velocity fluctuations with a prescribed energy spectrum model. The proposed approach is assessed by performing large-eddy simulations of a sustained homogeneous isotropic turbulence in a triply periodic box. Properties of this forcing technique are discussed, drawing on both spatial and time correlations and also on the shape of energy spectrum together with the level of resolved turbulent kinetic energy. A special attention is put on the control of resolved turbulent energy. In this framework, an efficient selective forcing technique is derived, making use of spectral space features. The results show that the proposed approach allows to drive efficiently the resolved kinetic energy toward its target value while preserving the integral length scale independent of the domain size. It is observed that the resulting longitudinal length scale is overestimated by 13%, while the two-time correlations are recovered when using stochastic frequencies.

### Inspection of structures interaction in laminar separation bubbles with extended proper orthogonal decomposition applied to multi-plane particle image velocimetry data

This work reports the application of an extended proper orthogonal decomposition (E-POD) procedure to multi-plane particle image velocimetry (PIV) measurements describing the evolution of laminar separation bubbles (LSBs). Measurements were performed over a flat plate installed between adjustable end-walls providing a prescribed adverse pressure gradient for two Reynolds numbers (Re = 70 000, 150 000) and free-stream turbulence intensity levels (Tu = 1.5%, 2.5%). A wall-normal and two wall-parallel measuring planes located at different distance from the wall were considered. POD was applied to the entire PIV planes as well as on their sub-domains, showing the main flow features occurring in the different regions of the LSB. Then, the application of E-POD on different plane partitions revealed the existing correlation between the main dynamics observed in the forward part of the bubble and the breakup events occurring in the reattachment region. The E-POD modes computed in the breakup region resemble streaky structures when PIV snapshots are projected onto the POD eigenvectors of the near wall plane. Otherwise, Kelvin–Helmholtz rolls dominate the E-POD modes obtained by projection of the snapshot matrices on the basis computed in the plane located far from the wall. The main scales of the coherent structures highlighted by the E-POD modes were also characterized by means of the streamwise and spanwise autocorrelation functions of E-POD filtered fields. Data in this work clearly highlight the similarity properties of the main flow features observed in LSBs once scaled with the momentum thickness of the boundary layer at the separation position.

### Can Minkowski tensors of a simply connected porous microstructure characterize its permeability?

We show that the permeability of periodic simply connected porous media can be reliably predicted from the Minkowski tensors (MTs) describing the pore microstructure geometry. To this end, we consider a large number of two-dimensional simulations of flow through periodic unit cells containing complex-shaped obstacles. The prediction is achieved by training a deep neural network using the simulation data with the MT elements as attributes. The obtained predictions allow for the conclusion that MTs of the pore microstructure contain sufficient information to characterize the permeability, although the functional relation between the MTs and the permeability could be complex to determine.

### Physics-informed neural networks for rarefied-gas dynamics: Thermal creep flow in the Bhatnagar–Gross–Krook approximation

This work aims at accurately solve a thermal creep flow in a plane channel problem, as a class of rarefied-gas dynamics problems, using Physics-Informed Neural Networks (PINNs). We develop a particular PINN framework where the solution of the problem is represented by the Constrained Expressions (CE) prescribed by the recently introduced Theory of Functional Connections (TFC). CEs are represented by a sum of a free-function and a functional (e.g., function of functions) that analytically satisfies the problem constraints regardless to the choice of the free-function. The latter is represented by a shallow Neural Network (NN). Here, the resulting PINN-TFC approach is employed to solve the Boltzmann equation in the Bhatnagar–Gross–Krook approximation modeling the Thermal Creep Flow in a plane channel. We test three different types of shallow NNs, i.e., standard shallow NN, Chebyshev NN (ChNN), and Legendre NN (LeNN). For all the three cases the unknown solutions are computed via the extreme learning machine algorithm. We show that with all these networks we can achieve accurate solutions with a fast training time. In particular, with ChNN and LeNN we are able to match all the available benchmarks.

### Competing effects of inertia, sheet elasticity, fluid compressibility, and viscoelasticity on the synchronization of two actuated sheets

Synchronization of two actuated sheets serves as a simple model for the interaction between flagellated microswimmers. Various factors, including inertia, sheet elasticity, and fluid viscoelasticity, have been suggested to facilitate the synchronization of two sheets; however, the importance of different contributions to this process still remains unclear. We perform a systematic investigation of competing effects of inertia, sheet elasticity, fluid compressibility, and viscoelasticity on the synchronization of two sheets. Characteristic time [math] for the synchronization caused by inertial effects is inversely proportional to sheet Reynolds number Re, such that [math] with ω being the wave frequency. Synchronization toward stable in-phase or opposite-phase configuration of two sheets is determined by the competition of inertial effects, sheet elasticity, fluid compressibility, and viscoelasticity. Interestingly, fluid viscoelasticity results in strong synchronization forces for large beating amplitudes and Deborah numbers De > 1, which dominates over other factors and favors the in-phase configuration. Therefore, our results show that fluid viscoelasticity can dramatically enhance synchronization of microswimmers. Our investigation deciphers the importance of different competing effects for the synchronization of two actuated sheets, leading to a better understanding of interactions between microswimmers and their collective behavior.

### Darcy–Carreau–Yasuda rheological model and onset of inelastic non-Newtonian mixed convection in porous media

An extension of Carreau and Carreau–Yasuda rheological models to porous media is proposed to study the onset of mixed convection of both pseudoplastic fluids (PF) and dilatant fluids (DF) in a porous layer heated from below in the presence of a horizontal throughflow. In comparison with Newtonian fluids, three more dimensionless parameters are introduced, namely, the Darcy–Weissenberg number Wi, the power–law index n, and the Yasuda parameter a. Temporal stability analysis of the basic state showed that in the absence of a throughflow (Wi = 0), the critical Rayleigh number and the critical wavenumber at the onset of convection are the same as for Newtonian fluids, namely, [math] and [math], respectively. When the throughflow is added (Wi > 0), it is found that moving transverse rolls (stationary longitudinal rolls) are the dominant mode of the instability for PF (for DF). Furthermore, depending on Wi, two regimes of instability were identified. In the weakly non-Newtonian regime (i.e., [math]), a destabilizing effect is observed for PF, while the reverse occurs for DF. These effects are more intense by reducing (increasing) the index n for PF (for DF). In this regime, a significant qualitative difference is found between the Darcy–Carreau model and the power–law model. However, in the strongly non-Newtonian regime, the two models lead to similar results. A mechanical energy budget analysis is performed to understand the physical effects of the interaction between the basic throughflow and the disturbances. It is also shown that the intrinsic macroscale properties of the porous medium may play a key role in the stabilizing/destabilizing effect. Finally, a comparison is made between the present theoretical predictions and recent mixed convection experiments in a Hele–Shaw cell.

### Editorial: On Transition (in <i>Physical Review Fluids</i> leadership)

Author(s): Beverley McKeon and Eric Lauga

[Phys. Rev. Fluids 6, 040001] Published Wed Apr 21, 2021

### Dynamics of polarizable spheroid in a shear flow subjected to a parallel magnetic field

Author(s): V. Kumaran

The orientation vector of a spheroid in a viscous shear flow rotates in closed Jeffrey orbits on a unit sphere. If the spheroid is polarizable and it is subjected to a magnetic field, the particle tends to align along the field. The transition between static and rotating states of a polarizable spheroid in a magnetic field subjected to shear flow is analyzed, and the phase boundaries and nature of the bifurcations are identified.

[Phys. Rev. Fluids 6, 043702] Published Wed Apr 21, 2021

### Water entry dynamics of spheres with heterogeneous wetting properties

Author(s): Daren A. Watson, Joshua M. Bom, Madison P. Weinberg, Christopher J. Souchik, and Andrew K. Dickerson

Water entry studies traditionally employ homogeneous projectiles of varying impactor shape, entry speed, and surface roughness. Surface heterogeneity is yet another means to manipulate splash dynamics. In this experimental study, we systematically investigate the water entry of smooth, free-falling, hemispherically-coated spheres for Froude numbers in the range of 2.8-6.7. Half-hydrophobic, half-hydrophilic spheres released in various orientations produce deep seal cavities, and provoke orientation dependent super-surface splash features and sphere dynamics.

[Phys. Rev. Fluids 6, 044003] Published Wed Apr 21, 2021

### Electrocatalytic reaction-driven flow

Author(s): Abimbola A. Ashaju, Jeffery A. Wood, and Rob G. H. Lammertink

Bimetallic Pt-Au nanorods in the form of microswimmers within an aqueous solution exhibit self-propulsion that is powered by self-electrophoresis. This bimetallic Pt-Au system can be immobilized to generate convective fluid flow, thereby acting as a micropump. Here we use a combined experimental and numerical approach to investigate the key elements, including the self-induced electric field, the proton gradients, and the reaction kinetics, that impact the chemomechanical actuation of the Pt-Au electrocatalytic system. Our findings contribute towards the fundamental understanding of fluid flow powered by an electrocatalytic micropump that applies to mass transport enhancement in systems.

[Phys. Rev. Fluids 6, 044004] Published Wed Apr 21, 2021

### Sedimentation of inertial monodisperse suspensions of cubes and spheres

Author(s): Arman Seyed-Ahmadi and Anthony Wachs

At a density ratio of 2, Galileo numbers of 70 and 160, and volume fractions in the range of 0.01 to 0.2, the pronounced angular velocities of cubes and the resulting orientation- and rotation-induced lift forces significantly promote transverse motions and the likelihood of escaping from clusters. Consequently, cube suspensions are found to be structurally more homogeneous than sphere suspensions, in addition to being more isotropic in terms of their momentum transfer properties.

[Phys. Rev. Fluids 6, 044306] Published Wed Apr 21, 2021

### Extensional viscosity and thinning of a fiber suspension thread

Author(s): Joris Château, Élisabeth Guazzelli, and Henri Lhuissier

Adding fibers to a liquid thread increases the viscosity, hence slows the early stretching of the thread, but it also alters the later breakup dynamics and induces a considerable variability in the thread necking shapes.

[Phys. Rev. Fluids 6, 044307] Published Wed Apr 21, 2021

### Physics of superfluid helium-4 vortex tangles in normal-fluid strain fields

Author(s): Demosthenes Kivotides and Anthony Leonard

Although normal-fluid vorticity tends to induce homogeneous, chaotic, quantum-vortex tangles, normal-fluid strain generates structured superfluid vorticity. In extensional flows, the latter is organized into vortex-sheet structures with hyperboloid geometry and fractal-like configurations.

[Phys. Rev. Fluids 6, 044702] Published Wed Apr 21, 2021

### Interfacial waves modulated by linear shear flow of the upper layer in a two-layer fluid with arbitrary layer depths

Both surface and internal freak waves can be regarded as special interfacial waves. Using a two-layer model, we investigated the influence of linear shear flow (LSF) in the upper layer on interfacial waves. Specially, the model was designed to study the effects of wind shear on surface freak waves and LSF on internal freak waves. Based on the model, a nonlinear Schrödinger equation was derived to describe interfacial-wave evolution. The unstable regions where interfacial freak waves occur were identified via analysis of modulational instability. According to these unstable regions, the elevation of interfacial freak waves was studied using the Peregrine Breather solution. It is found that the steepnesses and heights of surface freak waves decrease under positive vorticity and increase under negative vorticity during supercritical up-flow. In contrast, they increase under positive vorticity and decrease under negative vorticity during supercritical down-flow. The reason is that negative vorticity which has a convergent effect on the waves is easy to excite surface freak waves under supercritical up-flow, whereas positive vorticity has a convergent effect under supercritical down-flow. In addition, the steepnesses and heights of internal freak waves decrease under positive vorticity and uniform down-flow, whereas increase under negative vorticity and uniform up-flow. The convergent effect of negative vorticity and uniform up-flow promote the generation of internal freak waves.

### A study of Darcy–Bénard regular and chaotic convection using a new local thermal non-equilibrium formulation

The onset of Darcy–Bénard regular and chaotic convection in a porous medium is studied by considering phase-lag effects that naturally arise in the thermal non-equilibrium heat transfer problem between the fluid and solid phases. A new type of heat equation is derived for both the phases. Using a double Fourier series and a novel decomposition, an extended Vadasz–Lorenz model with three phase-lag effects is derived. New parameters arise due to the phase-lag effects between local acceleration, convective acceleration, and thermal diffusion. The principle of exchange of stabilities is found to be valid and the subcritical instability is discounted. The new perspective supports the finding of an analytical expression for the critical Darcy–Rayleigh numbers representing, respectively, the onset of regular and chaotic convection. The understanding of the transition from the local thermal non-equilibrium situation to the local thermal equilibrium one is also best explained through the new perspective. In its present elegant form, the extended Vadasz–Lorenz system with three phase-lag effects is analyzed using the largest Lyapunov exponent and the bifurcation diagram. It is found that the lag effects not only give rise to a quantitative difference in the above two metrics concerning chaos, but also present a qualitative difference as well in the form of the very nature of chaos.

### Propagation of one-dimensional planar and nonplanar shock waves in nonideal radiating gas

The present study seeks to investigate a quasilinear hyperbolic system of partial differential equations which describes the unsteady one-dimensional motion of a shock wave of arbitrary strength propagating through a nonideal radiating gas. We have derived an infinite hierarchy of the transport equation which is based on the kinematics of one-dimensional motion of shock front. By using the truncation approximation method, an infinite hierarchy of transport equations, which governs the shock strength and the induced discontinuities behind it, is derived to study the kinematics of the shock front. The first three transport equations (i.e., first, second, and third-orders) are used to study the growth and decay behavior of shocks in van der Waals radiating gas. The decay laws for weak shock waves in nonradiating gas are entirely recovered in the second-order truncation approximation. The results obtained by the first three approximations for shock waves of arbitrary strength are compared with the results predicted by the characteristic rule. Also, the effect of nonideal parameters and radiation on the evolutionary behavior of shock waves are discussed and depicted pictorially.

### Global order parameters for particle distributions on the sphere

Topology and geometry of a sphere create constraints for particles that lie on its surface, which they otherwise do not experience in Euclidean space. Notably, the number of particles and the size of the system can be varied separately, requiring a careful treatment of systems with one or several characteristic length scales. All this can make it difficult to precisely determine whether a particular system is in a disordered, fluid-like, or crystal-like state. Here, we show how order transitions in systems of particles interacting on the surface of a sphere can be detected by changes in two hyperuniformity parameters, derived from a spherical structure factor and cap number variance. We demonstrate their use on two different systems—solutions of the thermal Thomson problem and particles interacting via an ultra-soft potential of the generalized exponential model of order 4—each with a distinct parameter regulating their degree of ordering. The hyperuniformity parameters are able to not only detect the order transitions in both systems but also point out the clear differences in the ordered distributions in each due to the nature of the interaction leading to them. Our study shows that hyperuniformity analysis of particle distributions on the sphere provides a powerful insight into fluid- and crystal-like orders on the sphere.

### Investigation of thermocapillary migration of nanodroplets using molecular dynamics

Molecular dynamics is used to investigate the thermocapillary motion of a water nanodroplet suspended in benzene subjected to a constant temperature gradient. This framework lets us identify the average behavior of the fluid particles by revealing their mean evolution. We connect such statistics to the behavior of the temporally evolving nanodroplet, thereby providing a microphysical foundation to existing macroscopic models that rely on the assumption of continuum. It is shown that, despite the significant Brownian effects, the droplet exhibits the macrophysical expected behavior, i.e., it migrates toward the direction of the imposed temperature gradient. Thermophoretic effects are negligible and the functional relationships involved in such a process well resemble those of available analytical results. Additionally, we provide molecular dynamics calculations of the viscosity, thermal conductivity, and interfacial tension of benzene [using the Optimized Potentials for Liquid Simulations—All Atom (OPLSAA) molecular model] and water using the Transferable Intermolecular Potential with 4 Points (TIP4P) model at different temperatures and pressures. These findings will serve as a good reference for future simulations of similar molecular models.

### Effect of vortex and entropy sources in sound generation for compressible cavity flow

The present study reports the effect of different source terms on the near and far-field acoustic characteristics of compressible flow over a rectangular cavity using hybrid computational aeroacoustics methodology. We use a low dispersive and dissipative compressible fluid flow solver in conjunction with an acoustic perturbation equation solver based on the spectral/hp element method. The hybrid approach involves calculating the base fields and the acoustic sources from a fluid simulation in the first step. In the next step, the acoustic solver utilizes the variables to predict the acoustic propagation due to the given sources. The validation of the methodology against benchmark cases provides quite accurate results while compared against the existing literature. The study is then extended to assess the importance of the entropy source term for the flow over a rectangular cavity. The predictions of hybrid simulations with vortex and entropy source terms reproduce the perturbation pressure values very close to the existing direct numerical simulation results. Moreover, the results suggest that the use of just the vortex source terms over-predicts the perturbation pressure near the source region. Finally, we have carried out detailed simulations with all the source terms to investigate the noise sources for compressible flow over the cavity for different Mach number ranges ([math]). The obtained acoustic spectra and the sound directivity are in close agreement with the reference experiment.

### Research on hydrodynamics of high velocity regions in a water-jet pump based on experimental and numerical calculations at different cavitation conditions

Cavitation is a common phenomenon and continues to be a primary concern in the fields of hydraulic machinery. To provide a reference for cavitation flow and cavitation performance improvement, this paper presents the experimental study on the cavitation flow structures of the water-jet pump. High-speed photography technology is used to capture the cavitation flow structures and reveal the physical process of cavitation evolution in the water-jet pump. Cavitation–vortex interaction was further explored by numerical simulations. By extracting 24 m/s water velocity isosurface and analyzing the water superficial velocity on the isosurface, the flow characteristics in the high-velocity fluid area under different cavitation stages are revealed. Then, by analyzing the vortex structure on the isosurface, the main factors affecting the development of the vortex structure on the high-velocity fluid area are summarized.