# Latest papers in fluid mechanics

### Boundary-layer transition over a rotating broad cone

Author(s): K. Kato, P. H. Alfredsson, and R. J. Lingwood

Twenty-four small roughness elements in the boundary layer on a rotating cone trigger stationary vortices, which grow and saturate, followed by a rapid growth of non-stationary modes and a transition to turbulence.

[Phys. Rev. Fluids 4, 071902(R)] Published Wed Jul 31, 2019

### Predicting the response of turbulent channel flow to varying-phase opposition control: Resolvent analysis as a tool for flow control design

Author(s): Simon S. Toedtli, Mitul Luhar, and Beverley J. McKeon

Resolvent analysis predicts and direct numerical simulation confirms that the effectiveness of opposition control depends on the phase between sensor and actuator. The results confirm the capability of resolvent analysis as a tool for flow control design and raise interesting flow physics questions.

[Phys. Rev. Fluids 4, 073905] Published Wed Jul 31, 2019

### Optimum air turbulence intensity for polydisperse droplet size growth

Author(s): M. Shyam Kumar, S. R. Chakravarthy, and Manikandan Mathur

Droplet size growth is usually enhanced by turbulence in the background air flow. Experimental measurements show the existence of an optimum air turbulent intensity for maximum droplet size growth in a polydisperse droplet field. The onset of clustering is shown to play an important role.

[Phys. Rev. Fluids 4, 074607] Published Wed Jul 31, 2019

### Statistics of single and multiple floaters in experiments of surface wave turbulence

Author(s): Nicolás F. Del Grosso, Lucía M. Cappelletti, Nicolás E. Sujovolsky, Pablo D. Mininni, and Pablo J. Cobelli

Laboratory experiments of floaters’ displacements in surface wave turbulence reveal that a combination of waves, eddies, and large-scale circulation team up to cause particle dispersion and preferential concentration. A simple physical model can reproduce all observations.

[Phys. Rev. Fluids 4, 074805] Published Wed Jul 31, 2019

### Drag force of polyethyleneglycol in flow measured by a scanning probe microscope

Author(s): Ruri Hidema, Seika Hayashi, and Hiroshi Suzuki

Drag force due to polyethyleneglycol in a flow was measured by using a scanning probe microscope. The conformation of the polymer in the flow was predicted to have a stem and ellipsoidal-flower shape. The drag force due to the deformed polymers predicted by this model was calculated and confirmed.

[Phys. Rev. Fluids 4, 074201] Published Tue Jul 30, 2019

### Kinetics of coarsening have dramatic effects on the microstructure: Self-similarity breakdown induced by viscosity contrast

Author(s): Hervé Henry and György Tegze

The viscous coarsening of a phase separated mixture is studied and the effects of the viscosity contrast between the phases are investigated. From an analysis of the microstructure, it appears that for moderate departure from the perfectly symmetric regime the self-similar bicontinuous regime is rob...

[Phys. Rev. E 100, 013116] Published Mon Jul 29, 2019

### Experimental estimation of turbulence modification by inertial particles at moderate ${\mathrm{Re}}_{λ}$

Author(s): D. O. Mora, A. Cartellier, and M. Obligado

We advance a new method to estimate the turbulent kinetic energy of the carrier phase in the presence of sub-Kolmogorov particles εp. Our results suggest that particles affect the carrier phase turbulent cascade in a nontrivial manner at concentrations close to ϕv=10−5, and Reλ∈[200,600].

[Phys. Rev. Fluids 4, 074309] Published Mon Jul 29, 2019

### Experimental study of second-mode wave on a flared cone at Mach 6

Second-mode instability plays an important role in the transition of a hypersonic boundary layer. The second-mode wave on a flared cone at Mach 6 has been investigated experimentally through the Nanoparticle-tracer based Planar Laser Scattering (NPLS) technique in this paper. Different behaviors of the second-mode wave ranging from linear growth to deformation are visualized under different unit Reynolds numbers. The propagation velocity of the second-mode wave is quantitatively calculated, and the spectral properties of the second-mode wave have been analyzed by the power spectrum density. The characteristic frequency of the second-mode wave calculated from the NPLS images agrees well with the results measured by the transducers. Evolution of the wall-normal distribution of disturbance shows that high frequency harmonics are generated during the growth process of the second-mode wave and its normal distribution range shrinks with the increase in its frequency. The bispectral analysis indicates that the high degree of phase coupling may be the reason for the deformation of the second-mode wave. The nonlinear interaction between the disturbance waves is strong during the deformation stage of the second-mode waves.

### Algebraic non-equilibrium wall-stress modeling for large eddy simulation based on analytical integration of the thin boundary-layer equation

An algebraic nonequilibrium wall-stress model for large eddy simulation is discussed. The ordinary differential equation (ODE) derived from the thin-layer approximated momentum equation, including the temporal, convection, and pressure gradient terms, is considered to form the wall-stress model. Based on the concept of the analytical wall function (AWF) for Reynolds-averaged turbulence models, the profile of the subgrid scale (SGS) eddy viscosity inside the wall-adjacent cells is modeled as a two-segment piecewise linear variations. This simplification makes it possible to analytically integrate the ODE near the wall to algebraically give the wall shear stress as the wall boundary condition for the momentum equation. By applying such integration to the wall-normal velocity component, the methodology to avoid the log-layer mismatch is also presented. Coupled with the standard Smagorinsky model, the proposed SGS-AWF shows good performance in turbulent channel flows at Reτ = 1000–5000 irrespective of the grid resolutions. This SGS-AWF is also confirmed to be superior to the traditional equilibrium wall-stress model in a turbulent backward-facing step flow.

### Understanding the secondary separation from an inclined square cylinder with sharp and rounded trailing edges

The steady separated flow past a square cylinder at 45° incidence and having a sharp/rounded base is a unique kind of separated flow around a symmetric bluff obstacle. At low Reynolds numbers (Re ≈ 6–8), this flow displays diverse features that are not known to be displayed by common symmetric bluff bodies, such as circular/square cylinders at zero incidence. The uniqueness of this flow was first highlighted by Kumar et al. [“Steady separation of flow from an inclined square cylinder with sharp and rounded base,” Comput. Fluids 171, 29–40 (2018)] in their recent numerical investigation concerning the onset of initial separation. They reported detailed flow kinematics resulting from separation of the laminar boundary layer via secondary mode, primary mode, and their combination. In this work, based on stabilized finite-element computations, the fluid dynamic aspects of primary and secondary separation are delved. The parameters considered are the normalized corner radius at the cylinder base and Re. Exploration of the influence of base radius on the occurrence/absence of the secondary separation is the main objective. The occurrence of secondary separation is a function of base radius. It occurs only with small or no rounding at the base, i.e., when the pressure gradient close to the base is favorable or mildly adverse. Irrespective of the base radius, the onset of secondary separation occurs at a constant Re value of 7.3. The drag decays as Re−0.62; it becomes invariant when Re is held constant. A new nondimensional parameter η accommodating the effects of pressure recovery and radius of curvature is introduced. The drag exhibits no sensitivity to η.

### Wake-induced vibration of a circular cylinder at a low Reynolds number of 100

Wake-induced vibration (WIV) of a circular cylinder in the wake of a stationary bluff body at a low Reynolds number of 100 is numerically investigated in this work. Square prism, rectangular plate, and triangular prism with the same projected width as the diameter of the circular cylinder are employed as the upstream bluff body to examine the effect of obstacle’s shape on the wake interference and WIV. The downstream circular cylinder is allowed to oscillate in both inline and crossflow directions. Three spacing ratios of 2, 4, and 6 are considered in the computations that carried out for a wide range of reduced velocities (Ur = 2–20). In terms of shear layer reattachment, vortex impingement, and wake interference, three distinct flow regimes are identified for the upstream-stationary-downstream-vibrating tandem cylinders, i.e., continuous reattachment regime, alternating reattachment regime, and coshedding regime. The wake flow pattern is sensitive to the spacing ratio and the reduced velocity. Due to the vigorous streamwise response, the gap between the tandem cylinders varies over time and hence the switching of wake regime. Both the hydrodynamic forces and vibration response are tightly associated with the wake interaction. Among the three configurations, the cylinder behind a square prism possesses the largest cross-flow amplitude, while the cylinder behind a plate and that behind a triangular prism present more oscillating characteristics in the response amplitude, due mainly to the unstable and irregular vortex evolution.

### Lift force acting on a pair of clean bubbles rising in-line

In this study, we experimentally observed the motion of a pair of bubbles initially positioned in line, especially focusing on the intermediate Reynolds number case, i.e., 20 < Re < 60. We observed three types of motion at different Reynolds numbers. At a low Reynolds number (Re < 20), the trailing bubble collided with the leading bubble like a pair of rigid spheres. At a high Reynolds number (100 < Re), the trailing bubble moved out from the original vertical line joining the two bubbles. At intermediate Reynolds numbers (20 < Re < 60), small differences in bubble size affected the motion. When the leading bubble was larger than or equal to the trailing bubble, the trailing bubble first approached the leading bubble and later moved out from the initial vertical line owing to a lift force. When the leading bubble was smaller than the trailing bubble, the trailing bubble first approached the leading bubble, and then a repulsive force acted on both bubbles so that both of them moved out from the vertical line in opposite directions. These motions are attributed to two effects, the first is potential effects at short distance between bubbles, and the second is the wake of the leading bubble.

### Nonlinear stability results for plane Couette and Poiseuille flows

Author(s): Paolo Falsaperla, Andrea Giacobbe, and Giuseppe Mulone

We prove that the plane Couette and Poiseuille flows are nonlinearly stable if the Reynolds number is less than ReOrr(2π/(λsinθ))/sinθ when a perturbation is a tilted perturbation in the direction x′ which forms an angle θ∈(0,π/2] with the direction i of the basic motion and does not depend on x′. R...

[Phys. Rev. E 100, 013113] Published Fri Jul 26, 2019

### Clustering and energy spectra in two-dimensional dusty gas turbulence

Author(s): Vikash Pandey, Prasad Perlekar, and Dhrubaditya Mitra

This work presents two-dimensional simulations of particles embedded in a turbulent flow. The particles are capable of modifying the flow by interacting with the fluid. The authors study the behavior of this system as the Stokes number and the particle concentration change, and uncover a new scaling behavior that shows a dependence on those two variables.

[Phys. Rev. E 100, 013114] Published Fri Jul 26, 2019

### Electrical conductivity and tortuosity of solid foam: Effect of pore connections

Author(s): V. Langlois, V. H. Trinh, and C. Perrot

Numerical and analytical methods at both micro- and mesoscales are used to study how the electrical resistivity and the high-frequency tortuosity of solid foam are modified by the presence of membranes that partially or totally close the cell windows connecting neighbor pores. Finite-element-method ...

[Phys. Rev. E 100, 013115] Published Fri Jul 26, 2019

### Experimental investigation of the interaction of a weak planar shock with grid turbulence in a counter-driver shock tube

Author(s): Takahiro Tamba, Gaku Fukushima, Masaya Kayumi, Akira Iwakawa, and Akihiro Sasoh

The interaction of a planar shock wave with grid generated turbulence finds that at first the turbulence increases the projection thickness of the shock and then at higher intensities fragments the shock.

[Phys. Rev. Fluids 4, 073401] Published Fri Jul 26, 2019

### Basset-Boussinesq history force of a fluid sphere

Author(s): Dominique Legendre, Azeddine Rachih, Claire Souilliez, Sophie Charton, and Eric Climent

Direct numerical simulations are used to characterize the equivalent slip length at a spherical drop interface under Stokes flow conditions. An analytic form of the memory kernel for the force acting on a viscous drop is proposed and validated.

[Phys. Rev. Fluids 4, 073603] Published Fri Jul 26, 2019

### Evolution of wall shear stress with Reynolds number in fully developed turbulent channel flow experiments

Author(s): Pierre-Alain Gubian, Jordan Stoker, James Medvescek, Laurent Mydlarski, and B. Rabi Baliga

An experimental study concludes that beyond Reτ∼600, the wall shear stress (τw) evolves to an asymptotic state in which the statistical moments, probability density function, and power spectra of τw become independent of Reynolds number.

[Phys. Rev. Fluids 4, 074606] Published Fri Jul 26, 2019

### Detour induced by the piston effect in the oscillatory double-diffusive convection of a near-critical fluid

The nonlinear oscillatory double-diffusive convection in a thermodynamically near-critical binary fluid layer is investigated to explore the interactions between the piston effect and natural convection in the presence of subcritical bifurcation. The bifurcation diagram of the system is studied. Two subcritical bifurcation branches are depicted, which, together with the trivial branch of pure diffusion, are connected by two hysteresis loops. To understand the role of the piston effect, the Boussinesq counterpart of the near-critical system is considered and compared. Results show that the onset of convection is significantly altered by the piston effect. For the Boussinesq system, the lower boundary layer becomes unstable, brings on finite-amplitude perturbations, and leads to a statistically steady state. However, the near-critical system features a two-stage evolution. In the first stage, the lower boundary layer becomes unstable and then returns to stability. As soon as the temperature field relaxes into the second stage, a change of criterion occurs, and the fluid becomes unstable again. The residual convection motions amplify and finally result in finite-amplitude convection. By this means, the near-critical system becomes insensitive to the existence of the higher equilibrium state in hysteresis loops, and detours relative to the Boussinesq system are observed. This paper gives new insights into the piston effect and its interactions with natural convection from a dynamic system point of view. The conclusions can be extended to other situations where subcritical bifurcations exist.

### Heteroclinic and homoclinic connections in a Kolmogorov-like flow

Author(s): Balachandra Suri, Ravi Kumar Pallantla, Michael F. Schatz, and Roman O. Grigoriev

Recent studies suggest that unstable recurrent solutions of the Navier-Stokes equation provide new insights into dynamics of turbulent flows. In this study, we compute an extensive network of dynamical connections between such solutions in a weakly turbulent quasi-two-dimensional Kolmogorov flow tha...

[Phys. Rev. E 100, 013112] Published Thu Jul 25, 2019