# Latest papers in fluid mechanics

### Emission modes in electro co-flow

We apply an electric field to a moderately conducting liquid surrounded by another co-flowing liquid, all inside a glass-based microfluidic device, and study and classify the resulting emission modes. The viscosity and flow rate of the co-flowing liquid affect the number of modes observed in classical electrospray as well as their geometrical characteristics. In particular, we observe a two-dimensional whipping mode not described before. We also provide a qualitative description of some of the modes, including dripping, electrodripping, microdripping, the cone-jet mode, and both the two- and three-dimensional whipping modes.

### Multiphase buoyant plumes with soluble drops or bubbles

Author(s): Shigan Chu and Andrea Prosperetti

The loss of buoyancy because of dissolution is mitigated or enhanced by changes in ambient liquid density. A scaling analysis identifies three parameters: dissolution rate vs plume rise time, the effect of dissolved material on liquid density, and the drop or bubble rise velocity vs the plume velocity.

[Phys. Rev. Fluids 4, 084306] Published Thu Aug 29, 2019

### Modulation instability and rogue waves for shear flows with a free surface

Author(s): Q. Pan, R. H. J. Grimshaw, and K. W. Chow

The effect of shear currents on rogue waves on a free surface is modeled by the nonlinear Schrödinger equation. Curvature of velocity profiles (or vorticity gradient) and the relative motion of the wave packet and shear current play critical roles, through enhanced growth rates of disturbances.

[Phys. Rev. Fluids 4, 084803] Published Thu Aug 29, 2019

### Coherent structures in tornado-like vortices

The dynamics of tornadolike vortices is investigated through a set of novel physical experiments and modal analyses for a wide range of swirl ratios (0.22 ≤ S ≤ 0.96). Various physical phenomena such as wandering, vortex breakdown, or transition from one-cell to two-cell structures are observed. To investigate the coherent structure of the tornado vortices, two different decomposition methods are applied: (i) proper orthogonal decomposition (POD), also referred to as principle component analysis, and (ii) a novel dynamic proper orthogonal decomposition to provide time evolutions of the POD modes. To foster the physical interpretation of these POD modes, we also applied modal decomposition on a simulated synthetic vortex. The results show that at low swirl ratios before vortex breakdown, the flow is characterized by a single vortex which is tilted at lower heights. For intermediate swirls, before vortex touchdown, the flow is characterized by a recirculation bubble with a single spiral rotating around it. By further increasing the swirl ratio, transition from a single spiral to a double spiral (one-cell to two-cell structures) occurs. Based on these observations, a simple vortex structure of tornadolike vortex is put forward which can be used to generate a low order, large scale turbulence model for these types of flows.

### Statistics of overpressure fluctuations behind a weak shock wave interacting with turbulence

The overpressure fluctuations behind a weak shock wave interacting with turbulence are studied by wind tunnel experiments, where a spherical shock wave propagates in grid turbulence. The experiments are conducted for various values of the shock Mach number MS0 of the shock wave and turbulent Mach number MT of the grid turbulence. The experimental results show that the root-mean-squared peak-overpressure fluctuation divided by the averaged peak-overpressure, σΔp/⟨Δp⟩, where the inherent noise caused by the experimental facility is removed, follows a power law of [math]. The probability density functions of the overpressure fluctuations are close to the Gaussian profile for a wide range of [math]. A shock deformation model based on the deformation due to nonuniform fluid velocity is proposed for the investigation of the influences of turbulence on the shock wave. The deformation changes the cross-sectional area of the ray tube, which is related to the shock Mach number fluctuation of the area. The model for a weak shock wave yields the relation [math], which agrees well with the experimental results. The model also predicts the Gaussianity of the peak-overpressure fluctuations behind the shock wave interacting with Gaussian velocity fluctuations. Good agreements between the model and experiments imply that the change in the shock wave characteristics by the interaction with turbulence is closely related to the shock wave deformation caused by the fluctuating turbulent velocity field.

### Computing exact coherent states in channels starting from the laminar profile: A resolvent-based approach

Author(s): Kevin Rosenberg and Beverley J. McKeon

We present an iterative method to compute traveling wave exact coherent states (ECS) in Couette and Poiseuille flows starting from an initial laminar profile. The approach utilizes the resolvent operator for a two-dimensional, three-component streamwise-averaged mean and exploits the underlying phys...

[Phys. Rev. E 100, 021101(R)] Published Wed Aug 28, 2019

### Periodic solutions and chaos in the Barkley pipe model on a finite domain

Author(s): K. Y. Short

Barkley's bipartite pipe model is a continuous two-state reaction-diffusion system that models the transition to turbulence in pipes, and reproduces many qualitative features of puffs and slugs, localized turbulent structures seen during the transition. Extensions to the continuous model, including ...

[Phys. Rev. E 100, 023116] Published Wed Aug 28, 2019

### Taylor-vortex flow in shear-thinning fluids

Author(s): S. Topayev, C. Nouar, D. Bernardin, A. Neveu, and S. A. Bahrani

This paper deals with the Taylor-Couette flow of shear-thinning fluids. It focuses on the first principles understanding of the influence of the viscosity stratification and the nonlinear variation of the effective viscosity μ with the shear rate γ̇ on the flow structure in the Taylor-vortex flow re...

[Phys. Rev. E 100, 023117] Published Wed Aug 28, 2019

### Exact solutions for shock waves in dilute gases

Author(s): F. J. Uribe and R. M. Velasco

In 1922 Becker found an exact solution for shock waves in gases using the Navier–Stokes–Fourier constitutive equations for a Prandtl number of value 3/4 with constant transport coefficients. His analysis has been extended to study some cases where an implicit solution can be found in an exact way. I...

[Phys. Rev. E 100, 023118] Published Wed Aug 28, 2019

### Stability analysis of electroconvection with a solid-liquid interface via the lattice Boltzmann method

Author(s): Kang Luo, Jian Wu, Alberto T. Pérez, Hong-Liang Yi, and He-Ping Tan

Electroconvection in dielectric liquid is extended from single phase to solid-liquid interaction. Stability criteria and bifurcation are numerically predicted by the lattice Boltzmann method. Effects of interface position, permittivity and mobility ratios, and electric conductivity are considered.

[Phys. Rev. Fluids 4, 083702] Published Wed Aug 28, 2019

### Effective forcing for direct numerical simulations of the shear layer of turbulent free shear flows

Author(s): Chandru Dhandapani, Kyupaeck Jeff Rah, and Guillaume Blanquart

Shear turbulence is simulated using numerically efficient triply periodic computational domains. The simulations focus on velocity fluctuations and achieve statistically stationary homogeneous shear turbulence. The numerical results agree well with experiments and simulations of free shear flows.

[Phys. Rev. Fluids 4, 084606] Published Wed Aug 28, 2019

### Enstrophy transfers in helical turbulence

Author(s): Shubhadeep Sadhukhan, Roshan Samuel, Franck Plunian, Rodion Stepanov, Ravi Samtaney, and Mahendra Kumar Verma

In fluid turbulence, enstrophy fluxes are associated either with velocity-to-vorticity transfers (vorticity stretching) or with vorticity-to-vorticity transfers (vorticity advection). In the inertial range, the four fluxes due to vorticity stretching are found to be larger than the one due to vorticity advection.

[Phys. Rev. Fluids 4, 084607] Published Wed Aug 28, 2019

### Effect of polymer-coated gold nanoparticle stabilizers on drop coalescence

Polymer-coated gold nanoparticles (PGNPs) can be used as stabilizers in immiscible polymer blends, similar to block-copolymers (BCs). However, the PGNP gold cores increase the magnitude of the disjoining pressure (Π), i.e., the van der Waals interaction for unit area, in the film between the drops, favoring coalescence. This might explain the counterintuitive 70% drainage time (td) reduction for polymeric drops stabilized by PGNPs compared to those stabilized by BCs, as reported in recent flow-induced head-on collision experiments in extensional flow, despite PGNPs being more surface active. Knowledge of the mechanisms determining td is fundamental for designing effective PGNP compatibilizers. Here, we performed a parametric study of those experiments via boundary integral simulations, treating PGNPs as surfactants and utilizing for the first time a disjoining pressure expression which includes the effect of interfacial PGNPs (ΠPGNP). In particular, we varied the PGNP concentration and core size in ΠPGNP, the surface diffusivity (Ds) via the surface Peclet number, and the surface elasticity via the Marangoni number. Flow-induced coalescence was very sensitive to all three parameters. td was reduced up to 60% for touching 3 nm core diameter PGNPs, increasing significantly the coalescence probability for drop sizes <5 µm, but the soft coronas diminished this effect considerably. Thus, other causes, besides the enhanced Π, had to be simultaneously present to explain the dramatic experimental td reduction; the most likely is a Ds higher than its Stokes-Einstein relation estimate and the PGNP ligands being in a dry-brush regime, leading to entropic attraction between the drop interfaces.

### Piston driven converging shock waves in a stiffened gas

The problem of a one-dimensional (1D) cylindrically or spherically symmetric shock wave converging into an inviscid, ideal gas was first investigated by Guderley[Starke kugelige und zylinrische verdichtungsstosse in der nahe des kugelmitterpunktes bzw. Der zylinderachse,” Luftfahrtforschung 19, 302 (1942)]. In the time since, many authors have discussed the practical notion of how Guderley-like flows might be generated. One candidate is a constant velocity, converging “cylindrical or spherical piston,” giving rise to a converging shock wave in the spirit of its classical, planar counterpart. A limitation of pre-existing analyses along these lines is the restriction to flows in materials described by an ideal gas equation of state (EOS) constitutive law. This choice is of course necessary for the direct comparison with the classical Guderley solution, which also features an ideal gas EOS. However, the ideal gas EOS is limited in its utility in describing a wide variety of physical phenomena and, in particular, the shock compression of solid materials. This work is thus intended to provide an extension of previous work to a nonideal EOS. The stiff gas EOS is chosen as a logical starting point due to not only its close resemblance to the ideal gas law but also its relevance to the shock compression of various liquid and solid materials. Using this choice of EOS, the solution of a 1D planar piston problem is constructed and subsequently used as the lowest order term in a quasi-self-similar series expansion intended to capture both curvilinear and nonideal EOS effects. The solution associated with this procedure provides correction terms to the 1D planar solution so that the expected accelerating shock trajectory and nontrivially varying state variable profiles can be obtained. This solution is further examined in the limit as the converging shock wave approaches the 1D curvilinear origin. Given the stiff gas EOS is not otherwise expected to admit a Guderley-like solution when coupled to the inviscid Euler equations, this work thus provides the semianalytical limiting behavior of a flow that cannot be otherwise captured using self-similar analysis.

### Multiscale investigation of Kolmogorov flow: From microscopic molecular motions to macroscopic coherent structures

It is extremely expensive to study turbulence using conventional molecular simulation methods such as direct simulation Monte Carlo and molecular dynamics methods, as the molecular scales and the turbulent characteristic scales are significantly separated. To bridge this gap, we employ a particle Fokker-Planck method, namely, the Langevin dynamics simulation method, to study two-dimensional Kolmogorov flow, which is induced by a spatially periodic external force in an unbounded domain. Our simulation results predict that when the Reynolds number (Re) exceeds the critical value, a sequence of bifurcations takes place in the flow as the Reynolds number increases, forming a variety of flow patterns. Correspondingly, the effective diffusion coefficient is enhanced due to convection. Two main regimes of the flow have been observed: the small-scale cellular structure regime (Rec < Re < 8Rec), and the large-scale coherent structure regime (Re > 8Rec). We demonstrate that Langevin dynamics can capture the double kinetic-energy cascade when the large-scale structure is formed in two-dimensional turbulence: the inverse energy cascade has a scaling law of k−4 due to energy condensation in the large-scale structures, while the direct energy cascade has an exponential decay corresponding to the dissipation mechanism. This work provides strong evidence that Langevin dynamics is a promising multiscale tool to study turbulence from molecular motions to large-scale coherent structures.

### Haines jumps: Pore scale mechanisms

Author(s): Zhonghao Sun and J. Carlos Santamarina

Sudden changes in pressure and fluid distribution are often observed in porous systems, and this work proposes and tests a physical model to explain this phenomenon. The analysis enables the authors to predict effects of various factors on the occurrence of such jumps, which are termed Haines instabilities.

[Phys. Rev. E 100, 023115] Published Tue Aug 27, 2019

### Particle tracking velocimetry applied to thermal counterflow in superfluid $^{4}\mathrm{He}$: Motion of the normal fluid at small heat fluxes

Author(s): B. Mastracci, S. Bao, W. Guo, and W. F. Vinen

Thermal counterflow of normal and superfluid components in superfluid helium leads to a form of turbulence confined to the superfluid component. Contrary to usual assumptions, these vortex filaments are shown to induce a strongly nonuniform flow in the normal fluid, even at small flow velocities.

[Phys. Rev. Fluids 4, 083305] Published Tue Aug 27, 2019

### Magnetic eddy viscosity of mean shear flows in two-dimensional magnetohydrodynamics

Author(s): Jeffrey B. Parker and Navid C. Constantinou

At large magnetic Reynolds numbers, magnetic induction leads to enhanced viscosity of mean shear flows. This effect is derived through simple physical arguments and verified in numerical simulations.

[Phys. Rev. Fluids 4, 083701] Published Tue Aug 27, 2019

### Method of regularized stokeslets: Flow analysis and improvement of convergence

Author(s): Boan Zhao, Eric Lauga, and Lyndon Koens

The Stokes flow created by regularized stokeslets (point forces) is analyzed. The authors determine the error made in the approximation compared to the singular solution, show how a source dipole appears generically in the far field, and propose an improved regularized solution.

[Phys. Rev. Fluids 4, 084104] Published Tue Aug 27, 2019

### Anisotropic energy transfers in rapidly rotating turbulence

We perform direct numerical simulations and analyze the ring-to-ring energy transfer in the three-dimensional hydrodynamic turbulence rendered anisotropic by rapid rotation. The rotation rate is taken to be so high that the Zeman scale is well beyond the Kolmogorov dissipation scale. Our main result is that, while the anisotropic transfer of energy is equatorward in the case of the decaying rotating turbulence, in the case of the forced rotating turbulence, the transfer is equatorward only for the scales larger than the forcing scale and poleward for the smaller scales. We also discuss in detail how our results are at odds with the corresponding results for the analogous magnetohydrodynamic turbulence.