# Latest papers in fluid mechanics

### Coherent structures in a compressible turbulent plane jet

Coherent structures represented by proper orthogonal decomposition (POD) modes from large-eddy simulation of a compressible plane jet are analyzed. The leading POD modes of the fluctuating velocity components u′, v′, and w′, and the pressure fluctuation p′ are considered. Spatial and temporal features of these modes are analyzed by the modes and the spectra of the temporal coefficients, respectively. Interactions between leading modes of u′, v′, and w′ and the relationship between the modes of u′, v′, and w′ and of the p′ are discussed. The results show that the leading mode of u′ is in the shape of longitudinal stripes, and the mode is dominated by the jet column frequency Stc. For spanwise fluctuation w′, the leading modes are a pair of modes in the shape of a train of ridges along streamwise, and they are dominated by the fundamental frequency St0. The leading modes for v′ are a pair of modes in a row of ribs. For the dominant frequencies of the v′ modes, suppression of subharmonic frequency at St0/2 and formation of sideband frequencies around (St0 ± Stc)/2 are observed. These spatiotemporal features suggest the mode of v′ is modulated by the modes of u′ and w′. Both the leading modes of p′ and of v′ are in the shape of puffs outside the averaged shear layer. These puff modes are related as an oscillation system, which is confirmed by the spectral-POD modes.

### Influence of thermal properties on hydrothermal waves in evaporating sessile droplets

The thermal properties of droplets have a significant effect on the evaporation of sessile droplets. In this study, the influence of nondimensional thermal properties on Marangoni instabilities, especially hydrothermal waves (HTWs), in a sessile droplet evaporating at a constant contact angle mode, is numerically investigated using a nondimensional mathematical model. The model considers the transient deformation of the droplet surface during evaporation in a wide range of Marangoni numbers from 1000 to 40 000, evaporative cooling numbers from 1 to 300, relative heat conductivities from 0.01 to 1000, and Prandtl numbers from 0.01 to 25.0. Included are the different kinds of fluids applied in previous works on Marangoni convection in evaporating sessile droplets. The substrate material varies from a vacuum insulation panel with a heat conductivity of 0.002 W/m·K to silver with 429 W/m·K. The results reveal that a sufficiently large Marangoni number, evaporative cooling number, and relative heat conductivity favor the appearance of HTWs, whereas a large Prandtl number inhibits the appearance of HTWs. The mixture mode of Bénard–Marangoni cells and longitudinal rolls or of longitudinal rolls and HTWs can occur for a small relative heat conductivity. The influence of these thermal properties on the characteristics and dynamic behaviors of HTWs are analyzed and the critical Marangoni numbers for the appearance of HTWs are determined. This work can be helpful for understanding the influence of thermal properties on HTWs in sessile droplets.

### Effects of velocity shear layer on detonation propagation in a supersonic expanding combustor

This study investigates the mechanism of detonation propagation in a stoichiometric hydrogen–oxygen mixture with non-uniform flow velocity entering an expanding combustor. For simulation of the detonation propagation, the Navier–Stokes equations with a one-step two-species chemistry model are solved by employing the hybrid sixth-order weighted essentially non-oscillatory centered difference scheme. The self-sustaining mechanism of detonation propagation in an expanding combustor under the action of non-uniform supersonic flow with a velocity shear layer is revealed. The results show that under the influence of velocity shear layer, two different unburned jets are produced behind the detonation front. These jets are induced by the velocity shear layers and the Prandtl–Meyer expansion fan. The two jets interact and mix gradually. The interaction between the mixed unburned jets and highly unstable shear layers creates large-scale vortices that intensify the turbulent mixing of the unburned jets. Meanwhile, the baroclinic mechanism generates numerous vortices on the boundary of the unburned jet. These vortices promote the mixing of the burned and unburned gases, which eventually leads to the rapid consumption of the unburned pockets. The heat released due to the burning of the unreacted pockets behind the detonation wave supports a self-sustaining propagation of the detonation wave. When the velocity difference among the shear layers increases, the surface fluctuation of the detonation wave increases.

### Large eddy simulation of incident flows around polygonal cylinders

In this study, we carry out large eddy simulation of incident flow around polygonal cylinders of side number [math] at Reynolds number [math]. In total, six incidence angles (α) are studied on each cylinder ranging from face to corner orientations, thus covering the entire α spectrum. Special focus is put on the time-mean aerodynamic forces including lift, drag, and vortex shedding frequencies as well as the near wake flow features. It is found that because of y-plane asymmetry of polygonal cross sections at most incidence angles, the flow separation characteristics and hence the induced base pressure distribution and the aerodynamic forces exhibit unique and complex dependence on α and N. While the general inverse relation of drag coefficient and Strouhal number previously proposed from experimental observations at principal orientations still holds at arbitrary α, the variation of the two is found to be non-monotonic on both α and N. We also found that compared to the absolute time mean shear layer length measured from the final separation point, the extent of them stretched to the wake, measured from the cylinder center, is a powerful scaling factor for all the quantities investigated, including the wake characteristic length scales. In particular, the difference between the top and the bottom shear layer (due to geometrical asymmetry at arbitrary α) describes the variation of the non-zero time mean lift coefficient reasonably well, whose sign varies with N non-monotonically.

### From limited observations to the state of turbulence: Fundamental difficulties of flow reconstruction

Author(s): Tamer A. Zaki and Mengze Wang

Is it possible to reconstruct all the scales of turbulence from limited observations? If so, what is the minimum resolution of observations for a successful reconstruction? How much information about a turbulent flow field can be decoded from an isolated, instantaneous measurement? These fundamental questions are addressed using variational data assimilation, where the observations are infused in simulations and are decoded using the Navier-Stokes equations. We highlight the “dual butterfly effect” and how the stochasticity of turbulence obfuscates the interpretation of measurements.

[Phys. Rev. Fluids 6, 100501] Published Wed Oct 06, 2021

### Fall and break-up of viscous miscible drops in a Hele-Shaw cell

Author(s): Clément Toupoint, Sylvain Joubaud, and Bruce R. Sutherland

We study the fall of pancake-shaped drops in a Hele-Shaw cell filled with a more viscous ambient fluid in the case where the drop and ambient fluid are miscible. We propose a theoretical expression for the falling velocity of the drops which takes into account elongated drops with width smaller than the gap of the cell. We also provide experimental evidence for the break-up of miscible drops, which can be caused by internal fluid motion within the drop, or by an instability in the shape of the drop.

[Phys. Rev. Fluids 6, 103601] Published Wed Oct 06, 2021

### Marginal regeneration-induced drainage of surface bubbles

Author(s): Jonas Miguet, Marina Pasquet, Florence Rouyer, Yuan Fang, and Emmanuelle Rio

When a soap film drains, marginal regeneration refers to the rise of patches that are thinner than the rest of the film. In this work the rise velocities and sizes of buoyant patches are measured and found to be in good agreement with a Rayleigh-Taylor like instability and a model based on a balance of gravitational and surface viscous forces, as suggested in the literature. Thus, in an environment saturated in humidity, to eliminate evaporation effects, marginal regeneration approximately describes the film drainage at the apex of a draining bubble.

[Phys. Rev. Fluids 6, L101601] Published Wed Oct 06, 2021

### Nonequilibrium effects in high enthalpy gas flows expanding through nozzles

An approach based on the direct simulation Monte Carlo method is proposed to model a core flow in a converging–diverging nozzle. The area of applicability of this approach is defined by the Boltzmann equation, which allows fully kinetic models that accurately capture thermal and chemical nonequilibrium to be applied to gas flows where the flow regime rapidly changes from continuum to transitional. The approach is validated through comparison with available experimental data. The examination of nonequilibrium and reaction rate effects for Caltech's T5 shock tunnel condition has shown little impact of nonequilibrium but demonstrated significant sensitivity of nitric oxide (NO) density to all exchange reaction and NO recombination rates. The use of the most recent theoretical and experimental rates results in a factor of two lower NO density at the nozzle exit as compared to the conventional Park rates, which indicates that re-visiting of the latter may be necessary. Multi-parametric sensitivity study of T5 conditions has not provided an explanation for a large drop in free-stream temperature and NO density over time, under constant flow velocity, observed recently in T5. Modeling of High Enthalpy Shock Tunnel Göttingen conditions has demonstrated considerable nonequilibrium between vibrational modes of N2, NO, and O2; it has also shown that the vibration–dissociation coupling strongly influences mole fractions of NO and O2.

### Contact line dynamics in curtain coating of non-Newtonian liquids

The rheological characteristics of liquids play an important role in the flow near dynamic contact lines, where the deformation rates are extremely large. The liquid contact line dynamics and the free surface configuration in the curtain coating of polymer solutions were experimentally studied using visualization to determine the effect of two rheological characteristics: shear thinning and extensional thickening. The critical web speeds for heel formation, where the contact line on the moving substrate shifts upstream of the falling curtain, and air entrainment, where the contact line shifts downstream and air bubbles appear, were determined over a range of flow rates. The critical conditions were compared to the behavior observed for a Newtonian liquid. Moreover, the contact line dynamics were described by three dimensionless parameters: the Deborah number, the Ohnesorge number, and the ratio of the web speed to the liquid curtain velocity at the contact line.

### Simple analytic model for peristaltic flow and mixing

Author(s): Ruy Ibanez, Mohammad Shokrian, Jong-Hoon Nam, and Douglas H. Kelley

Small-amplitude peristaltic flows occur in many biological systems, and may occur in the inner ear. We present a simple analytic model for such flows, validated using simulations and measurements from a laboratory model of the inner ear. We demonstrate that Lagrangian transport dynamics can be reproduced accurately with our simple analytic model.

[Phys. Rev. Fluids 6, 103101] Published Tue Oct 05, 2021

### Asymmetric coalescence of two droplets with different surface tensions is caused by capillary waves

Author(s): Michiel A. Hack, Patrick Vondeling, Menno Cornelissen, Detlef Lohse, Jacco H. Snoeijer, Christian Diddens, and Tim Segers

When two droplets with different surface tensions collide, the shape evolution of the merging droplets is asymmetric. Here, we reveal the importance of capillary waves in this process, and systematically study the influence of both inertia and surface tension. Counterintuitively, the Marangoni effect reduces the asymmetry.

[Phys. Rev. Fluids 6, 104002] Published Tue Oct 05, 2021

### The effect of Schmidt number on gravity current flows: The formation of large-scale three-dimensional structures

The Schmidt number, defined as the ratio of scalar to momentum diffusivity, varies by multiple orders of magnitude in real-world flows, with large differences in scalar diffusivity between temperature, solute, and sediment driven flows. This is especially crucial in gravity currents, where the flow dynamics may be driven by differences in temperature, solute, or sediment, and yet the effect of Schmidt number on the structure and dynamics of gravity currents is poorly understood. Existing numerical work has typically assumed a Schmidt number near unity, despite the impact of Schmidt number on the development of fine-scale flow structure. The few numerical investigations considering high Schmidt number gravity currents have relied heavily on two-dimensional simulations when discussing Schmidt number effects, leaving the effect of high Schmidt number on three-dimensional flow features unknown. In this paper, three-dimensional direct numerical simulations of constant-influx solute-based gravity currents with Reynolds numbers [math] and Schmidt number 1 are presented, with the effect of Schmidt number considered in cases with [math] and (500, 10). These data are used to establish the effect of Schmidt number on different properties of gravity currents, such as density distribution and interface stability. It is shown that increasing Schmidt number from 1 leads to substantial structural changes not seen with increased Reynolds number in the range considered here. Recommendations are made regarding lower Schmidt number assumptions, usually made to reduce computational cost.

### Rogue wave generation in wind-driven water wave turbulence through multiscale phase-amplitude coupling, phase synchronization, and self-focusing by curved crests

Rogue wave events (RWEs), localized high amplitude extreme events, uncertainly emerge in various nonlinear waves. For RWE generation, modulation instability leading to amplitude soliton formation for one-dimensional (1D) systems; and the additional wave directional property and the ratio of nonlinearity to spectrum bandwidth on the modulation instability for two-dimensional (2D) systems, are the accepted mechanisms. However, those studies have mainly focused on RWEs in weakly disordered wave states dominated by a single scale, but to a much lesser extent on wave turbulence with multiscale excitations. Wind-driven water surface wave turbulence widely occurs in nature. Unraveling RWE generation in wind-driven water surface wave turbulence is an important issue. Here, using multidimensional empirical mode decomposition, we experimentally investigate the dynamics of decomposed multiscale spatiotemporal waveforms of wind-driven water wave turbulence in the 2 + 1D space. We demonstrate how the cascaded amplitude modulation of the faster (higher frequency) modes by the phases of the slower modes, the phase synchronization of the largest peaks in the bursts of fast modes emerging in the crest regions of the medium modes, and self-focusing by the curved crests of the three fastest modes lead to RWE generation.

### Sloshing in vertical cylinders with circular walls: The effect of radial baffles

The behavior of sloshing eigenvalues and eigenfunctions is studied for vertical cylindrical containers that have circular walls and constant (possibly infinite) depth. The effect of breaking the axial symmetry due to the presence of radial baffles is analyzed. It occurs that the lowest eigenvalues are substantially smaller for containers with baffles going throughout the depth; moreover, all eigenvalues are simple in this case. On the other hand, the lowest eigenvalue has multiplicity two in the absence of baffle. It is shown how these properties affect the location of maxima and minima of the free surface elevation and the location of its nodes.

### Large-eddy simulation of a multi-injection flame in a diesel engine environment using an unsteady flamelet/progress variable approach

In this work, large-eddy simulations (LESs) are conducted for a multiple-injection flame in a diesel engine environment using an unsteady flamelet/progress variable (UFPV) approach in which differential diffusion is considered. The suitability of the UFPV tabulation approach is first evaluated through a priori analyses using the state-of-the-art direct numerical simulation (DNS) dataset. Both the instantaneous data and the conditional values for the major and minor species' mass fractions are compared between the UFPV and the DNS. The comparisons show that the proposed UFPV tabulation approach can give good predictions for the multiple-injection flame at different injection phases. While the gas temperature and major species mass fractions can be accurately predicted with or without differential diffusion being considered in the UFPV flamelet library, the prediction accuracy for the highly diffusive species (e.g., hydrogen) in the main injection phase can be noticeably improved when differential diffusion is taken into account. The fully coupled LES/UFPV simulations show that the overall structure of the multiple-injection flame can be predicted, and the conditional thermo-chemical values are close to the filtered DNS dataset. The reasons for the remaining discrepancies found in the a priori analyses and the a posteriori simulations using the UFPV approach are analyzed.

### Compressibility in suddenly expanded subsonic flows

This paper concerns implicit large eddy simulations of subsonic flows through a symmetric suddenly expanded channel. We aim at shedding light on the flow physics at a relatively high Reynolds number of 10 000, based on the inlet bulk velocity and the step height of the channel, and examine the compressibility effects for two Mach numbers, Ma = 0.1 and Ma = 0.5. Comparisons with experimental measurements are provided. In addition, we investigate the structure of the separated regions, turbulence structures—through the Reynolds stress anisotropy componentality—and turbulence kinetic energy budgets. The results reveal that compressibility influences particular flow physics.

### Reduced models of unidirectional flows in compliant rectangular ducts at finite Reynolds number

Soft hydraulics, which addresses the interaction between an internal flow and a compliant conduit, is a central problem in microfluidics. We analyze Newtonian fluid flow in a rectangular duct with a soft top wall at steady state. The resulting fluid–structure interaction is formulated for both vanishing and finite flow inertia. At the leading-order in the small aspect ratio, the lubrication approximation implies that the pressure only varies in the streamwise direction. Meanwhile, the compliant wall's slenderness makes the fluid–solid interface behave like a Winkler foundation, with the displacement fully determined by the local pressure. Coupling flow and deformation and averaging across the cross section leads to a one-dimensional reduced model. In the case of vanishing flow inertia, an effective deformed channel height is defined rigorously to eliminate the spanwise dependence of the deformation. It is shown that a previously used averaged height concept is an acceptable approximation. From the one-dimensional model, a friction factor and the corresponding Poiseuille number are derived. Unlike the rigid duct case, the Poiseuille number for a compliant duct is not constant but varies in the streamwise direction. Compliance can increase the Poiseuille number by a factor of up to four. The model for finite flow inertia is obtained by assuming a parabolic vertical variation of the streamwise velocity. To satisfy the displacement constraints along the edges of the channel, weak tension is introduced in the streamwise direction to regularize the Winkler-foundation-like model. Matched asymptotic solutions of the regularized model are derived.

### Analysis of multiple steady states for natural convection of Newtonian fluids in a square enclosure

Multiple steady states are investigated for natural convection of fluids in a square enclosure with non-isothermally hot bottom wall, isothermally cold side walls, and thermally insulated top wall. A robust computation scheme involving steady-state governing equations has been developed to compute the steady states as a function of Rayleigh number ([math]) for two different Prandtl numbers (Pr = 0.026 and 0.1). Penalty Galerkin finite element method with Newton–Raphson solver is employed for the solution of the governing equations, while the solution branches are initiated by varying initial guess to the Newton–Raphson solver. In this context, a dual-perturbation scheme involving perturbations of the boundary conditions and various process parameters has been designed leading to the rich spectrum of the symmetric and asymmetric solution branches for the current symmetric problem. It is found that multiple steady states occur beyond a critical value of Ra, which depends on the magnitude of Pr. In addition to the basic solution branch (corresponding to the solutions obtained via uniform initial guesses), nineteen additional solution branches (six symmetric and thirteen asymmetric) are obtained for Pr = 0.026, while four additional solution branches (two symmetric and two asymmetric) are obtained for Pr = 0.1. The solution branches are associated with a wide spectrum of flow structures (24 distinct types for Pr = 0.026 excluding the reflection symmetric mirror images of the asymmetric solutions), which are reported for the first time. The flow structures lead to various heating scenarios within the enclosure resulting in a significant variation of heat transfer rates (more than 50%). The current results are important for the practical applications. The spectrum of the possible scenarios revealed in this work can be pivotal to design the optimal processes based on the process requirement (targeted heating or enhanced heating rates).

### Natural convection over vertical and horizontal heated flat surfaces: A review of recent progress focusing on underpinnings and implications for heat transfer and environmental applications

Natural convection arising over vertical and horizontal heated flat surfaces is one of the most ubiquitous flows at a range of spatiotemporal scales. Despite significant developments over more than a century contributing to our fundamental understanding of heat transfer in natural convection boundary layers, certain “hidden” characteristics of these flows have received far less attention. Here, we review scattered progress on less visited fundamental topics that have strong implications to heat and mass transfer control. These topics include the instability characteristics, laminar-to-turbulent transition, and spatial flow structures of vertical natural convection boundary layers and large-scale plumes, dome, and circulating flows over discretely and entirely heated horizontal surfaces. Based on the summarized advancements in fundamental research, we elaborate on the selection of perturbations and provide an outlook on the development of perturbation generators and methods of altering large-scale flow structures as a potential means for heat and mass transfer control where natural convection is dominant.

### Open-channel flows through emergent rigid vegetation: Effects of bed roughness and shallowness on the flow structure and surface waves

Free-surface flows through a staggered cylinder array were investigated in an open-channel flume. The cylinders simulated rigid emergent vegetation. Specifically, we studied four flow cases with a two-factor design comprising flow rate (7 and [math]) and bed-surface state (hydraulically rough and smooth). We have primarily assessed the effects of bed roughness and shallowness on the time-averaged flow structure and the transverse fluctuating flow motion in the cylinder wake. Secondarily, the effects of the former on the vortex-shedding-induced surface waves were quantified. To gain further insight into the bed roughness effect on flow structure, we conducted transient flow simulations using a hybrid Reynolds-Averaged Navier–Stokes/Large Eddy Simulation turbulence model. For all cases, downstream of a cylinder, an upward flow occurs and two counterrotating secondary current cells develop. The two cells bring high-momentum fluid from the high-speed region into the cylinder wake, resulting in a near-bed streamwise velocity-bulge. The measured upward flow and velocity-bulge are greater for the rough-bed cases than for the smooth-bed cases. The simulated upward flow and velocity-bulge increase with an increasing roughness height, while secondary currents decay faster in the longitudinal direction. For the rough-bed cases, in the cylinder wake, the transverse fluctuating flow motion is hindered by the rough-bed induced turbulence over the whole water column, irrespective of the shallowness level. Coupled with the fluctuating flow motion, we have observed for three flow cases noticeable surface oscillations (termed “seiche waves”), whose amplitude decreases with decreasing flow depth. Under the combined effects of strong shallowness and a rough bed, seiche waves vanished.