# Latest papers in fluid mechanics

### Nonlinear dynamics of two coupled bubbles oscillating inside a liquid-filled cavity surrounded by an elastic medium

Author(s): Alexander A. Doinikov, Diane Bienaimé, S. Roberto Gonzalez-Avila, Claus-Dieter Ohl, and Philippe Marmottant

A theory is developed to model the nonlinear dynamics of two coupled bubbles inside a spherical liquid-filled cavity surrounded by an elastic medium. The aim is to study how the conditions of full confinement affect the coupled oscillations of the bubbles. To make the problem amenable to analytical ...

[Phys. Rev. E 99, 053106] Published Thu May 09, 2019

### Characteristics of mean flow and turbulence in bubble-in-chain induced flows

Author(s): Binbin Wang and Scott A. Socolofsky

Mean flow and turbulence in bubble-in-chain induced flows are experimentally observed at various release frequencies and flow rates. We find that horizontal water velocity profiles collapse to a universal Gaussian distribution and one-dimensional velocity spectra to a consistent slope of −3.

[Phys. Rev. Fluids 4, 054302] Published Thu May 09, 2019

### Chaotic few-body vortex dynamics in rotating Bose-Einstein condensates

Author(s): Tiantian Zhang, James Schloss, Andreas Thomasen, Lee James O'Riordan, Thomas Busch, and Angela White

A study of vortex dynamics in a confined superfluid shows that a system of three co-rotating quantum vortices and one vortex of opposite rotation exhibit chaotic dynamics. We find the onset of chaos is seeded through the close approach and separation of vortices in a scattering event.

[Phys. Rev. Fluids 4, 054701] Published Thu May 09, 2019

### Numerical study of the landslide tsunami in the South China Sea using Herschel-Bulkley rheological theory

The Herschel-Bulkley rheological theory is used to describe the viscoplastic debris landslide flow. The shallow water equations considering the time-dependent deformation of the seafloors are adopted to simulate the generation, propagation, and run-up of the landslide induced tsunami. The one-way coupled method of the landslide induced tsunami is implemented through satisfying the kinematic bottom boundary condition. The 1998 Papua New Guinea landslide tsunami is simulated to validate the numerical model by comparing with measurements. We found that the mechanism of the 1992 Hainan Island tsunami in the South China Sea is due to a submarine landslide by comparing the numerical results between earthquake and landslide. With respect of the Baiyun slide, the effects of remolding rate, initial, and residual yield strength on landslide and tsunami are studied numerically. To distinguish the potential landslide tsunami hazard in the South China Sea, the scenarios of the landslides with the volume of 10, 50, 100, and 200 km3 in the Baiyun slide and 1200 km3 in the Brunei slide are presented. Comparison with the nondeformation model in the near-field illustrates the crucial role of rheological property in the landslide tsunami modeling. Furthermore, the characteristics of the propagation of the landslide tsunami in the South China Sea and coastal hazards are analyzed.

### Thin reaction zones in constant-density turbulent flows at low Damköhler numbers: Theory and simulations

Propagation of a single-reaction wave in a constant-density turbulent flow is studied by considering reaction rates that depend on the reaction progress variable c in a highly nonlinear manner. Analysis of Direct Numerical Simulation (DNS) data obtained recently from 26 reaction waves characterized by low Damköhler (0.01 < Da < 1) and high Karlovitz (6.5 < Ka < 587) numbers reveals the following trends. First, the ratio of consumption velocity UT to rms turbulent velocity u′ scales as square root of Da in line with Damköhler’s classical hypothesis. Second, the ratio of fully developed turbulent wave thickness to an integral length scale of turbulence decreases with increasing Da and tends to scale with inverse square root of Da, in line with the same hypothesis. Third, contrary to the widely accepted concept of distributed reaction zones, reaction-zone broadening is quite moderate even at Da = 0.01 and Ka = 587. Fourth, contrary to the same concept, UT/u′ is mainly controlled by the reaction-surface area. Fifth, UT/u′ does not vary with the laminar-reaction-zone thickness, provided that Da is constant. To explain the totality of these DNS results, a new theory is developed by (i) exploring the propagation of a molecular mixing layer attached to an infinitely thin reaction sheet in a highly turbulent flow and (ii) hypothesizing that the area of the reaction sheet is controlled by turbulent mixing. This hypothesis is supported by order-of-magnitude estimates and results in the aforementioned Damköhler’s scaling for UT/u′. The theory is also consistent with other aforementioned DNS results and, in particular, explains the weak influence of the laminar-reaction-zone thickness on UT/u′.

### Evolution of wave pulses in fully nonlinear shallow-water theory

We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated, and motion of the dispersive shock edges is studied within the Whitham theory of modulations. Simple analytical formulas are obtained for asymptotic stage of evolution of initially localized pulses. Analytical results are confirmed by exact numerical solutions of the fully nonlinear shallow-water equations.

### Investigation of supersonic turbulent flows over a sphere by fully resolved direct numerical simulation

In this work, a fully resolved direct numerical simulation study of the interaction between supersonic turbulent flow and inertial particle is carried out. For the compressible flow, an eighth-order bandwidth optimization weighted essentially nonoscillatory scheme is used for shock capturing, and the central finite difference scheme is used for the spatial discretization of diffusion terms. The three-dimensional ghost zone immersed boundary method is adopted for solid-fluid interface identification. These numerical schemes are integrated in a direct numerical simulation solver, and its validation is demonstrated by comparing to several benchmark cases. Such a developed method is then used to attack the problem of an upstream supersonic turbulent flow over a spherical particle. Three cases with different inflow turbulence intensities are studied. It is shown that with the turbulence intensity increasing the drag force coefficient presents a smaller relative increase compared to the incompressible situation. Analysis of the bow shock-turbulence interaction is also reported. Similar to the normal shock-turbulence interaction, both the Kolmogorov and Taylor scales decrease after being compressed by the shock. Moreover, both the streamwise and transverse Reynolds stresses have a peak at the shock position. These results indicate the significance of taking the effects of shock into consideration when modeling the modulation of a solid particle to the compressible turbulence.

### Effect of near-wake jet on the lock-in of a freely vibrating square cylinder

We present a numerical study of a freely vibrating square cylinder with steady bleeding at its base side. In particular, we focus on the suppression of vortex-induced vibration (VIV) and the reduction of drag force for the elastically mounted square cylinder at a laminar flow condition via near-wake jet. We examine the base bleeding mechanism in the near-wake region of a square cylinder and its influence over the flow dynamics and the wake characteristics for both stationary (nonlock-in) and freely vibrating (lock-in) conditions. We consider the near-wake jet parameter as a function of the bleed coefficient (Cq), which is the ratio of near-wake jet flow velocity to the freestream velocity and depends on the Reynolds number (Re) based on the diameter of the cylinder. Investigations of the hydrodynamic coefficients and the flow features are carried out for the laminar Re range, namely, Re = 40, 60, 100, and 150. A single dominant frequency peak is observed in the lift coefficient spectrum plot for all the Reynolds numbers considered, but two peaks are observed for Re = 150 at Cq = 0.175 and 0.2. Higher Cq values behave like a splitter plate thereby preventing the interaction of alternating shear layers. The variation of the mean drag is associated with the pressure distribution around the cylinder surface and along the streamwise locations. This leads to a thinner wake width, weaker vortices, and higher vortex shedding frequency as observed earlier in the literature. The sharp spikes of pressure coefficient at the base side of the cylinder are observed for Re ∈ [40, 150] due to the near-wake jet, accounting for the fluctuations of drag force coefficient. We demonstrate the formation of multiple vortices at the wake region due to the near-wake jet from our detailed qualitative analysis. We observe counter-rotating pair of recirculating fluids flanking at the near-wake jet location and examine the recovery of base pressure due to the jet flow. We demonstrate the splitting of big circulation fluid bubble into many smaller counter-rotating fluids due to high-velocity jet flow, resulting into the stabilization of flow profiles in the wake region. We extend this investigation to quantify the effect of the near-wake jet on the two-degree-of-freedom cylinder system at the representative Reynolds number Re = 100 and three mass ratios [math] = 1, 2, and 3. We demonstrate the reduction of peak transverse VIV amplitude by 90% in comparison to the plain cylinder counterpart.

### Linear stability analysis of a surfactant-laden shear-imposed falling film

A study of the linear stability analysis of a shear-imposed fluid flowing down an inclined plane is performed when the free surface of the fluid is covered by an insoluble surfactant. The purpose is to extend the earlier work [H. H. Wei, “Effect of surfactant on the long-wave instability of a shear-imposed liquid flow down an inclined plane,” Phys. Fluids 17, 012103 (2005)] for disturbances of arbitrary wavenumbers. The Orr-Sommerfeld boundary value problem is formulated and solved numerically based on the Chebyshev spectral collocation method. Two temporal modes, the so-called surface mode and surfactant mode, are detected in the long-wave regime. The surfactant mode becomes unstable when the Péclet number exceeds its critical value. In fact, the instability of the surfactant mode occurs on account for the imposed shear stress. Energy budget analysis predicts that the kinetic energy of the infinitesimal disturbance grows with the imposed shear stress. On the other hand, the numerical results reveal that both surface and surfactant modes can be destabilized by increasing the value of the imposed shear stress. Similarly, it is demonstrated that the shear mode becomes more unstable in the presence of the imposed shear stress. However, it can be stabilized by incorporating the insoluble surfactant at the free surface. Apparently, it seems that inertia does not play any role in the surfactant mode in the moderate Reynolds number regime. Furthermore, the competition between surface and shear modes is discussed.

### The drag reduction performance of low Reynolds number pulsating flow in flexible rectangular channels

This work employed theoretical and experimental methods to study the drag reduction performance of flexible channels for low Reynolds number pulsating flow. A novel theoretical model was proposed to describe flow in a flexible rectangular channel. According to the model, the drag reduction of the flexible channel was speculated. Subsequently, experiments were carried out to verify the theoretical results and to illuminate the drag reduction performance of the flexible channel in detail under the impacts of pulsating frequency, nondimensional velocity amplitude, average Reynolds number, and the thickness of the flexible wall. The results indicated that the flexible channel exhibited superior drag reduction performance for pulsating flow as compared to that for steady flow. Meanwhile, the drag reduction rate increased with the increase of pulsating frequency, nondimensional velocity amplitude, and average Reynolds number, and smaller thickness of the flexible wall was in favor of drag reduction at the same flow parameters. Moreover, the current experimental data were utilized to establish a correlation predicting the drag reduction rate of the flexible channel for pulsating flow, which fits 76.4% of 195 data within ±25%.

### Numerical investigation of piston-modal wave resonance in the narrow gap formed by a box in front of a wall

Piston-modal wave resonance between a ship section and a bottom mounted terminal is studied by employing a numerical wave flume based on OpenFOAM® package. A systematic investigation on the piston-modal behavior is performed to characterize the influence of fluid viscosity and flow rotation. Around the resonant frequency, the fluid viscosity and flow rotation not only dissipate the wave amplitude in the narrow gap, but also increase the wave amplitude in the upstream of the box. The dynamic mechanism behind the phenomenon is found to be the interaction between the energy dissipation induced by the fluid vortical flow and energy transformation associated with free surface motion. The increased incident wave amplitude can cause the normalized wave amplitudes and wave forces to deviate more from the potential flow results, while the variation of reflection coefficient is dependent on box-wall geometries. All of these phenomena imply a more significant effect of fluid viscosity and flow rotation with the increase of incident wave amplitude, but the energy dissipation is not the only factor in piston-modal resonance.

### Experimental verification of anomalous surface tension temperature dependence at the interface between coexisting liquid-gas phases in magnetic and Stockmayer fluids

Our early experimental investigation has demonstrated the anomalous surface tension temperature dependence σ(T) at the interface between coexisting liquid-gas phases in magnetic fluids that undergo field-induced first-order phase transition. The σ(T) dependence is anomalous because the drops of a liquid phase condensed under the action of the applied magnetic field H at high temperature T2 exhibit larger surface tension σ(T2) > σ(T1) than the drops condensed at low temperature T1 < T2. This study verifies and confirms the results of the previous experimental investigation of σ(T) in magnetic fluids by performing the experiment, which is based on the analysis of the Plateau-Rayleigh instability of a gas-liquid interface in a zero magnetic field. A novel explanation of this phenomenon is given in the framework of the Stockmayer model. The anomalous increase in σ(T) is explained by the increase in particle concentration difference in gas and liquid phases, which can be attributed to the high field intensity H needed to generate the phase transition at high temperature.

### Regime transition in the energy cascade of rotating turbulence

Author(s): T. Pestana and S. Hickel

Transition from a split to a forward kinetic energy cascade system is explored in the context of rotating turbulence using direct numerical simulations with a three-dimensional isotropic random force uncorrelated with the velocity field. Our parametric study covers confinement effects in high-aspect...

[Phys. Rev. E 99, 053103] Published Wed May 08, 2019

### Rayleigh-Taylor-instability experiments with elastic-plastic materials

Author(s): Rinosh Polavarapu, Pamela Roach, and Arindam Banerjee

A rotating wheel experimental facility was developed to investigate incompressible Rayleigh-Taylor instability in elastic-plastic materials. A soft solid (mayonnaise) was chosen as the elastic-plastic material for experiments; material properties that include shear modulus and yield strength were fu...

[Phys. Rev. E 99, 053104] Published Wed May 08, 2019

### Drop impact close to the edge of an inclined substrate: Liquid sheet formation and breakup

Author(s): S. Lejeune and T. Gilet

Experiments on the impact of a drop near the edge of an inclined substrate are reported. A liquid sheet forms beyond the edge, then fragments into droplets. This configuration is a minimal model of the crucial raindrop impacts on plant leaves that are responsible for the dispersal of crop diseases.

[Phys. Rev. Fluids 4, 053601] Published Wed May 08, 2019

### Deformation and stability of a viscous electrolyte drop in a uniform electric field

Author(s): Qiming Wang, Manman Ma, and Michael Siegel

The deformation and breakup of an axisymmetric electrolyte drop in a dielectric medium stretched by an electric field is studied. An accurate and efficient boundary integral method is developed to solve the time-dependent Stokes flow problem in the case of arbitrary Debye layer thickness.

[Phys. Rev. Fluids 4, 053702] Published Wed May 08, 2019

### Influence of Reynolds number on the motion of settling, bidisperse inertial particles in turbulence

Author(s): Mohammadreza Momenifar, Rohit Dhariwal, and Andrew D. Bragg

Using direct numerical simulation it is shown that even when bidisperse particles are settling rapidly, intermittent fluctuations allow turbulence to continue to play a key role in their relative motion, an effect increasing with Re. Low-order statistics relevant to collision rates are found to depend only weakly on Re.

[Phys. Rev. Fluids 4, 054301] Published Wed May 08, 2019

### Destruction-of-dissipation and time-scales in wall turbulence

This paper studies the dynamics and scalings of dissipation processes in wall turbulence, focussing on the destruction-of-dissipation tensor [math] (and its halftrace εε), which acts as destruction-by-molecular-viscosity mechanism in the transport equations for the dissipation tensor εij (or its halftrace ε). Budgets of [math]-transport (and εε-transport) are studied for low-Reynolds turbulent plane channel flow. These transport equations also include a destruction-by-molecular-viscosity mechanism, the destruction-of-destruction tensor [math] (or its halftrace [math]), and indeed, recursively, we identify terms [math] defined by correlations of [n + 1]-derivatives which correspond to the destruction mechanism of [math]. Using halftraces ε[n], we may define time-scales, whose study reveals that [math] is approximately equal to the Kolmogorov time-scale. The dependence of the time-scales on the Reynolds number is discussed.

### Numerical study of the material transport in the viscous vortex dipole flow

This paper presents a numerical study of the material transport of Lamb dipole(s) in the two-dimensional viscous flow. We focus on the properties of the rate of strain tensor, which has received less attention in the literature. It is noted that the eigenpairs of the tensor explicitly indicate the strength and direction of material stretching and compressing. The tensor provides a clear map of the material motion regardless of the complexity of the vortical flow. The strain rate field displays a rich structure as it contains five elliptic points and six hyperbolic points. It is interesting to observe that the left elliptic point of the strain rate field bifurcates into two at t > 0. Two kinds of material curves, circular and vertical, are used to illustrate the flow transport. The transport mechanism discussed here can be employed to explore the transport in more complex vortex flows.

### Second-order sensitivity in the cylinder wake: Optimal spanwise-periodic wall actuation and wall deformation

Author(s): E. Boujo, A. Fani, and F. Gallaire

Two-dimensional flows can be controlled efficiently with spanwise-periodic wall forcing or wall deformation. Optimal “wavy” controls for the linear stability of the laminar flow past a cylinder are obtained with an adjoint method.

[Phys. Rev. Fluids 4, 053901] Published Tue May 07, 2019