# Latest papers in fluid mechanics

### Universality and scaling in homogeneous compressible turbulence

Author(s): Diego A. Donzis and John Panickacheril John

Universality concepts have played a pivotal role in the development of complex systems. This has not been the case in compressible turbulence as no unifying set of parameters has been found to yield universal scaling laws. An analysis supported with DNS databases and studies across the literature shows how universality can indeed be achieved in homogeneous compressible turbulence from specific limiting behavior, paving the way toward a more unified fundamental understanding of compressible turbulence and development of robust compressible turbulence models.

[Phys. Rev. Fluids 5, 084609] Published Mon Aug 24, 2020

### Transitions between turbulent states in a two-dimensional shear flow

Author(s): Vassilios Dallas, Kannabiran Seshasayanan, and Stephan Fauve

The bifurcations of large-scale jets in a turbulent shear flow driven by a Kolmogorov forcing are studied. These bifurcations, seen also in the mean velocity profile of the forced-dissipative system, are then reproduced using a system at equilibrium, namely, the truncated Euler equations. Statistical properties of the large-scale mode exhibit 1/f noise and are in qualitative agreement in both systems.

[Phys. Rev. Fluids 5, 084610] Published Mon Aug 24, 2020

### On coherent structures of spatially oscillating planar liquid jet developing in a quiescent atmosphere

The momentum transport and entrainment of a developing plane jet are dominated by coherent structures. Percipience about the formation, evolution, and interaction of these coherent structures for oscillating planar jets remains unclear. In the present study, numerical investigations are reported for analyzing spatially oscillating planar jets by solving Navier–Stokes equations coupled with the volume of fluid method to track the air–water interface. Coherent structures in the flow for Reynolds numbers (Re) 4500 and 500 are identified using Q-criterion. It is demonstrated that for oscillating jets, the spread and entrainment increase with an increase in Re. These jet characteristics are greatly influenced by the head vortices, which transform into a pair of hairpin vortices, which further undergo leapfrogging. This jet front dynamics is found to be dampened by viscous forces. The numerical results also suggest the existence of sideways hairpin vortices that expel the fluid by forming a channel and are significantly subdued at low Re. A peculiar merging of span-wise Kelvin–Helmholtz rollers at low Re is also reported in the present study. Furthermore, the dominant flow structures are identified and analyzed using proper orthogonal decomposition and dynamic mode decomposition. The results demonstrate the dominance of coherent structures at the downstream for higher Re with vortices in the near field at the jet peaks also contributing to the flow field dynamics.

### Linearized lattice Boltzmann Method for time periodic electro-osmotic flows in micro- and nanochannels

Time periodic electro-osmosis (TPEO) is a popular means to pump liquids or manipulate species of interest in today’s micro- and nanofluidic devices. In this article, we propose a double distribution-function lattice Boltzmann (LB) model to describe its oscillatory flows coupled with electrokinetics in micro- and nanochannels. To remove advective effects, we derive the LB model from a linearized Boltzmann Bhatnagar–Gross–Krook-like equation and formulate its equations depending on the alternating current (AC) frequency, instead of time. This treatment facilitates a direct comparison of the LB results to experimental measurements in practical applications. We assessed accuracy of the proposed frequency-based Linearized LB model by simulating time periodic electro-osmotic flows (TPEOFs) with a thin and a thick electric double layer (EDL) at different Stokes parameters. The results are in excellent agreement with analytical solutions. The model was used to simulate TPEOFs with various EDL thicknesses and those driven by an AC electric field combined with an oscillatory pressure gradient. The simulations show distinct distributions of the electric potential and solution velocity subject to different length ratios and frequency ratios in the flows and interesting flow responses to compounding influences of the applied electric and mechanical driving fields. Importantly, diverse vortex patterns and vorticity variations were also revealed for TPEOFs in heterogeneously charged channels. These results demonstrate that the LB model developed in this article can well capture rich TPEO flow characteristics in micro- and nanochannels. It is effective for design and optimization of TPEO-based micro- and nanofluidic devices.

### Flow-structure interactions of two tandem inverted flags in a water tunnel

The dynamic behaviors and vortex interaction modes of two tandem inverted flags at different gap distances and flow velocities are investigated experimentally in this paper. The results show that the straight, flapping, and deflected modes can still be observed with a successive increase in the flow velocity. The fixed-phase, different-frequency, changing-phase, alternating-phase, and aperiodic flapping modes are further found in the flapping mode. Considering the fixed phase difference and predominance of the fixed-phase mode, we mainly focus on this mode. The amplitude of the front flag is almost similar to that of an isolated flag due to the unaffected leading-edge vortex when they are both in the flapping mode, while it is smaller for the rear flag, indicating the great significance of the rear flag amplitude for studying the dynamic behaviors of two tandem inverted flags. First, the relation between the amplitude of the rear flag and the phase difference contains two linear segments with almost the same slope and a constant segment, fully demonstrating their strong correlation rather than the irrelevance. Second, the rear flag and the trailing-edge vortex (TEV) of the front flag are found to interact via the strong and weak interaction modes. Only in the strong interaction mode can the rear flag extract energy from the TEV of the front flag at lower critical flow velocity, resulting in a larger amplitude than that of the front flag. In general, a small gap distance is more conducive to energy harvesting at low flow velocity, while a large gap distance is more beneficial at high flow velocity.

### Stress growth shearfree flow from the Oldroyd 8-constant framework

Sudden inception of shearfree flows (also called stress growth in extension) is an extremely useful set of rheological measurement techniques for bringing out fluid nonlinearities. The previous predictions of these departures from linearity employed molecular simulation or finite difference solutions. In this work, we deepen our understanding of the physics of these departures by uncovering the exact solutions to a large and diverse framework of constitutive equations: the Oldroyd 8-constant framework. Specifically, we derive the exact analytical solutions for the first and second elongational viscosities in shearfree flow from the Oldroyd 8-constant framework including (I) uniaxial elongational flow, (II) biaxial stretching flow, and (III) planar elongational flow. We close our work with a worked example on analyzing a highly branched system.

### Thermohydraulic performance of a novel curved serpentine coil

Conventional coil designs, such as helical and flat serpentine (FS) coils, are commonly employed for heat transfer applications due to their higher heat transfer performance and compactness. In the last few decades, chaotic coil designs have attracted the attention of a few researchers due to their superior thermohydraulic performance. In this paper, we present a novel and simple chaotic coil design termed the curved serpentine (CS-θ) coil, which is a modified version of the conventional FS coil. The straight tubes of length L in the FS coil are bent as arcs of radius R1 and subtended angle θ (i.e., L = R1 × θ), which are interconnected with U-bends of radius R2. The laminar flow of water through the CS-θ coil is numerically investigated, and the peaks and valleys in the local Nusselt number and friction factor at various axial locations are explained with the help of velocity and temperature contours and secondary flow patterns. The chaotic nature of flow through these coils is explained with the help of streamlines and transverse flow vectors, transversal intersection of the trajectories, and the Lyapunov spectrum. The thermohydraulic performance (η) of this coil is found superior to conventional FS and helical coils. It is found that the CS-θ coils, in which the flow is fully developed just before entering the U-bend, can achieve the best thermohydraulic performance. We also propose generalized correlations for predicting the average Nusselt number and friction factor in the CS-θ coils with a maximum deviation of ±10% and ±7.5%, respectively.

### Quantification of convective and diffusive transport during CO2 dissolution in oil: A numerical and analytical study

In this study, we use an analytical approach and the interpolation-supplemented lattice Boltzmann method (ISLBM) to quantify convective and diffusive transport during CO2 dissolution. In the first step, we use a turbulence analogy and the ISLBM to determine the relationship between the Rayleigh number (Ra) and the ratio of the pseudo-diffusion coefficient to the molecular diffusion coefficient [math]. We then use experimental data from two oil samples, condensate and crude oils, to validate the obtained relationship between [math] and Ra. We also use the Sherwood number (Sh) and total mixing and diffusive transport curves to analyze different periods during CO2 dissolution for condensate and crude oils. We focus, in particular, on how Ra affects the characteristics of density-driven fingers and the convection field. Our results show that there is a logarithmic trend between [math] and Ra. Analysis of the total mixing and diffusive curves indicates that the CO2 dissolution process can be divided into three distinct periods, namely, diffusive transport, early convection, and late convection. We find that more than 50% of the ultimate CO2 dissolution occurs in the early convection period. We also show that the analytical results obtained for the critical time and critical depth at the onset of convection is in good agreement with those of the ISLBM. After the onset of convection, the formation of initial fingers leads to enhanced convective transport, with marked implications for the concentration variance and mixing rate.

### Turbulence, pseudo-turbulence, and local flow topology in dispersed bubbly flow

Bubbly turbulent flow in a channel is investigated using interface-resolved direct numerical simulation. An efficient coupled level-set volume-of-fluid solver based on a fast Fourier transform algorithm is implemented to enable a high resolution and fast computation at the same time. Up to 384 bubbles are seeded in the turbulent channel flow corresponding to 5.4% gas volume fraction. Bubbles are clustered in the channel center due to the downward flow direction. The bubbles induce additional pseudo-turbulence in the channel center and are also able to attenuate the energy in the boundary layer by reducing the shear production. Turbulent kinetic energy budget indicates a significant buoyancy production in the channel center. A local equilibrium between buoyancy production and dissipation is observed here besides the shear production peak in the boundary layer. Comparing the local production and dissipation indicates a coexistence of boundary layer turbulence near the wall and bubble-induced pseudo-turbulence in the channel center. The liquid phase and gas phase are coupled through the complex liquid–gas interface. Local flow topology analysis is depicted in the liquid phase around the bubbles as well as in the gas phase. The flow topology of the liquid phase and the gas phase differs from each other significantly. Local dissipation is more dominant in the liquid phase near the bubble interface, whereas local enstrophy is preferred in the gas phase. In the liquid phase, a high dissipation event is preferred close to the interface, whereas a high enstrophy event is dominant away from the interface.

### Darcy–Bénard–Bingham convection

The present paper is the first to consider Darcy–Bénard–Bingham convection. A Bingham fluid saturates a horizontal porous layer that is subjected to heating from below. It is shown that this simple extension to the classical Darcy–Bénard problem is linearly stable to small-amplitude disturbances but nevertheless admits strongly nonlinear convection. The Pascal model for a Bingham fluid occupying a porous medium is adopted, and this law is regularized in a frame-invariant manner to yield a set of two-dimensional governing equations that are then solved numerically using finite difference approximations. A weakly nonlinear theory of the regularized Pascal model is used to show that the onset of convection is via a fold bifurcation. Some parametric studies are performed to show that this nonlinear onset of convection arises at increasing values of the Darcy–Rayleigh number as the Rees–Bingham number increases and that, for a fixed Rees–Bingham number, the wavenumber at which the rate of heat transfer is maximized increases with the Darcy–Rayleigh number.

### Three-dimensional viscous Rayleigh-Taylor instability at the cylindrical interface

Author(s): R. H. Zeng, J. J. Tao, and Y. B. Sun

In this paper, the rotational part of the disturbance flow field caused by viscous Rayleigh-Taylor instability (RTI) at the cylindrical interface is considered, and the most unstable mode is revealed to be three-dimensional for interfaces of small radii R. With an increase in R, the azimuthal wave n...

[Phys. Rev. E 102, 023112] Published Fri Aug 21, 2020

### Deformation of porous flexible strip in low and moderate Reynolds number flows

Author(s): M. Pezzulla, E. F. Strong, F. Gallaire, and P. M. Reis

The combination of porosity and permeability of a fluid-loaded structure strongly influences its behavior, but separating the two effects has traditionally proven challenging. Here, results from an experimental and numerical investigation are presented in which the porosity is fixed while systematically varying the permeability of cantilevered strips, which are towed through a viscous fluid. Their steady-state deformations and the associated drags at low and moderate Reynolds (Re) numbers are studied. At moderate Re, the permeability plays an important role, whereas its effect is small for low Re.

[Phys. Rev. Fluids 5, 084103] Published Fri Aug 21, 2020

### Fluctuations and correlations of reactive scalars near chemical equilibrium in incompressible turbulence

Author(s): Wenwei Wu (吴文伟), Enrico Calzavarini, François G. Schmitt, and Lipo Wang (王利坡)

In reacting systems in turbulent fluid environments, a competition exists between the chemical reactions that tend to dump reactant concentration fluctuations and enhance their correlation intensity, and the turbulent mixing that, on the contrary, increases fluctuations and removes relative correlations. It is shown that close to chemical equilibrium, a unique control parameter—the Damkhöler number, based on the reactant Taylor microscale—allows quantitative predictions of the reactants’ statistical properties.

[Phys. Rev. Fluids 5, 084608] Published Fri Aug 21, 2020

### Experimental investigation of wave tip variability of impacting waves

We present an experimental study on the variation in wave impact location and present a mechanism for the development of free surface instabilities on the wave crest for repeatable plunging wave impacts on a vertical wall. The existence of free surface instabilities on an impacting wave is well known, but their characteristics and formation mechanism are relatively unknown. The development of the global wave shape is measured using a visualization camera, whereas the local wave shape is measured with an accurate stereo-planar laser-induced fluorescence technique. A repeatable wave is generated with negligible system variability. The global wave behavior resembles that of a plunging breaker, with a gas pocket cross-sectional area defined by an ellipse of constant aspect ratio. The variability of the local wave profile increases significantly as it approaches the wall. The impact location varies by ∼0.5% of the wave height or more than a typical pressure sensor diameter. Additionally, the wave tip accelerates to a velocity of [math] compared to the global wave velocity of [math]. The difference in impact location and velocity can result in a pressure variation of ∼25%. A mechanism for instability development is observed as the wave tip becomes thinner and elongates when it approaches the wall. A flapping liquid sheet develops that accelerates the wave tip locally and this triggers a spanwise Rayleigh–Taylor instability.

### Low Reynolds number turbulent flows over elastic walls

We study the laminar and turbulent channel flow over a viscous hyper-elastic wall and show that it is possible to sustain an unsteady chaotic turbulent-like flow at any Reynolds number by properly choosing the wall elastic modulus. We propose a physical explanation for this effect by evaluating the shear stress and the turbulent kinetic energy budget in the fluid and elastic layer. We vary the bulk Reynolds number from 2800 to 10 and identify two distinct mechanisms for turbulence production. At moderate and high Reynolds numbers, turbulent fluctuations activate the wall oscillations, which, in turn, amplify the turbulent Reynolds stresses in the fluid. At a very low Reynolds number, the only production term is due to the energy input from the elastic wall, which increases with the wall elasticity. This mechanism may be exploited to passively enhance mixing in microfluidic devices.

### Thermal transpiration in molecular gas

The thermal transpiration of molecular gas is investigated based on the model of Wu et al. [“A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases,” J. Fluid Mech. 763, 24–50 (2015)], which is solved by a synthetic iterative scheme efficiently and accurately. A detailed investigation of the thermal slip coefficient, Knudsen layer function, and mass flow rate for molecular gas interacting with the inverse power-law potential is performed. It is found that (i) the thermal slip coefficient and Knudsen layer function increase with the viscosity index determined by the intermolecular potential. Therefore, at small Knudsen number, gas with a larger viscosity index has a larger mass flow rate; however, at late transition and free molecular flow regimes, this is reversed. (ii) The thermal slip coefficient is a linear function of the accommodation coefficient in Maxwell’s diffuse–specular boundary condition, while its variation with the tangential momentum accommodation coefficient is complicated in Cercignani–Lampis’s boundary condition. (iii) The ratio of the thermal slip coefficients between monatomic and molecular gases is roughly the ratio of their translational Eucken factors, and thus, molecular gas always has a lower normalized mass flow rate than monatomic gas. (iv) In the transition flow regime, the translational Eucken factor continues to affect the mass flow rate of thermal transpiration, but in the free molecular flow regime, the mass flow rate converges to that of monatomic gas. Based on these results, accommodation coefficients were extracted from thermal transpiration experiments of air and carbon dioxide, which are found to be 0.9 and 0.85, respectively, rather than unity used in the literature. The methodology and data presented in this paper are useful, e.g., in the pressure correction of capacitance diaphragm gauge when measuring low gas pressures.

### Velocity measurements of dilute particulate suspension over and through a porous medium model

We experimentally examine pressure-driven flows of 1%, 3%, and 5% dilute suspensions over and through a porous media model. The flow of non-colloidal, non-Brownian suspensions of rigid and spherical particles suspended in a Newtonian fluid is considered at very low Reynolds numbers. The model of porous media consists of square arrays of rods oriented across the flow in a rectangular channel. Systematic experiments using high-spatial-resolution planar particle image velocimetry and index-matching techniques are conducted to accurately measure the velocity measurements of both very dilute and solvent flows inside and on top of the porous media model. We found that for 1%, 3%, and 5% dilute suspensions, the fully developed velocity profile inside the free-flow region is well predicted by the exact solution derived from coupling the Navier–Stokes equation within the free flow-region and the volume-averaged Navier Stokes equation for the porous media. We further analyze the velocity and shear rate at the suspension–porous interface and compare these data with those of pure suspending fluid and the related analytical solutions. The exact solution is used to define parameters necessary to calculate key values to analyze the porous media/fluid interaction, such as Darcy velocity, penetration depth, and fractional ratios of the mass flow rate. These parameters are comparable between the solvent, dilute suspensions, and exact solution. However, we found clear effects between the solvent and the suspensions, which shows different physical phenomenon occurring when particles are introduced into a flow moving over and through a porous media.

### Spinning behavior of flow-acoustic resonant fields inside a cavity: Vortex-shedding modes and diametral acoustic modes

The spinning behavior of flow-acoustic resonant fields inside an axisymmetric cavity configuration was numerically investigated in four flow conditions containing different resonances between vortex-shedding modes and diametral acoustic modes. Zonal large-eddy simulations (ZLESs) were conducted to determine the aeroacoustic and aerodynamic fields simultaneously. In the ZLESs, a shear stress transport turbulence model was used to model the relatively steady flow field inside the inlet and outlet sections. Simultaneously, the wall-modeled LES formulation was used in the cavity section to resolve the highly complex flow-acoustic resonant fields. The ZLES results were well validated by the experimental results in the literature in terms of the frequency, amplitude, and spatial features of the acoustic pressure pulsations. Subsequently, the spinning behavior and mechanism of the excited diametral acoustic modes and the resonant vortex-shedding modes were comprehensively illustrated. The results showed that the excited diametral acoustic mode span anticlockwise along the cavity circumference, resulting in intense acoustic-pressure fluctuations several times greater than at the inlet dynamic-pressure head, together with longitudinal pressure propagations. Using proper orthogonal decomposition analysis, the spinning mechanism was found to be closely related to the interaction between the α-mode and the β-mode, which had fixed temporal and spatial phase lags. Thereafter, the first vortex-shedding mode gave rise to a strong spinning motion of the resonant flow field, while the second vortex-shedding mode created a slight spinning motion. The corresponding phase-dependent flow fields at consecutive planes along the cavity circumference revealed the spatiotemporal evolution of the velocity variations, surface streamlines, and vorticity variations of the shedding vortices. Large-scale helical vortex tubes were formed within the cavity volume due to the strong spinning behavior.

### Particle modeling of the spreading of coronavirus disease (COVID-19)

By the end of July 2020, the COVID-19 pandemic had infected more than 17 × 106 people and had spread to almost all countries worldwide. In response, many countries all over the world have used different methods to reduce the infection rate, such as case isolation, closure of schools and universities, banning public events, and forcing social distancing, including local and national lockdowns. In our work, we use a Monte Carlo based algorithm to predict the virus infection rate for different population densities using the most recent epidemic data. We test the spread of the coronavirus using three different lockdown models and eight various combinations of constraints, which allow us to examine the efficiency of each model and constraint. In this paper, we have tested three different time-cyclic patterns of no-restriction/lockdown patterns. This model’s main prediction is that a cyclic schedule of no-restrictions/lockdowns that contains at least ten days of lockdown for each time cycle can help control the virus infection. In particular, this model reduces the infection rate when accompanied by social distancing and complete isolation of symptomatic patients.

### Flow field induced by a dielectric barrier discharge plasma actuator analyzed with bi–orthogonal decomposition

A typical dielectric barrier discharge (DBD) plasma actuator generates complex periodic flow structures in burst mode. Efficient use of these actuators depends on clear understanding of the relationship between the operational parameters of the actuator and flow structure. The present study reports the temporal and spatial evolution of these flow structures by utilizing the bi-orthogonal decomposition (BOD) technique. The flow induced by the actuator is captured using a time resolved particle image velocimetry (2D–2C–TR–PIV) system. The BOD of flow field is carried out using instantaneous velocity field data. The DBD plasma actuator is operated at different combinations of duty cycle, α (50% ≤ α ≤ 90%), and burst frequency, fb (10 Hz ≤ fb ≤ 90 Hz). The modal energy content is used to characterize the flow field as a function of operating variables, i.e., α and fb of the actuation signal. The mean mode of the decomposition successfully approximates the time averaged behavior of the induced flow field. The mean mode energy level increases with the increase in both α and fb with a more pronounced effect observed as a function of fb. The coherent structures are located close to the near wall at high burst frequency. The non-dimensional entropy decreases with the increase in both α and fb with a more pronounced effect of fb than that of α. The decrease in entropy value indicates that space–time complexities are reduced at higher burst frequency. The topos of higher order modes reveal the presence of coherent structures that grow in time and convect along the wall like a train of vortices. The chronos of mode 2 and mode 3 is locked in with respect to the burst frequency. However, the chronos of mode 4 and mode 5 shows frequency doubling at lower burst frequency actuation and frequency halving at higher burst frequency actuation. The entropy value or space–time complexity of flow structures generated by DBD plasma actuator is related to the nonlinear vortex interaction mechanism, i.e., period doubling and period halving of chronos.