# Latest papers in fluid mechanics

### 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.

### Bubble dynamics and pressure field characteristics of underwater detonation gas jet generated by a detonation tube

An underwater detonation tube (DT) experiment is carried out in a water tank to investigate the bubble dynamics and pressure field characteristics of an underwater detonation gas jet. In the experiment, a 0.78 liter DT filled with a 0.29 MPa methane–oxygen mixture (equivalent to 0.85 mg of TNT, trinitrotoluene) is detonated. By means of high-speed photography and pressure field measurements, the jet process is divided into four different stages. The evolution patterns and features of the four stages are characterized according to the morphology of the detonation gas bubble, and the dimensionless parameters of the bubble dynamics are defined and calculated using image post-processing. The transmitted shock wave and pressure pulsations of the bubble oscillations are extracted using a low-pass filter with a cutoff frequency of 1000 Hz. The time intervals between consecutive pressure peaks are compared with the oscillation periods obtained from parameter studies of bubble dynamics. The bubble dynamics generated by the sudden release of detonation products in the first oscillation are found to be similar to those of underwater explosions. An expansion-necking structure is observed, formed by the impulsive release of the remaining detonation gas from the DT. A numerical simulation is conducted under the same filling conditions as the experiment to supplement the experimental results. The experiment demonstrates the feasibility of underwater detonation gas jets, which could provide an alternative means of generating pulsation bubbles.

### Energetic motions in turbulent partially filled pipe flow

Turbulent partially filled pipe flow was investigated using stereoscopic particle imaging velocimetry in the cross-stream plane for a range of flow depths at a nominally constant Reynolds number of 30 000 (based on the bulk velocity and hydraulic diameter). Unlike full pipe flow, which is axisymmetric, the turbulent kinetic energy exhibits significant azimuthal (and radial) variation. Proper orthogonal decomposition (POD) of the fluctuating velocity field indicates that the leading-order POD modes occupy the “corners” where the free surface meets the pipe wall and that these modes, which are closely linked to the instantaneous cellular structure, contribute nearly a quarter of the overall turbulent kinetic energy. Spatial distributions of the large- and very-large-scale motions (LSMs/VLSMs) estimated from pseudo-instantaneous three-dimensional velocity fields reveal a preference for the sides (in close proximity to the free surface) and bottom quadrant of the pipe. That the LSMs and VLSMs are shown to populate a region spanning the width of the free surface, as well as the corners, strongly suggests that there is a dynamical connection between LSMs/VLSMs and the instantaneous cellular structures in turbulent partially filled pipe flow, which can explain the spatial redistribution of the turbulent kinetic energy.

### Energetic motions in turbulent partially filled pipe flow

Turbulent partially filled pipe flow was investigated using stereoscopic particle imaging velocimetry in the cross-stream plane for a range of flow depths at a nominally constant Reynolds number of 30 000 (based on the bulk velocity and hydraulic diameter). Unlike full pipe flow, which is axisymmetric, the turbulent kinetic energy exhibits significant azimuthal (and radial) variation. Proper orthogonal decomposition (POD) of the fluctuating velocity field indicates that the leading-order POD modes occupy the “corners” where the free surface meets the pipe wall and that these modes, which are closely linked to the instantaneous cellular structure, contribute nearly a quarter of the overall turbulent kinetic energy. Spatial distributions of the large- and very-large-scale motions (LSMs/VLSMs) estimated from pseudo-instantaneous three-dimensional velocity fields reveal a preference for the sides (in close proximity to the free surface) and bottom quadrant of the pipe. That the LSMs and VLSMs are shown to populate a region spanning the width of the free surface, as well as the corners, strongly suggests that there is a dynamical connection between LSMs/VLSMs and the instantaneous cellular structures in turbulent partially filled pipe flow, which can explain the spatial redistribution of the turbulent kinetic energy.

### Jetting behavior as a bubble bursts in free space

The phenomenon of bubble bursting is very common in nature and is of prime importance in various technologies and industrial processes. Similar to interfacial bubbles, the process of a bubble bursting in free space, that is, the rupture of bubbles surrounded by air, often results in jet flows. However, the location and mechanism of the jet flows are different from those produced by interfacial bubbles. This paper describes the results of several experiments conducted to investigate the behavior of a bubble bursting in free space, especially the jet flows that occur at the end of the process. The results show that viscosity has a strong inhibitory effect on both the droplets (film drops and jet drops) and the jet resulting from bubble bursting. Based on experimental results, we establish a phase diagram for the jetting behavior in terms of the Reynolds number (Re) and the Ohnesorge number (Oh) and discover the existence of threshold conditions. Jetting occurs in the zone where Oh is less than some threshold value Ohc and Re is greater than some threshold value Rec, whereas a liquid clump appears in the zone where Oh > Ohc and Re < Rec. For 0.002 < Oh < 0.272 and 65 < Re < 52 633, we find that Rec = 503 ± 136 and Ohc = 0.079 ± 0.001. A schematic of the events that occur during bubble bursting depicting the forces at play is subsequently analyzed, and the role of viscosity at the moment of jetting is highlighted. The results of this study can be used to inhibit or increase the formation of droplets in numerous applications.

### On spontaneous appearance of internal waves in an open-pool-type research reactor

Variation of temperature in time and space was recorded at multiple vertical locations in the course of initiation of a heated water layer in an open-pool research reactor of the Soreq Nuclear Research Center. The pool was initially filled with warm water, and heavier cooler water was then injected at the bottom of the facility. Different modes of coolant injection were employed in two different experiments. In both cases, a finite width thermocline that separated cool water at the lower part of the pool from the warm water in its upper part was observed. The thermocline gradually moved up eventually attaining a constant raise velocity. In both experiments, the thermocline characteristics were different, but wave-trains with notable temperature fluctuations were observed within the thermocline. The characteristic frequencies of oscillations were below the Brunt–Väisälä frequencies that characterize the density gradient within the thermoclines. The finite dimensions of the tank impose conditions in which standing internal waves with the length commensurate with tank size can be expected. The oscillations were thus associated with resonant internal waves excited by disturbances introduced by the coolant flow at the lower part of the pool. In both experiments, the measured wave spectra agree with the results of linear analysis of two-layer and three-layer stratification models.

### Flows between orthogonally stretching parallel plates

Navier–Stokes equilibrium solutions of a viscous fluid confined between two infinite parallel plates that can independently stretch or shrink in orthogonal directions are studied. It is assumed that the admissible solutions satisfy spatial self-similarity in the stretching or shrinking perpendicular coordinates. The nonlinear steady boundary-value problem is discretized using a spectral Legendre method, and equilibrium solutions are found and tracked in the two-dimensional parameter space by means of pseudo-arclength continuation Newton–Krylov schemes. Different families of solutions have been identified, some of which are two-dimensional and correspond to the classical Wang and Wu self-similar flows arising in a plane channel with one stretching–shrinking wall [Wang, C.-A. and Wu, T.-C., “Similarity solutions of steady flows in a channel with accelerating walls,” Comput. Math. Appl. 30, 1–16 (1995)]. However, a large variety of three-dimensional solutions have also been found, even for low stretching or shrinking rates. When slightly increasing those rates, some of these solutions disappear at saddle-node bifurcations. By contrast, when both plates are simultaneously stretching or shrinking at higher rates, a wide variety of new families of equilibria are created and annihilated in the neighborhood of cuspidal codimension-2 bifurcation points. This behavior has similarities with the one observed in other planar and cylindrical self-similar flows.

### Stability of a reverse Karman vortex street

The reverse vortex street differs from the ordinary Karman vortex street in the direction of the rotation of the vortices. Such a street is formed behind the oscillating airfoils in the flow. It is of interest in connection with studies of the aerodynamics of flapping wings. It is known that the vortex wake behind a symmetric airfoil performing symmetric oscillations in a certain range of parameters becomes asymmetric, which leads to the appearance of a nonzero average lift. Reasons of the symmetry violation are associated with the instability of the reverse vortex street, but the mechanism of this instability is currently not well understood. In this work, the analysis of the stability of the reverse vortex street is carried out on the basis of the theory developed by Karman for infinite rows of point vortices. In contrast to the Karman model, in this work, semi-infinite rows with periodically arising new vortices at their ends are considered. This is the first time this model has been used. It is shown that the periodic appearance of new vortices radically affects the characteristics of the street stability. It is found that the violation of the symmetry of the reverse vortex street is associated with its instability to bending perturbations, while the ordinary Karman vortex street behind the body is unstable to varicose perturbations. Regions of instability are determined.

### Comparative study on numerical performances of log-conformation representation and standard conformation representation in the simulation of viscoelastic fluid turbulent drag-reducing channel flow

In this paper, a new derivation process of the log-conformation governing equation for viscoelastic fluid flows is presented by using the Taylor series definition of the matrix logarithm. Based on the log-conformation representation (LCR) and standard conformation representation (CR) methods, the turbulent drag-reducing channel flow of viscoelastic fluid described by the Oldroyd-B constitutive model is simulated by the finite difference method. The comparison illustrates that the turbulent drag reduction (DR) effect under the condition of a low Weissenberg number (Wi = 1) or moderate Weissenberg number (Wi = 5) can be successfully reproduced by the CR method but is very difficult to be obtained by the LCR method at the same grid resolution if the commonly used interpolation approaches in the computing domain (i.e., log domain) are employed. Further research reveals that the interpolation method of log-conformation tensor involved is one of the dominant reasons responsible for the disability to obtain a turbulent DR effect by using the LCR method. If the interpolation is performed in a physical domain, the turbulent DR effect can be reproduced by using the LCR method. If the interpolation involved in the CR method is carried out in a log domain, the turbulent DR phenomenon can still be simulated but with a weakened DR effect. In sum, this study demonstrates that the commonly used interpolation approaches in the log domain should be responsible for the poor performance of the LCR method.