# Latest papers in fluid mechanics

### Scale-dependent anisotropy in forced stratified turbulence

Author(s): C. J. Lang and Michael L. Waite

Anisotropy of stratified turbulence at different length scales is investigated with direct numerical simulation. Large scales, which are dominated by pancake vortices, are the most anisotropic, while the Ozmidov and dissipation scales are increasingly isotropic at larger buoyancy Reynolds number.

[Phys. Rev. Fluids 4, 044801] Published Wed Apr 03, 2019

### Inertial flow past a finite-length axisymmetric cylinder of aspect ratio 3: Effect of the yaw angle

Author(s): Jean-Lou Pierson, Franck Auguste, Abdelkader Hammouti, and Anthony Wachs

The flow past a finite-length yawed three-dimensional cylinder is investigated using direct numerical simulations. Various wake patterns are identified including the shedding of single-sided hairpin-shaped vortices.

[Phys. Rev. Fluids 4, 044802] Published Wed Apr 03, 2019

### Non-wetting droplets in capillaries of circular cross-section: Scaling function

Steady motion of long, non-wetting droplets carried by a surrounding liquid in a circular capillary has been the subject of many experimental, theoretical, and numerical simulation studies. Theoretical approaches, even after the application of lubrication approximation in hydrodynamic equations and after neglecting inertia and gravity effects, still lead to a numerical procedure to determine the speed of a droplet or the thickness of the film between a droplet and the wall of the capillary. Here, we develop the lubrication approximation further to introduce an analytical formula for the speed of droplets as a function of the capillary number and of the ratio of the viscosity coefficients of the two immiscible phases. We achieve this by identification of a scaling function within the lubrication approximation. The equations that we propose here corroborate well with the results of numerical simulations of droplet flow in circular capillaries.

### Steady streaming viscometry of Newtonian liquids in microfluidic devices

We report a novel technique capable of measuring the kinematic shear viscosity of Newtonian liquids with steady streaming flows in microfluidic devices. This probe-free microrheological method utilizes sub-kilohertz liquid oscillation frequencies around a cylindrical obstacle, ensuring that the inner streaming layer is comparable in size to the cylinder radius. To calibrate the viscometer, the evolution of the inner streaming layer as a function of the oscillation frequency for a liquid of known viscosity is characterized using standard particle tracking techniques. Once calibrated, we show how the steady streaming viscometer can be used to measure low-viscosity liquids.

### Thermocapillary thin-film flows on a compliant substrate

Author(s): Youchuang Chao and Zijing Ding

We study the dynamics of a thin liquid film on a compliant substrate in the presence of thermocapillary effect. A set of long-wave equations are derived to investigate the effects of fluid gravity (G), fluid inertia (Re), and Marangoni stresses (Ma) on the dynamics of the liquid film and the complia...

[Phys. Rev. E 99, 043101] Published Tue Apr 02, 2019

### Spontaneous oscillations, beating patterns, and hydrodynamics of active microfilaments

Author(s): Brato Chakrabarti and David Saintillan

We develop a geometrically nonlinear model of the flagellar axoneme that accounts for the stochastic kinetics of molecular motors and results in spontaneous oscillations. We capture the beating patterns of sperm, cilia and Chlamydomonas and analyze their hydrodynamics through reduced order models.

[Phys. Rev. Fluids 4, 043102] Published Tue Apr 02, 2019

### Pressure and spanwise velocity fluctuations in turbulent channel flows: Logarithmic behavior of moments and coherent structures

Author(s): Ali Mehrez, Jimmy Philip, Yoshinobu Yamamoto, and Yoshiyuki Tsuji

The logarithmic behavior of moments of the pressure and spanwise velocity fluctuations in turbulent channels is studied. Configurations of geometrically self-similar hairpin eddies play a key role in such behavior.

[Phys. Rev. Fluids 4, 044601] Published Tue Apr 02, 2019

### Analytical prediction of the hydraulic jump detachment length in front of mounted obstacles in supercritical open-channel flows

Detached hydraulic jumps are major features of supercritical open-channel flows interacting with emerging obstacles. Such a flow pattern exhibits strong similarities with shock waves detached in front of bluff bodies in supersonic aerodynamic flows. This paper aims at evaluating the capacities of an analytical model, adapted from supersonic aerodynamics, to predict the hydraulic jump detachment length. The analytical predictions are compared to the measured hydraulic jumps from two experiments: (i) a uniform supercritical open-channel flow that skirts a mounted and emerging obstacle (with a horseshoe vortex) and (ii) a mounted and emerging obstacle moving at constant velocity in water at rest (without a horseshoe vortex). Moreover, numerical calculations of supercritical flow skirting emerging obstacles are undertaken, with a free-slip condition at the bed to remove the horseshoe vortex, while keeping the detached hydraulic jump. The comparison of the detachment lengths of these experimental, analytical, and computed hydraulic jumps reveals that two types of detachment lengths can be defined. The detachment length visible on experiments corresponds to the toe of the hydraulic jump, while the detachment length predicted by the analytical model rather corresponds to the location of flow regime transition from the supercritical to subcritical regime. The present work thus validates the analytical model for predicting the location of flow regime transition (for configurations without a horseshoe vortex) but not for predicting the toe of the hydraulic jump. We finally confirm the strong connections between two distinct phenomena: a hydraulic jump in water flow and a shock wave in gas flow.

### A comparison of pre-impact gas cushioning and Wagner theory for liquid-solid impacts

The normal impact of a symmetric rigid body with an initially quiescent liquid half-space is considered using both Wagner theory and a model of viscous gas pre-impact cushioning. The predictions of these two theories are compared for a range of different body shapes. Both theories assume that the impactor has small deadrise angle. Novel solutions of the Wagner normal impact problem for a symmetric body with a power-law shape are presented, which generalize the well-known results for a parabola and a wedge. For gas cushioned pre-impacts, it is shown that a pocket of gas is entrained even for body shapes with a cusp at the body minimum. A scaling law is developed that relates the dimensions of the trapped gas pocket to the slope of the body. For pre-impact gas cushioning, surface tension is shown to smooth the liquid free-surface and delay the instant of touchdown for a smooth parabolic body, while for a wedge, increasing surface tension initially delays touchdown, before hastening touchdown as the importance of surface tension is increased further. For a flat-bottomed wedge, gas entrainment is again predicted in the gas-cushioning model although the location of initial touchdown, either on the transition between the wedge and the flat bottom or along the side of the wedge, now depends upon the parameters of the body shape.

### Wave profile along a ship hull, short farfield waves, and broad inner Kelvin wake sans divergent waves

The Neumann-Michell linear potential flow theory of the short farfield waves created by a ship that advances at a constant speed in calm water is coupled with nonlinear analytical relations for inviscid flow along the wave profile at the ship hull surface, i.e., the contact line between the ship hull surface and the free surface. This ad hoc coupling of linear farfield ship waves and a nonlinear nearfield flow along a ship waterline determines short farfield ship waves in terms of the free-surface elevation along the ship hull surface, and provides insight into the influence of nearfield nonlinearities (most significant at a ship waterline) on short farfield ship waves. For the Wigley parabolic ship model, nearfield nonlinearities are found to be relatively weak and to have a limited, although appreciable, influence on short farfield waves. The steepness of divergent ship waves is also analyzed. This analysis shows that, for a full-scale Wigley hull, divergent waves are too steep to exist inside a broad inner Kelvin wake with angle roughly equal to 13°, i.e., a third of Kelvin’s 39° ship wake angle.

### Influence of electric field on deformation of a drop in shear flow

The dynamics of a droplet in shear flow under the influence of an external electric field are investigated by performing extensive numerical simulations. The study is carried out by solving two-dimensional electrohydrodynamic equations, and the interface is captured using a volume-of-fluid approach. It is observed that with an increase in the drop size, a confined drop exhibits enhanced deformation and preferred orientation with the flow direction. For the case of dielectric fluids, the deformation of the drops can be either enhanced or reduced by varying the permittivity ratio and electric field strength. The nature of the polarisation forces acting at the interface can be either compressive or tensile depending on the magnitude of the permittivity ratio. The local electric field intensity inside the drop is significantly altered due to the permittivity contrast between the fluids. The computations for leaky dielectric fluids reveal that the deformation of the drop can be effectively tuned by altering the permittivity as well as the conductivity ratios. The nature of charge accumulation and the electric forces acting at the interface are critically dependent on the relative contrast between the electric properties of both the phases. The conductivity ratio decides the magnitude and nature of charge at the upper and lower portions of the droplet interface, thereby fundamentally maneuvering the droplet dynamics under the applied electric field.

### Experimental investigation of liquid film cooling in hypersonic flow

Film cooling is generally considered as a promising active cooling technology for developing thermal protection systems of hypersonic vehicles; however, most of experimental and numerical studies of film cooling mainly concentrated on gaseous film cooling. Since the phase change of liquid coolants can absorb a large amount of latent heat, liquid film cooling should have more potential advantages, especially for severe environments accompanied by hypersonic flight. To address this issue, the film cooling using water as a coolant was experimentally investigated in hypersonic flow. Experiments were carried out in a detonation tunnel, at a hypersonic Mach number of 6 using a 25° apex-angle wedge. Characteristic physical quantities, such as surface temperature rise, shock wave structure, film thickness, and cover area, are measured by thermocouples, schlieren, and a specially devised liquid film measurement system. The experimental results verify that the liquid film cooling is feasible in hypersonic flow and also indicate that it is featured with maintaining aerodynamic performances due to the weak effect on the main flow caused by coolant injection. Inspired by these results, liquid film flow characteristics and its influencing factors including mass flow rate, dynamic pressure, coolant injection direction, and surface tension are investigated to guide the design of a thermal protection system.

### Microscopic velocity field measurements inside a regular porous medium adjacent to a low Reynolds number channel flow

This study examines experimentally the hydrodynamic interaction between a regular porous medium and an adjacent free-flow channel at low Reynolds numbers (Re < 1). The porous medium consists of evenly spaced micro-structured rectangular pillars arranged in a uniform pattern, while the free-flow channel features a rectangular cross-sectional area. The overall arrangement comprises a polydimethylsiloxane microfluidic model where distilled water, doped with fluorescent particles, is the examined fluid. Using micro-particle image velocimetry, single-phase quantitative velocity measurements are carried out at the pore scale to reveal the microscopic characteristics of the flow for such a coupled system. Interfacial velocity-slip and stress-jump coefficients are also evaluated with a volume-averaging method based on the Beavers-Joseph and Ochoa-Tapia-Whitaker models, respectively. The results show that, from a microscopic point of view, parallel flow at the interface is not obtained due to the periodically generated U-shaped flow profile between the interface pillars. However, the interface coefficients show no sensitivity to moderate flow angles. The highly resolved experimental information obtained in this study can also be used for the validation of numerical models providing a unique dataset for free-flow and porous media coupled systems.

### Transport and dispersion of active particles in periodic porous media

Author(s): Roberto Alonso-Matilla, Brato Chakrabarti, and David Saintillan

The long-time transport of active Brownian particles flowing through a porous lattice is studied using generalized Taylor dispersion theory and Langevin simulations. The effects of motility, lattice geometry, and fluid flow on the asymptotic spreading of a dilute cloud of microswimmers are unraveled.

[Phys. Rev. Fluids 4, 043101] Published Mon Apr 01, 2019

### Magnetohydrodynamic effects in a shock-accelerated gas cylinder

Author(s): Wolfgang J. Black, Roy C. Allen, W. Curtis Maxon, Nicholas Denissen, and Jacob A. McFarland

We numerically study the effect of magnetic field orientation and strength on a shock-accelerated gas cylinder susceptible to the Richtmyer-Meshkov instability. We find regimes where fluid mixing increases with field strength and a preferential field orientation for damping the instability.

[Phys. Rev. Fluids 4, 043901] Published Mon Apr 01, 2019

### Sphere entry through an oil lens floating on water

Author(s): Linda B. Smolka and Clare K. McLaughlin

Entry of a sphere impacting an oil lens floating on a water surface is studied. An air-entraining cavity forms, lined by oil, which at collapse forms an oil filament connecting the upper and lower cavities. These dynamics are different than that of a sphere impacting water where no cavity forms at all.

[Phys. Rev. Fluids 4, 044001] Published Mon Apr 01, 2019

### High-enthalpy models for boundary-layer stability and transition

The prediction of the transition dynamics of high-enthalpy boundary-layer flows requires appropriate thermodynamic and transport models. This work quantifies the influence of transport, diffusion, collision, equilibrium, and chemical-kinetics modeling on the stability characteristics and the estimated transition-onset location of canonical boundary layers. The computed behavior of second-mode instabilities is consistently highly dependent on the base-flow’s boundary-layer height. The Blottner-Eucken-Wilke transport model is seen to underpredict the boundary-layer height, hence overpredicting the growth-rate distribution and forecasting the transition onset to occur ∼38% sooner. The other low-order transport models (Brokaw and Yos) returned very close results to the most-accurate Chapman-Enskog model. The use of Gupta et al.’s collisional data instead of Wright et al.’s more accurate data is also seen to predict the transition onset to occur ∼8% closer to the leading edge. The modeling of mass diffusion and the chemical-equilibrium constant is observed to have a negligible influence on the boundary-layer height and transition-onset-location estimations (less than 5% and 2%, respectively). For the analyzed conditions, all chemical models predict the same transition-onset location (±1%); since at the streamwise positions where perturbations have reached sufficiently large amplitudes, the flow is close to equilibrium and thus independent of the reaction rates. The use of different transport models for the perturbation terms, while maintaining the same model for the basic state, leads to negligible differences in the predictions. This further reinforces the thesis that the boundary-layer height calculation is paramount to the simulation of the development of second-mode instabilities.

### Construction of knotted vortex tubes with the writhe-dependent helicity

We propose a feasible method for constructing knotted vortex tubes with the finite thickness and arbitrary complexity and develop an accurate algorithm to implement this method in numerical simulations. The central axis of the knotted vortex tube is determined by the parametric equation of a given smooth and non-degenerate closed curve. The helicity of the vortex tube is only proportional to the writhe of the vortex axis, a geometric measure for coiling of vortex tubes. This vortex construction can facilitate the investigation of the conversion of writhe to twist in the helicity evolution of knotted vortex tubes. As examples, we construct velocity–vorticity fields of trefoil, cinquefoil, and septafoil vortex knots. These vortex knots are used as initial conditions in the direct numerical simulation of viscous incompressible flows in a periodic box. In the evolution of vortex knots from simple flows to turbulent-like flows, all the knots are first untied. Then the vortex topology is invariant and the helicity is almost conserved for the trefoil knot, whereas the helicity decays rapidly during the breakdown and coaxial interactions of pinch-off vortex rings for cinquefoil and septafoil knots.

### Control effect of micro vortex generators on leading edge of attached cavitation

In this study, we investigate the effects of micro vortex generators (VGs) installed close to the leading edge of a quasi-two-dimensional NACA0015 hydrofoil under cavitating and non-cavitating conditions. Our aim is to improve physical insight into interaction mechanisms of the boundary layer with the formation and stability of partial cavities. Under non-cavitating conditions, the proposed micro VGs effectively suppress laminar separation. However, under cavitating conditions, even very small micro VGs within the boundary layer promote the formation of counter-rotating cavitating vortices. In comparison with the smooth hydrofoil surface (without micro VGs), the cavitation onset is shifted toward the leading edge. Additionally, classical “fingering structures” and Tollmien–Schlichting waves are no longer present. Since the onset of the cavity does no longer appear at (or close to) the laminar separation line, a novel onset mechanism is observed experimentally. The mechanism consists of stable vortex cavitation, followed by vortex break-down into bubbly structures that are finally accumulated into an attached cavity region. By reduction in the height of the micro VGs, a delayed vortex break-down is found, leading to an increase in the length of the cavitating vortex pattern. This allows for enhanced control on the cavity dynamics, especially with respect to the penetration depth of the re-entrant jet. As a result of our investigation, we conclude that well suited micro VGs show a high potential to manipulate and control cavity dynamics.

### Numerical study of the shear-thinning effect on the interaction between a normal shock wave and a cylindrical liquid column

Based on adaptive mesh refinement, the SIM (Sharp-Interface Method) is utilized to numerically study the interaction between a shock wave and a liquid column as well as the evolution of the flow field. The SIM consists of the LSM (Level Set Method) and the GFM (Ghost Fluid Method). The LSM tracks the gas-liquid interface, and the GFM generates the virtual domains near the interface based on the gas-liquid interface condition. The hybridized GFM has been developed by integrating the Riemann GFM and the modified GFM together, which ensures the accuracy of the interface Riemann problem in the small deformation region of the interface while ensuring that the large interface deformation can be processed correctly. By comparing with the experimental results and the numerical results in previous literature, the good agreement shows that the above algorithm can accurately simulate the interactions between shock waves and liquid columns along with achieving the evolutions of the sharp gas-liquid interfaces. Based on the algorithm above, the interactions between the shock waves and the inviscid, the Newtonian, and the shear-thinning liquid columns are simulated, respectively. The numerical results indicate that the viscous effect can cause the bending of the liquid column and large deformation in the high shearing region. However, the shear thinning effect alleviates the bending and the deformation of the liquid column in the high shear region.