# Latest papers in fluid mechanics

### Editorial: The 2020 François Naftali Frenkiel Award for Fluid Mechanics

Author(s): John Kim and Gary Leal

[Phys. Rev. Fluids 6, 010001] Published Thu Jan 21, 2021

### A primitive variable discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

A conservative primitive variable discrete exterior calculus (DEC) discretization of the Navier–Stokes equations is performed. An existing DEC method [M. S. Mohamed, A. N. Hirani, and R. Samtaney, “Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes,” J. Comput. Phys. 312, 175–191 (2016)] is modified to this end and is extended to include the energy-preserving time integration and the Coriolis force to enhance its applicability to investigate the late-time behavior of flows on rotating surfaces, i.e., that of the planetary flows. The simulation experiments show second order accuracy of the scheme for the structured-triangular meshes and first order accuracy for the otherwise unstructured meshes. The method exhibits a second order kinetic energy relative error convergence rate with mesh size for inviscid flows. The test case of flow on a rotating sphere demonstrates that the method preserves the stationary state and conserves the inviscid invariants over an extended period of time.

### Tear-film breakup: The role of membrane-associated mucin polymers

Author(s): Anjishnu Choudhury, Mohar Dey, Harish N. Dixit, and James J. Feng

Mucin polymers in the tear film protect the corneal surface from pathogens and modulate the tear-film flow characteristics. Recent studies have suggested a relationship between the loss of membrane-associated mucins and premature rupture of the tear film in various eye diseases. This work aims to el...

[Phys. Rev. E 103, 013108] Published Wed Jan 20, 2021

### Hydrodynamic interactions between swimming microorganisms in a linearly density stratified fluid

Author(s): Rishabh V. More and Arezoo M. Ardekani

Oceans and lakes sustain intense biological activity due to the motion of marine organisms, which has significant ecological and environmental impacts. The motion of individual organisms and their interactions with each other play a significant role in the collective motion of swimming organisms. Ho...

[Phys. Rev. E 103, 013109] Published Wed Jan 20, 2021

### Rebound of large jets from superhydrophobic surfaces in low gravity

Author(s): Karl Cardin, Sheng Wang, Olivier Desjardins, and Mark Weislogel

The rebound of large water jets from a superhydrophobic substrate in the low-gravity environment of a drop tower is investigated. A regime map is constructed from drop tower test data. Scaling laws and simulations are used to identify boundaries between jet rebound regimes and to predict landing flow geometry.

[Phys. Rev. Fluids 6, 014003] Published Wed Jan 20, 2021

### Film coating by directional droplet spreading on fibers

Author(s): Tak Shing Chan, Carmen L. Lee, Christian Pedersen, Kari Dalnoki-Veress, and Andreas Carlson

Plants and insects use slender conical structures to transport and collect small droplets that are propelled along conical structures by capillary action. It is shown that these droplets can deposit a film with a thickness that depends on the fiber’s radius and the droplet size, highlighting that the coating is affected by finite size effects relevant to film deposition on fibers of any slender geometry. These self-propelled droplets have significant potential to create passively coated structures.

[Phys. Rev. Fluids 6, 014004] Published Wed Jan 20, 2021

### Molecular viscosity and diffusivity effects in transitional and shock-driven mixing flows

Author(s): F. S. Pereira, F. F. Grinstein, D. M. Israel, and R. Rauenzahn

This paper investigates the importance of molecular viscosity and diffusivity for the prediction of transitional and shock-driven mixing flows featuring high and low Reynolds and Mach number regions. Two representative problems are computed with implicit large-eddy simulations using the inviscid Eul...

[Phys. Rev. E 103, 013106] Published Tue Jan 19, 2021

### Compressibility effects in turbulent transport of the temperature field

Author(s): I. Rogachevskii and N. Kleeorin

Compressibility effects in a turbulent transport of temperature field are investigated by applying the quasilinear approach for small Péclet numbers and the spectral τ approach for large Péclet numbers. The compressibility of a fluid flow reduces the turbulent diffusivity of the mean temperature fie...

[Phys. Rev. E 103, 013107] Published Tue Jan 19, 2021

### Sound of effervescence

Author(s): Mathis Poujol, Régis Wunenburger, François Ollivier, Arnaud Antkowiak, and Juliette Pierre

An experimental study focuses on the airborne sound generated during bubble bursting at the surface of a liquid bath. It is found that the acoustic frequency drifts and increases, consistent with a Helmholtz-type resonance of the cavity being more and more opened as the thin film in the air retracts. As an extension, a simple model based on a collection of drifting Helmholtz resonators is proposed, capturing the main features of the fizzing sound of an effervescing beverage.

[Phys. Rev. Fluids 6, 013604] Published Tue Jan 19, 2021

### Theoretical framework for energy flux analysis of channels under drag control

Author(s): Xi Chen, Jie Yao, and Fazle Hussain

A new framework analyzes energy flux in turbulent channels under various controls, enabling estimations of drag reduction and net power saving, and also suggesting a perspective of composite control for future exploration.

[Phys. Rev. Fluids 6, 013902] Published Tue Jan 19, 2021

### Origin of hydrodynamic instability from noise: From laboratory flow to accretion disk

Author(s): Subham Ghosh and Banibrata Mukhopadhyay

The problem of the origin of turbulence, and hence, transport of angular momentum, in accretion flows (particularly cold flows) as well as laboratory flows like plane Couette flow, prevails due to their stability under linear perturbation. We attempt to resolve this long-standing issue with linear analysis by considering an extra stochastic force with a nonzero mean (m). We show that these flows become unstable, and the corresponding maximum growth rate (Im(β)max) increases, if the mean is increased, with other parameters fixed. Since accretion flow has a central sink a fluid parcel must take less time to become nonlinear than to cross the local analysis region, consistent with our analysis.

[Phys. Rev. Fluids 6, 013903] Published Tue Jan 19, 2021

### Pattern selection in oscillatory longwave Marangoni convection with nonlinear temperature dependence of surface tension

Author(s): Alexander B. Mikishev and Alexander A. Nepomnyashchy

Pattern selection in oscillatory long-wave Marangoni convection in a heated thin layer of liquid with weak heat flux from the free surface is investigated. The research is performed under the assumption that the surface tension of the liquid nonlinearly depends on the temperature. The pattern selection is analyzed for square, rhombic, and hexagonal planforms.

[Phys. Rev. Fluids 6, 014002] Published Tue Jan 19, 2021

### Triple-deck analysis of the steady flow over a rotating disk with surface roughness

Author(s): Claudio Chicchiero, Antonio Segalini, and Simone Camarri

A theory based on a triple-deck approach is developed to rapidly assess the velocity field over a rotating disk with surface roughness. The theory results are validated with numerical simulations and suggest new ways to incorporate roughness in flow calculations.

[Phys. Rev. Fluids 6, 014103] Published Tue Jan 19, 2021

### Application of the Gram–Schmidt factorization of the deformation gradient to a cone and plate rheometer

In this paper, we study the cone and plate rheometer using the Gram–Schmidt factorization of the deformation gradient. This new solution has several advantages over the traditional approach. It is shown that with the use of these kinematics, one can avoid the need for using a convected, curvilinear, coordinate system, which often leads to cumbersome calculations. Here, the use of a convected coordinate system has been replaced with a certain orthonormal coordinate system that arises from the Gram–Schmidt factorization of the deformation gradient. Moreover, by using this solution procedure, it is possible to obtain the normal stress differences and shear stress explicitly. Therefore, this solution procedure opens up a possibility for characterizing material properties by using only a cone and plate rheometer.

### Instability of a tangential discontinuity surface in a three-dimensional compressible medium

Compressible flows appear in many natural and technological processes, for instance, the flow of natural gases in a pipe system. Thus, a detailed study of the stability of tangential velocity discontinuity in compressible media is relevant and necessary. The first early investigation in two-dimensional (2D) media was given more than 70 years ago. In this article, we continue investigating the stability in three-dimensional (3D) media. The idealized statement of this problem in an infinite spatial space was studied by Syrovatskii in 1954. However, the omission of the absolute sign of cos θ with θ being the angle between vectors of velocity and wave number in a certain inequality produced the inaccurate conclusion that the flow is always unstable for entire values of the Mach number M. First, we revisit this case to arrive at the correct conclusion, namely that the discontinuity surface is stabilized for a large Mach number with a given value of the angle θ. Next, we introduce a real finite spatial system such that it is bounded by solid walls along the flow direction. We show that the discontinuity surface is stable if and only if the dispersion relation equation has only real roots, with a large value of the Mach number; otherwise, the surface is always unstable. In particular, we show that a smaller critical value of the Mach number is required to make the flow in a narrow channel stable.

### Classification of the major nonlinear regimes of oscillations, oscillation properties, and mechanisms of wave energy dissipation in the nonlinear oscillations of coated and uncoated bubbles

Acoustic waves are dissipated when they pass through bubbly media. Dissipation by bubbles takes place through thermal damping (Td), radiation damping (Rd), and damping due to the friction of the liquid (Ld) and friction of the coating (Cd). Knowledge of the contributions of Td, Rd, Ld, and Cd during nonlinear bubble oscillations will help in optimizing bubble and ultrasound exposure parameters for the relevant applications by maximizing a desirable outcome or oscillation pattern. In this work, we investigate the mechanisms of dissipation in bubble oscillations and their contribution to the total damping (Wtotal) in various nonlinear regimes. By using a bifurcation analysis, we have classified nonlinear dynamics of bubbles that are sonicated with their third superharmonic (SuH) and second SuH resonance frequency (fr), pressure dependent resonance frequency (PDfr), fr, subharmonic (SH) resonance (fsh = 2fr), pressure dependent SH resonance (PDfsh), and 1/3 order SH resonance, which are important exposure ranges for various applications. The corresponding Td, Rd, Ld, Cd, Wtotal, scattering to dissipation ratio, maximum wall velocity, and maximum backscattered pressure from non-destructive oscillations of bubbles were calculated and analyzed using the bifurcation diagrams. Universal ultrasound exposure parameter ranges are revealed in which a particular non-destructive bubble related phenomenon (e.g., wall velocity) is enhanced. The enhanced bubble activity is then linked to relevant ultrasound applications. This paper represents the first comprehensive analysis of the nonlinear oscillations regimes, the corresponding damping mechanisms, and the bubble related phenomena.

### How to deform an egg yolk? On the study of soft matter deformation in a liquid environment

In this paper, we report a novel experimental study to examine the response of a soft capsule bathed in a liquid environment to sudden external impacts. Taking an egg yolk as an example, we found that the soft matter is not sensitive to translational impacts but is very sensitive to rotational, especially decelerating-rotational, impacts, during which the centrifugal force and the shape of the membrane together play a critical role in causing the deformation of the soft object. This finding, as the first study of its kind, reveals the fundamental physics behind the motion and deformation of a membrane-bound soft object, e.g., egg yolk, cells, and soft brain matter, in response to external impacts.

### Studying the flow dynamics and heat transfer of stranded conductor cables using large eddy simulations

Stranded cables are widely used in applications where their heat transfer and fluid dynamics are important, but they have not been extensively studied. This paper investigates, using large eddy simulations with the dynamic Smagorinsky sub-grid scale model, a helically wound stranded conductor cable in comparison to a circular cylinder at a Reynolds number of 1000 and Prandtl number of 0.7. The cylinder and the cable were normal to the flow. The triply decomposed heat transport equations were derived, and proper orthogonal decomposition was applied to the fluctuating vorticity and temperature fields to determine the total, coherent, and incoherent terms in the heat transport equations. The results showed that the stranded cable, relative to circular cylinder, has (i) three-dimensional mean flow and heat transfer, especially within and around recirculation region, (ii) 9% higher drag and 8% higher base pressure magnitude, (iii) near-stagnant flow in the gaps between the strands, which results in a significant variation in the local Nusselt number, (iv) ∼15% lower span-wise averaged local Nusselt number in the attached boundary layer, suggesting that surface modifications should be addressed to enhance heat transfer, (v) ∼36° variation in the separation angle along the span, (vi) 12% higher turbulent kinetic energy and 39% higher spanwise normal Reynolds stresses, (vii) insignificant difference in shedding frequency, suggesting similar flow induced vibrations to the cylinder, (viii) asymmetry in the flow and heat fields around the x axis, (ix) significantly different coherent temperature fields and dynamics, and (x) in general, high heat energy transport close to the cable rear side.

### A modal wave-packet model for the multi-mode Richtmyer–Meshkov instability

A model for multimode perturbations subject to the Richtmyer–Meshkov (RM) instability is presented and compared with simulations and experiments for conditions relevant to inertial confinement fusion. The model utilizes the single mode response to the RM impulse whereby its amplitude h(k, t) first grows with an initial velocity V0 ∝ kh(k, 0) that eventually decays in time as 1/kV0t. Both the growth and saturation stages are subject to nonlinearities since they depend explicitly on the initial amplitude. However, rather than using the individual mode amplitude h(k, t), nonlinearity is taken to occur when the root-mean-square amplitude hrms(k, t) of a wave-packet within wavenumbers k ± δk becomes comparable to 1/k. This is done because nearby sidebands can act in unison for an auto-correlation distance 1/δk beyond nonlinearity as observed in the beam-plasma instability. Thus, the nonlinear saturation amplitude for each mode is reduced from the usual 1/k by a phase space factor that depends on the physical dimensionality, as in the Haan model for the Rayleigh–Taylor instability. In addition, for RM, the average value of khrms for the initial spectrum is used to calculate a nonlinear factor FNL that reduces V0, as observed for single modes. For broadband perturbations, the model describes self-similar growth ∝tθ as successively longer wavelength modes reach saturation. The growing and saturated modes must be discerned because only the former promote θ and are enhanced by reshock and spherical convergence. All of these flows are described here by the model in good agreement with simulations and experiments.

### Impacts of fuel nonequidiffusivity on premixed flame propagation in channels with open ends

The present study scrutinizes premixed flame dynamics in micro-channels, thereby shedding light on advanced miniature micro-combustion technologies. While equidiffusive burning (when the Lewis number Le = 1) is a conventional approach adopted in numerous theoretical studies, real premixed flames are typically non-equidiffusive (Le ≠ 1), which leads to intriguing effects, such as diffusional-thermal instability. An equidiffusive computational study [V. Akkerman et al., Combust. Flame 145, 675–687 (2006)] reported regular oscillations of premixed flames spreading in channels having nonslip walls and open extremes. Here, this investigation is extended to non-equidiffusive combustion in order to systematically study the impact of the Lewis number on the flame in this geometry. The analysis is performed by means of computational simulations of the reacting flow equations with fully-compressible hydrodynamics and one-step Arrhenius chemical kinetics in channels with adiabatic and isothermal walls. In the adiabatic channels, which are the main case of study, it is found that the flames oscillate at low Lewis numbers, with the oscillation frequency decreasing with Le, while for the Le > 1 flames, a tendency to steady flame propagation is observed. The oscillation parameters also depend on the thermal expansion ratio and the channel width, although the impacts are rather quantitative than qualitative. The analysis is subsequently extended to the isothermal channels. It is shown that the role of heat losses to the walls is important and may potentially dominate over that of the Lewis number. At the same time, the impact of Le on burning in the isothermal channels is qualitatively weaker than that in the adiabatic channels.