# Latest papers in fluid mechanics

### Three-dimensional spectral proper orthogonal decomposition analyses of the turbulent flow around a seal-vibrissa-shaped cylinder

The flow around a seal-vibrissa-shaped cylinder (SVSC) is numerically investigated using the large eddy simulation framework at a Reynolds number of 20 000. Compared with a circular cylinder (CC), the wake of the SVSC presents more stable three-dimensional separation, a longer vortex formation length, and a weaker vortex strength. The mean drag and fluctuation of the lift coefficient are 59.5% and 87.7% lower than those of the CC, respectively. Three-dimensional spectral proper orthogonal decomposition (SPOD) is used to investigate the turbulent flow around these two types of cylinders in terms of the spatial modes, mode energy, mode coefficients, and reconstructed flow by a reduced-order modeling. Four typical vortex shedding patterns are first extracted by SPOD for the SVSC, producing crescent-, twist-, branch-, and knot-shaped vortices. A concept model is proposed for the wake dynamics of the SVSC, allowing the formation and transformation of these modes to be elucidated. Detailed analysis of the impact of the flow pattern on the associated forces indicates that the dominant out-phase vortex shedding at the upper and lower saddle planes makes a significant contribution to the reduction in lift fluctuations.

### Effects of wing-to-body mass ratio on insect flapping flights

Bio-flyers of insects, birds, and bats are observed to have a broad range of wing-to-body mass ratio (WBMR) from 0.1% to 15%. The WBMR and wing mass distribution can lead to large inertial forces and torques in fast-flapping wings, particularly in insect flights, comparable with or even greater than aerodynamic ones, which may greatly affect the aerodynamic performance, flight stability, and control, but still remain poorly understood. Here, we address a simulation-based study of the WBMR effects on insect flapping flights with a specific focus on unraveling whether some optimal WBMR exists in balancing the flapping aerodynamics and body control in terms of body pitch oscillation and power consumption. A versatile, integrated computational model of hovering flight that couples flapping-wing-and-body aerodynamics and three degree of freedom body dynamics was employed to analyze free-flight body dynamics, flapping aerodynamics, and power cost for three typical insects of a fruit fly, a bumblebee, and a hawkmoth over a wide range of Reynolds numbers (Re) and WBMRs. We found that the realistic WBMRs in the three insect models can suppress the body pitch oscillation to a minimized level at a very low cost of mechanical power. We further derived a scaling law to correlate the WBMR with flapping-wing kinematics of stroke amplitude (Φ), flapping frequency (f), and wing length (R) in terms of [math], which matches well with measurements and, thus, implies that the WBMR-based body pitch minimization may be a universal mechanism in hovering insects. The realistic WBMR likely offers a novel solution to resolve the trade-off between body-dynamics-based aerodynamic performance and power consumption. Our results indicate that the WBMR plays a crucial role in optimization of flapping-wing dynamics, which may be useful as novel morphological intelligence for the biomimetic design of insect- and bird-sized flapping micro-aerial vehicles.

### Computational analysis of obstructive disease and cough intensity effects on the mucus transport and clearance in an idealized upper airway model using the volume of fluid method

This study provides a quantitative analysis to investigate the effects of cough intensity and initial mucus thickness on the mucus transport and clearance in a mouth-to-trachea airway geometry using an experimentally validated Volume of Fluid (VOF) based multiphase model. In addition, the accuracy of simplifying mucus as Newtonian fluid is also quantified by the comparisons of mucus transport and clearance efficiencies with the simulations using realistic shear-thinning non-Newtonian fluid viscosities as a function of shear rate. It proves that the VOF model developed in this study can capture air–mucus interface evolution and predict the mucus transport behaviors driven by the expiratory cough waveforms. Numerical results show that noticeable differences can be identified between the simulations using simplified Newtonian fluid and the realistic non-Newtonian fluid viscosity models, which indicates that an appropriate non-Newtonian fluid model should be applied when modeling mucus transport to avoid the possible inaccuracy induced by the Newtonian fluid simplification. Furthermore, the results also indicate that an intense cough can enhance the mucus clearance efficiency in chronic obstructive pulmonary disease (COPD) upper airways. Additionally, although higher mucus clearance efficiency is observed for severe COPD conditions with a thicker mucus layer, there is a possibility of mucus accumulation and obstruction in the upper airway for such a COPD condition if the cough is not strong enough, which will possibly cause further breathing difficulty. The VOF model developed in this study can be further refined and integrated with discrete phase models to predict the mucus clearance effect on inhaled particles explicitly.

### Enhanced air stability of superhydrophobic surfaces with flexible overhangs of re-entrant structures

The stability of air plastron entrapped in a submerged superhydrophobic (SHPo) surface determines the sustainability of the surface properties including drag reduction, self-cleaning, and anti-icing. To increase the stability for high water pressure, various microstructures have been adopted for SHPo surfaces. A re-entrant structure is a typical example to provide high stability for air plastrons. This work proposes flexible overhangs of the re-entrant structures as a new strategy for additional stability. Several SHPo surfaces with re-entrant structures of different sizes are fabricated, and their Young's moduli (E) are controlled from 715.3 kPa to 2509 kPa. Pressurization of water and air diffusion from the plastrons to the surrounding water cause deformation of the air–water meniscus until air plastron disruption starts to occur. The critical water pressure for air plastron disruption is gradually increased as the E of the overhangs decreases. The critical value is also increased as the gap distance between the adjacent overhangs increases. When the water pressure is less than the critical value, the air plastron is also gradually disrupted by the air diffusion. The lifetime elapsed to the air disruption increases by 19%–44% as the value of E decreases. The present results would pave the way for utilizing flexible overhangs of re-entrant structures as a novel approach for increasing the air stability of SHPo surfaces.

### How <i>Euglena gracilis</i> swims: Flow field reconstruction and analysis

Author(s): Nicola Giuliani, Massimiliano Rossi, Giovanni Noselli, and Antonio DeSimone

*Euglena gracilis* is a unicellular organism that swims by beating a single anterior flagellum. We study the nonplanar waveforms spanned by the flagellum during a swimming stroke and the three-dimensional flows that they generate in the surrounding fluid. Starting from a small set of time-indexed imag...

[Phys. Rev. E 103, 023102] Published Mon Feb 08, 2021

### Mechanism of hysteresis in shock wave reflection

Author(s): Yan-Chao Hu (胡延超), Wen-Feng Zhou (周文丰), Zhi-Gong Tang (唐志共), Yan-Guang Yang (杨彦广), and Zhao-Hu Qin (秦兆虎)

This paper reports on the mechanism of the hysteresis in the transition between regular and Mach shock wave reflections. We disclose that, for a given inflow Mach number, a stable reflection configuration should maintain the minimal dissipation. As the wedge angle varies, the set of the minimal diss...

[Phys. Rev. E 103, 023103] Published Mon Feb 08, 2021

### Announcement: PRFluids publishes Invited Perspective on Grand Challenges in Environmental Fluid Mechanics

[Phys. Rev. Fluids 6, 020001] Published Mon Feb 08, 2021

### Confronting Grand Challenges in environmental fluid mechanics

Author(s): T. Dauxois, T. Peacock, P. Bauer, C. P. Caulfield, C. Cenedese, C. Gorlé, G. Haller, G. N. Ivey, P. F. Linden, E. Meiburg, N. Pinardi, N. M. Vriend, and A. W. Woods

Environmental fluid mechanics underlies a wealth of natural, industrial, and, by extension, societal challenges. As we strive toward a more sustainable planet, there is a wide range of problems to be tackled, from fundamental advances in understanding and modeling of stratified turbulence and consequent mixing to applied studies of pollution transport in the ocean, atmosphere, and urban environments. The discussions and outcomes of a recent Les Houches School of Physics meeting are summarized here with the intent of providing a resource for the community going forward and a plan of action for the coming decade.

[Phys. Rev. Fluids 6, 020501] Published Mon Feb 08, 2021

### Erythrocyte-erythrocyte aggregation dynamics under shear flow

Author(s): Mehdi Abbasi, Alexander Farutin, Hamid Ez-Zahraouy, Abdelilah Benyoussef, and Chaouqi Misbah

Aggregates of red blood cells (RBCs) are normally dissociated reversibly by moderate flow stresses. Numerical simulations show that the RBCs doublet may be robust even for very high shear stress compromising oxygen delivery to organs and tissues. A link with pathological conditions (several common blood diseases) is demonstrated.

[Phys. Rev. Fluids 6, 023602] Published Mon Feb 08, 2021

### Nonisothermal effects on water potential measurement in a simple geometry

Author(s): Pierre Lidon, Etienne Perrot, and Abraham D. Stroock

In nature, unsaturated porous media, like soils or plant tissues, are often submitted to temperature gradients which can trigger water transport. A nanofluidic tool is employed here to measure the changes in water potential in response to temperature variations in a model geometry. Variations of -7.9 MPa/K are observed in agreement with previous measurements but which differ from a simple modeling, pointing at subtle couplings between natural convection and the Soret effect at play in the setup.

[Phys. Rev. Fluids 6, 023801] Published Mon Feb 08, 2021

### Modified Stokes drift due to resonant interactions between surface waves and corrugated sea floor with and without a mean current

Author(s): Akanksha Gupta and Anirban Guha

A unidirectional surface gravity wave over a flat bottom topography causes a unidirectional Stokes drift of floating particles. However, rippled bottom topography can resonantly interact with incident surface waves and generate reflected waves. This introduces a backward drift component that counters the unidirectional forward motion of the floating particles. Hence rippled bottom topography can act as a non-surface-invasive particle trap or reflector and thus help in mitigating ocean pollution.

[Phys. Rev. Fluids 6, 024801] Published Mon Feb 08, 2021

### Double-diffusive sedimentation at high Schmidt numbers: Semi-Lagrangian simulations

Author(s): Jean-Baptiste Keck, Georges-Henri Cottet, Eckart Meiburg, Iraj Mortazavi, and Christophe Picard

When particle-laden freshwater is placed above clear saltwater, the ensuing sedimentation process can take one of two forms: For small dimensionless settling velocities, it will be double diffusive in nature, whereas for large settling velocities it will be dominated by Rayleigh-Taylor instability. A high-performance semi-Lagrangian computational approach is introduced that allows for the investigation of these processes in three dimensions.

[Phys. Rev. Fluids 6, L022301] Published Mon Feb 08, 2021

### Wind- and gravity-forced drop depinning

Author(s): Edward B. White and Jason A. Schmucker

Contact-angle hysteresis enables drops to pin to surfaces in the presence of wind or gravity forcing. Under what combined forcing conditions do drops depin and run back along a surface? On noninclined surfaces, drops depin at a constant critical Weber number across a wide range of Bond numbers. On inclined surfaces, two regimes of wind- and gravity-dominated forcing are observed, but a simple correlation may still describe critical depinning conditions.

[Phys. Rev. Fluids 6, 023601] Published Fri Feb 05, 2021

### Orr mechanism in transition of parallel shear flow

Author(s): Yuxin Jiao, Yongyun Hwang, and Sergei I. Chernyshenko

The precise role of the Orr mechanism in transition of parallel shear flow is investigated. We found two transition scenarios, oblique and streak transition, in which the Orr mechanism plays a central role in triggering transition. In the oblique transition, the spanwise velocity perturbation amplified with the Orr mechanism initiates both streak amplification and breakdown, whereas in the streak transition, the role of the Orr mechanism is limited only to the streak breakdown at the late stage of transition.

[Phys. Rev. Fluids 6, 023902] Published Fri Feb 05, 2021

### Particle capture by drops in turbulent flow

Author(s): Arash Hajisharifi, Cristian Marchioli, and Alfredo Soldati

Three-phase turbulent flows are crucial in a number of practical problems involving particulate abatement, from scavenging of air pollutants by precipitation to scrubbing processes. These flows are extremely rich in physics and challenging to simulate. Through direct numerical simulations of turbulence, coupled with a phase field interface description and Lagrangian particle tracking, the capture dynamics of small solid particles by large deformable drops is examined in detail. The role of the topologically changing drop interface in connection with the local turbulence structure is highlighted, and a simple transport model for predicting capture efficiency is derived.

[Phys. Rev. Fluids 6, 024303] Published Fri Feb 05, 2021

### Direct numerical simulations of a statistically stationary streamwise periodic boundary layer via the homogenized Navier-Stokes equations

Author(s): Joseph Ruan and Guillaume Blanquart

This work focuses the simulation of incompressible flat-plate boundary layers in streamwise periodic domains under our proposed homogenized Navier-Stokes equations. These simulations are conducted without needing multiple stations while also achieving statistical stationarity. The global quantities and profiles obtained via this method are comparable to those obtained via spatially developing simulations. These results were obtained at a computational cost approximately an order of magnitude lower than that of the spatially developing simulations.

[Phys. Rev. Fluids 6, 024602] Published Fri Feb 05, 2021

### Numerical investigation of shock-turbulent mixing layer interaction and shock-associated noise

Direct numerical simulation of shock-turbulent mixing layer interaction (STMLI) is conducted in this paper to study the influence of shock-turbulent interaction (STI) on the turbulence evolution and shock-associated noise. The results show that turbulent kinetic energy and pressure fluctuation around the interaction point of STI are both first increased and then reduced to a smaller value than that in the fully developed region of the turbulent mixing layer, while the Reynolds-stress anisotropy at the upper edge of STMLI is changed under the compression–expansion effect induced by the distorted shock tip and the reflected expansion wave. Additionally, it is found that shock-associated noise would increase the overall sound pressure level (OASPL) and amplify the high-frequency noise at the upstream observers. By applying the shock-leakage theory, the turbulence scale analysis, and the spectrum analysis, two generation mechanisms of shock-associated noise are identified: first, the influence of turbulence on the shock wave results in the shock unsteady movement, which generates a sound wave with cylindrical wave front; second, STI decreases the turbulence scale and increases the pressure fluctuation in the high-frequency band so as to strengthen the small-scale turbulence to radiate out more high-frequency noise. Finally, the shock strength effect on shock-associated noise is explored, and the shock-associated noise reduction is observed when decreasing the shock strength. By converting the OASPL difference to the equivalent acoustic pressure difference, a linear correlation between the shock-associated noise source strength and the shock strength is found.

### Forced convection past a semi-circular cylinder at incidence with a downstream circular cylinder: Thermofluidic transport and stability analysis

The present study analyzes the transport characteristics and associated instability of a forced convective flow past a semi-circular cylinder at incidence with a downstream circular cylinder. Considering air as an operating fluid, unsteady computations are performed for the ranges of incidence angles [math] and Reynolds numbers (Re) (0° ≤ ϕ ≤ 90°, [math]). The numerical model is adequately validated with the available experimental and numerical data from the literature. It is found that the presence of the upstream semi-circular cylinder at various incidence angles yields a rotational effect on the flow structures that evolve from the downstream circular cylinder. The modulation of the incidence angle reveals three separation regimes of the shed-vortex structures, which shows wake confluence. The dependencies of the coefficient of drag [math] and the root mean square values of the lift coefficient [math] on the angles of incidence are examined for both of the cylinders. The frequency of vortex shedding increases with increasing ϕ and attains its peak value at ϕ ∼ 30°. The forced convective heat transfer for the semi-circular cylinder decreases with increasing ϕ, whereas a contrasting trend is observed for the circular cylinder until ϕ ∼ 45°. The global stability analysis through the dynamic mode decomposition shows a stabilizing flow situation for the present range of operating parameters.

### Influence of surface sublimation on the stability of the supersonic boundary layer and the laminar–turbulent transition

We report a theoretical study of the properties of a supersonic boundary layer and its linear stability under conditions of surface material sublimation. Calculations were performed for an adiabatic boundary layer for a flat plate with a naphthalene coating at a free-stream Mach number of M = 3 (for the first instability mode disturbances). In the boundary layer, surface sublimation generates a binary mixture flow (air and foreign vapors). This flow is studied using local self-similar boundary layer equations, and it is shown that the rise in the flow stagnation temperature and the corresponding evaporation of the wall material cause significant wall cooling and an increase in the near-wall density of the binary mixture. This modification of the boundary layer profiles leads to a decrease in the disturbance amplification rates. This is confirmed by calculations based on linear stability theory (LST). Boundary-layer stabilization occurs with an increase in stagnation temperature. The influence of surface sublimation on the position of the laminar–turbulent transition was estimated by means of the LST-based e N method. The possibility of increasing the transition Reynolds number by application of the sublimation coating is demonstrated. The results of pilot boundary layer transition experiments performed in a hot-shot wind tunnel are reported. For the first time, a delay in the transition due to the application of a naphthalene coating was experimentally demonstrated. It is also shown that surface sublimation leads to an increase in the growth rates of the second and third instability modes for a Mach 8 boundary layer.

### Effects of system rotation on diffusion of the disturbances in inhomogeneous strongly stratified flow

This study is an extension of our previous study [O. Iida, “Turbulent structure of stably stratified inhomogeneous flow,” Phys. Fluids 30, 045101 (2018)] where direct numerical simulations of a spectral method are performed for an inhomogeneous flow under stable density stratification by the inclusion of a fringe region where an artificial body force is imposed to make the flow locally disturbed, and thus, generated disturbances are horizontally diffused into the undisturbed laminar region. In this study, moreover, additional effects of system rotation on diffused disturbances are investigated in detail. As a result, we find that rotation makes the horizontally diffused disturbances anticyclonic vortices and that with a further increase in rotation, the horizontal diffusion is significantly attenuated, and their horizontal and vertical lengths decrease and increase, respectively. In addition, it is found that attenuating the energy cascade in the vertical direction simultaneously attenuates the horizontal enlargement of anticyclonic vortices.