# Latest papers in fluid mechanics

### Numerical simulation of two coalescing turbulent forced plumes in linearly stratified fluids

A computational fluid dynamic model that can solve the Reynolds-averaged Navier-Stokes equations and the species transport equation is developed to simulate two coalescing turbulent forced plumes, which are released with initial momentum and buoyancy flux into a linearly stable stratified environment. The velocity fields, turbulence structures, and entrainment of two plumes with different source separations and source buoyancy fluxes are analyzed quantitatively, in comparison with a series of physical experiments. An empirical parameterization is proposed to predict the amplification of the maximum rise height of two coalescing forced plumes caused by superposition and mutual entrainment. The maximum values of both turbulent kinetic energy and turbulence dissipation rate decrease monotonically with the increase in source separation of the two turbulent plumes. However, the trajectory of the maximum turbulent viscosity attained in the plume cap region presents two notable enhancements. This variation may be attributed to the turbulence transported from the touching region and the strong mixing around the neutrally buoyant layer between two plumes, while the mixing is caused by the lateral convection and the rebound after overshooting. The plume entrainment coefficient in near vent stems has a positive relationship with the source Richardson number. A transition of flow regimes to plume-like flows would occur when the contribution of initial momentum is important. The entrainment coefficient will decrease in the touching region of two plumes due to mutual entrainment, while the superposition of plumes can lead to distortion of the boundary of plume sectors.

### Analog cosmology with two-fluid systems in a strong gradient magnetic field

Author(s): Zack Fifer, Theo Torres, Sebastian Erne, Anastasios Avgoustidis, Richard J. A. Hill, and Silke Weinfurtner

Inflation refers to the exponential expansion of the early universe that can explain many of the properties we see today. The authors of this work propose an experimental analog in which the interface between two immiscible, magnetic fluids shows inflationary behavior. The work shows that waves created at the interface could reproduce known solutions of inflationary models, and suggests a variety of other cosmological scenarios that could be simulated.

[Phys. Rev. E 99, 031101(R)] Published Wed Mar 27, 2019

### Effect of pressure on joint cascade of kinetic energy and helicity in compressible helical turbulence

Author(s): Zheng Yan, Xinliang Li, Jianchun Wang, and Changping Yu

Direct numerical simulations of three-dimensional compressible helical turbulence are carried out at a grid resolution of 10243 to investigate the effect of pressure, which is important for the joint cascade of kinetic energy and helicity in compressible helical turbulence. The principal finding is ...

[Phys. Rev. E 99, 033114] Published Wed Mar 27, 2019

### Localized Faraday patterns under heterogeneous parametric excitation

Author(s): Héctor Urra, Juan F. Marín, Milena Páez-Silva, Majid Taki, Saliya Coulibaly, Leonardo Gordillo, and Mónica A. García-Ñustes

Faraday waves are a classic example of a system in which an extended pattern emerges under spatially uniform forcing. Motivated by systems in which uniform excitation is not plausible, we study both experimentally and theoretically the effect of heterogeneous forcing on Faraday waves. Our experiment...

[Phys. Rev. E 99, 033115] Published Wed Mar 27, 2019

### Liquid spreading on cold surfaces: Solidification-induced stick-slip dynamics

Author(s): Rémy Herbaut, Philippe Brunet, Laurent Limat, and Laurent Royon

Spreading of liquid on a cold substrate with freezing is investigated. Experimental investigation of the criterion for a solidification-induced pinning of the liquid near the triple line finds that below a temperature-dependent velocity, spreading shows stick-slip dynamics.

[Phys. Rev. Fluids 4, 033603] Published Wed Mar 27, 2019

### On the inherent bias of swirling strength in defining vortical structure

The traditional practice of using rotational motion as the principal attribute of coherent vortical structures in the buffer region of near-wall turbulent flow is shown to create a biased accounting of the role of vorticity within the structures. Vorticity associated with rotation is given a favored consideration against vorticity that is equally strong but not associated with rotation. Using data from a highly resolved direct numerical simulation of channel flow, it is shown that describing the structures based on the properties of the rotational field leads to a distorted view of the actual structures that are present. As a practical matter, this means that where hairpins are typically considered to be the flow structures, a more accurate description of the coherent events is that they are elongated mushroom-shaped vortical objects ejecting over low speed streaks. In this, hairpin-shaped rotational regions are embedded in the lobes of the mushrooms.

### Enhanced imbibition from the cooperation between wetting and inertia via pulsatile forcing

We study the dynamics of microfluidic interfaces driven by pulsatile pressures in the presence of neutral and hydrophilic walls. For this, we propose a new phase field model that takes inertia into account. For neutral wetting, the interface dynamics is characterized by a response function that depends on a non-dimensional frequency, which involves the time scale associated with inertia. We have found a regime, for large values of this non-dimensional frequency, in which inertia is relevant, and our model is necessary for a correct description of the dynamics. For hydrophilic walls, the dynamics of the contact line with pulsatile forcing is basically undistinguishable to the dynamics of imbibition solely due to wetting. However, we observe that the presence of inertia causes the interface to advance faster than in the absence of pulsatile forcing. This is because pulsatile forcing induces inertia at the bulk to cooperate with wetting creating an enhancement of the imbibition process. We characterize this complex dynamics with transitory exponents that, at early times, are larger than the Washburn ones, and tend to the Washburn exponent at long times, when the interface feels less and less the driving force applied at the entrance of the microchannel, and the dynamics is dominated solely by wetting.

### Harmonic linearized Navier-Stokes equation on describing the effect of surface roughness on hypersonic boundary-layer transition

Laminar-turbulent transition is crucially influenced by wall roughness. This paper develops a numerical approach based on the harmonic linearized Navier-Stokes (HLNS) equations to accommodate the scattering effect of the rapidly distorted mean flow induced by a two-dimensional hump or indentation at the wall on the oncoming instability modes (including the Mack first and second modes) in a hypersonic boundary layer. Due to the ellipticity of the scattering system when the roughness width is comparable with the instability wavelength, the traditional linear stability theory and the linear parabolized stability equation do not apply, and therefore, the HLNS approach has advantages in both accuracy and efficiency. The impact of a roughness is characterized by a transmission coefficient, which is the ratio of the asymptotic amplitude downstream of the roughness to that upstream. At a Mach number of 5.92, the dependence of the transmission coefficient on the frequency and the oblique angle of the oncoming mode and the size and location of the hump/indentation is studied systematically. It is confirmed that the synchronization frequency appears as a critical frequency, above and below which the oncoming instability modes are suppressed and enhanced by the roughness, respectively, which provides fundamental basis to the laminar-flow control in hypersonic boundary layers.

### Using vortex identifiers to build eddy-viscosity subgrid-scale models for large-eddy simulation

Author(s): Xingjun Fang, Bing-Chen Wang, and Donald J. Bergstrom

A generalized framework of incorporating vortex identifiers into subgrid-scale models for large-eddy simulation is presented. The proposed models can automatically identify the under-resolved vortex stretching process and drain energy from the inertial subrange.

[Phys. Rev. Fluids 4, 034606] Published Tue Mar 26, 2019

### Scattering of surface shallow water waves on a draining bathtub vortex

Author(s): Semyon Churilov and Yury Stepanyants

Wave scattering on a bathtub vortex in shallow water is studied in the linear approximation. The results obtained are relevant to the interpretation of laboratory experiments and can be considered the hydrodynamic model of wave scattering by a rotating black hole in general relativity.

[Phys. Rev. Fluids 4, 034704] Published Tue Mar 26, 2019

### On two-dimensional self-similar axisymmetric vortices

Superpositions of Lamb-Oseen axisymmetric vortices with Gaussian vorticity having zero net circulation and finite kinetic energy in unbounded domain are considered. Their evolution is described by self-similar solutions depending on a certain combination of space, time, and viscous diffusion. It is shown that the structure of a popular self-similar solution for a shielded vortex with Gaussian fluid rotation rate corresponds to two Lamb-Oseen vortices with opposite sign and nearly the same spatial scale. The radial structure of a combined vortex with different spatial scales is well suited for characterization of realistic vortical structures like atmospheric hurricanes. The linear stability of the combined vortex is investigated. The results have important implications for better understanding of vortex structures in two-dimensional flow.

### A non-dimensional parameter for classification of the flow in intracranial aneurysms. II. Patient-specific geometries

A simple parameter, called the Aneurysm number (An) which is defined as the ratio of transport to vortex time scales, has been shown to classify the flow mode in simplified aneurysm geometries. Our objective is to test the hypothesis that An can classify the flow in patient-specific intracranial aneurysms (IA). Therefore, the definition of this parameter is extended to anatomic geometries by using hydraulic diameter and the length of expansion area in the approximate direction of the flow. The hypothesis is tested using image-based flow simulations in five sidewall and four bifurcation geometries, i.e., if An ≲ 1 (shorter transport time scale), then the fluid is transported across the neck before the vortex could be formed, creating a quasi-stationary shear layer (cavity mode). By contrast, if An ≳ 1 (shorter vortex time scale), a vortex is formed. The results show that if An switches from An ≲ 1 to An ≳ 1, then the flow mode switches from the cavity mode to the vortex mode. However, if An does not switch, then the IAs stay in the same mode. It is also shown that IAs in the cavity mode have significantly lower An, temporal fluctuations of wall shear stress and oscillatory shear index (OSI) compared to the vortex mode (p < 0.01). In addition, OSI correlates with An in each flow mode and with pulsatility index in each IA. This suggests An to be a viable hemodynamic parameter which can be easily calculated without the need for detailed flow measurements/ simulations.

### A non-dimensional parameter for classification of the flow in intracranial aneurysms. I. Simplified geometries

Non-dimensional parameters are routinely used to classify different flow regimes. We propose a non-dimensional parameter, called Aneurysm number (An), which depends on both geometric and flow characteristics, to classify the flow inside aneurysm-like geometries (sidewalls and bifurcations). The flow inside aneurysm-like geometries can be widely classified into (i) the vortex mode in which a vortex ring is formed and (ii) the cavity mode in which a stationary shear layer acts similar to a moving lid of a lid-driven cavity. In these modes, two competing time scales exist: (a) a transport time scale, Tt, which is the time scale to develop a shear layer by transporting a fluid particle across the expansion region, and (b) the vortex formation time scale, [math]. Consequently, a relevant non-dimensional parameter is the ratio of these two time scales, which is called Aneurysm number: An = Tt/[math]. It is hypothesized, based on this definition, that the flow is in the vortex mode if the time required for vortex ring formation [math] is less than the transport time Tt (An ≳ 1). Otherwise, the flow is in the cavity mode (An ≲ 1). This hypothesis is systematically tested through numerical simulations on simplified geometries and shown to be true through flow visualizations and identification of the main vortex and shear layer. The main vortex is shown to evolve when An ≳ 1 but stationary when An ≲ 1. In fact, it is shown that the flows with An ≲ 1 (cavity mode) are characterized by much smaller fluctuations of wall shear stress and oscillatory shear index relative to flows with An ≳ 1 (vortex mode) because of their quasi-stationary flow pattern (cavity mode) compared to the evolution and breakdown of the formed vortex ring (vortex mode).

### Elastohydrodynamics of swimming helices: Effects of flexibility and confinement

Author(s): John LaGrone, Ricardo Cortez, and Lisa Fauci

We examine the swimming of an elastic helix rotated by a torque at its base, both in free-space and confined to a tube. The image depicts the envelope of an excursion of a filament centerline over one rotation; the blue is the surface of the finite-radius helical filament at one snapshot in time.

[Phys. Rev. Fluids 4, 033102] Published Mon Mar 25, 2019

### Experimental study of convection in the compressible regime

Author(s): Rémi Menaut, Yoann Corre, Ludovic Huguet, Thomas Le Reun, Thierry Alboussière, Michael Bergman, Renaud Deguen, Stéphane Labrosse, and Marc Moulin

Compressible thermal convection is experimentally studied. In the large apparent gravity of a rotor centrifuge, using xenon gas, an adiabatic temperature difference of 14 °C over a height equal to 4 cm is obtained. Large Coriolis forces impose a quasigeostrophic regime.

[Phys. Rev. Fluids 4, 033502] Published Mon Mar 25, 2019

### Diffusion-driven transition between two regimes of viscous fingering

Author(s): Thomas E. Videbæk and Sidney R. Nagel

Diffusion between miscible fluids in the viscous-fingering instability produces an unexpected transition into a novel pattern. Usually thought of as a two-dimensional phenomena, this works shows the importance of three-dimensional structure to the patterns that form.

[Phys. Rev. Fluids 4, 033902] Published Mon Mar 25, 2019

### Inviscid flow separation at the crest of an erodible dune

Author(s): F. Charru and P. Luchini

Potential flow analysis is used to find the elevation profile of traveling dunes of given volume and locate the brink point where the flow separates without singularity.

[Phys. Rev. Fluids 4, 034304] Published Mon Mar 25, 2019

### Streamline segment statistics propagation in inhomogeneous turbulence

Author(s): A. Rubbert, M. Albers, and W. Schröder

Streamline segment statistics are collected from tomographic particle image velocimetry and direct numerical simulation data of a turbulent wavy channel flow. The model equation for such statistics is adapted for inhomogeneous turbulence. The novel formulation is applied to explain the observations and identify the locally acting mechanisms.

[Phys. Rev. Fluids 4, 034605] Published Mon Mar 25, 2019

### Vorticity dynamics of the three-dimensional Taylor-Green vortex problem

The three-dimensional (3D) Taylor-Green Vortex (TGV) flow problem has been used to study turbulence from genesis to eventual decay governed by the 3D Navier-Stokes equation. The evolution of the TGV shows that the solution becomes unstable at very early times and eventually becomes turbulent, but a study of this transition has not been advanced so far. The computations are performed using a high accuracy compact scheme on a uniform grid, with the fourth-order Runge-Kutta time integration method. The vector potential-vorticity ([math])-formulation of the governing equations is solved in a cubic periodic domain with one complete basic unit of a TGV cell in the interior of the domain at t = 0. The TGV problem allows one to study the vorticity dynamics using highly accurate formulation because of periodic boundary conditions. Simulations performed for different Reynolds numbers and grid resolutions reveal that numerical error in computations induce a period-doubling bifurcation, which leads to new spatial symmetries maintained up to intermediate times, followed by simultaneous stretching and fragmentation of vortices resulting in a decaying turbulent flow. The compensated energy spectrum of the 3D TGV flow displays inertial subrange at t = 9, after which the generated turbulence starts decaying. The power law for turbulent kinetic energy decay is analyzed, and the decay exponent is noted to approach unity as time increases.

### Thermal effects on the instability of coaxial liquid jets in the core of a gas stream

The breakup of coaxial liquid jets in a co-flowing gas stream under the radial thermal field is studied by the linear instability theory. A simplified physical model is established, and an analytical dimensionless dispersion relation for temporally axisymmetric perturbations is derived and solved numerically. The outer liquid-gas surface tension coefficient is assumed to be a linear function of temperature. Due to the radial temperature gradients, the time-dependent spatial variation of surface tension gives rise to a shear stress and induces Marangoni force upon the flow. The effects of different process parameters on the characteristics of unstable modes including the para-sinuous mode and the para-varicose mode are explored. It is found that the para-sinuous mode always dominates the jet instability in the parametric regions and the increasing temperature ratio of the surrounding gas stream and the inner liquid jet (T31) can reduce the maximum growth rates of unstable modes and corresponding dominant wavenumbers. The Reynolds number destabilizes the jet instability, and the Weber number suppresses it at relatively long wavelengths for both isothermal and non-isothermal situations. The Marangoni number and the Peclet number have a destabilizing effect for T31 < 1, but it is opposite for T31 > 1. These theoretical predictions would provide insight into underlying physical mechanisms of thermal jet breakup and compound droplet formation.