# Latest papers in fluid mechanics

### Transverse jet lock-in and quasiperiodicity

Author(s): Takeshi Shoji, Elijah W. Harris, Andrea Besnard, Stephen G. Schein, and Ann R. Karagozian

An experimental study explores the dynamics of lock-in and quasiperiodicity phenomena associated with upstream shear layer instabilities for a gaseous transverse jet exposed to axisymmetric excitation. Various dynamical responses are dependent on the jet-to-crossflow momentum flux ratio.

[Phys. Rev. Fluids 5, 013901] Published Tue Jan 07, 2020

### Experimental investigation of three-dimensional flow around particles in a turbulent channel flow

Author(s): Farzad Ahmadi, Sean Sanders, and Sina Ghaemi

Simultaneous three-dimensional measurement of the velocity of beads and the surrounding flow is carried out in a turbulent channel flow. The results show that the quasi-steady drag is not sufficient to model the dynamics of the beads in the near-wall region.

[Phys. Rev. Fluids 5, 014302] Published Tue Jan 07, 2020

### Input-output system identification of a thermoacoustic oscillator near a Hopf bifurcation using only fixed-point data

Author(s): Minwoo Lee, Yu Guan, Vikrant Gupta, and Larry K. B. Li

We present a framework for performing input-output system identification near a Hopf bifurcation using data from only the fixed-point branch, prior to the Hopf point itself. The framework models the system with a van der Pol–type equation perturbed by additive noise, and identifies the system parame...

[Phys. Rev. E 101, 013102] Published Mon Jan 06, 2020

### Fine vortex structure and flow transition to the geostrophic regime in rotating Rayleigh-Bénard convection

Author(s): Jun-Qiang Shi, Hao-Yuan Lu, Shan-Shan Ding, and Jin-Qiang Zhong

High-resolution measurements of velocity fields reveal the fine structure of vortices and indicate flow-regime transition in rapidly rotating Rayleigh-Bénard convection.

[Phys. Rev. Fluids 5, 011501(R)] Published Mon Jan 06, 2020

### Obstructed viscoplastic flow in a Hele-Shaw cell

Author(s): Masoud Daneshi, Jordan MacKenzie, Neil J. Balmforth, D. Mark Martinez, and Duncan R. Hewitt

Experiments are conducted to explore the flow of Carbopol past obstacles in a narrow slot, and they are compared with model predictions. Flow patterns markedly lack the fore-aft symmetry expected theoretically, which suggests this results from rheological hysteresis near the yield point.

[Phys. Rev. Fluids 5, 013301] Published Mon Jan 06, 2020

### Effect of viscosity and density ratios on two drops rising side by side

Author(s): Mounika Balla, Sivanandan Kavuri, Manoj Kumar Tripathi, Kirti Chandra Sahu, and Rama Govindarajan

Three-dimensional dynamics of a spherical drop pair rising side-by-side in a surrounding, denser, fluid is investigated. We show that two liquid drops move away from each other when a single drop would have risen vertically. Interesting drop trajectories without large shape deformations are found.

[Phys. Rev. Fluids 5, 013601] Published Mon Jan 06, 2020

### Transient growth in thermocapillary liquid layers

Author(s): Kai-Xin Hu, Sheng Zheng, and Qi-Sheng Chen

Transient growth in thermocapillary liquid layers is examined by nonmodal stability theory. Rather large transient growth occurs in subcritical flows at small Prandtl numbers. The growth decreases with Prandtl number but increases with Biot number, while its energy comes from the basic flow.

[Phys. Rev. Fluids 5, 014001] Published Mon Jan 06, 2020

### Stokes theory of thin-film rupture

Author(s): D. Moreno-Boza, A. Martínez-Calvo, and A. Sevilla

A theoretical and numerical analysis of the rupture of a nonwetting, ultrathin liquid film placed on a solid substrate reveals that the lubrication description experiences a crossover to a universal self-similar solution of the Stokes equations prior to the singularity.

[Phys. Rev. Fluids 5, 014002] Published Mon Jan 06, 2020

### Similarity of dissipation and enstrophy in particle-induced small-scale turbulence

Author(s): Zhuo Wang, Kun Luo, Junhua Tan, Dong Li, and Jianren Fan

Direct numerical simulations and the immersed boundary method show that finite-size particles greatly enhance small-scale motions. Enstrophy and dissipation become similar in this augmented small-scale turbulence, as manifest in statistical relations and spatial distributions. This kind of similarity also exists in single-phase high-Reynolds-number turbulence but not in low-Reynolds-number turbulence.

[Phys. Rev. Fluids 5, 014301] Published Mon Jan 06, 2020

### Near-inertial waves and geostrophic turbulence

Author(s): Jim Thomas and S. Arun

The two-mode quasigeostrophic model and associated turbulence phenomenology is a holy grail of geophysical fluid dynamics. An illustration of how wind-generated near-inertial waves in the ocean modify the quasigeostrophic turbulence phenomenology is presented.

[Phys. Rev. Fluids 5, 014801] Published Mon Jan 06, 2020

### Application of the Schwarz-Christoffel map to the Laplacian growth of needles and fingers

Author(s): N. R. McDonald

A numerical procedure based on the Schwarz-Christoffel map suitable for the study of the Laplacian growth of thin two-dimensional protrusions is presented. The protrusions take the form of either straight needles or curved fingers satisfying Loewner's equation, and are represented by slits in the co...

[Phys. Rev. E 101, 013101] Published Fri Jan 03, 2020

### Quincke rotation driven flows

Author(s): M. Belovs and A. Cēbers

In density-matched suspensions of Quincke particles, macroscopic flow arises due to the synchronization of their rotations at electric-field values smaller than the threshold field for the spontaneous rotation of a single particle.

[Phys. Rev. Fluids 5, 013701] Published Thu Jan 02, 2020

### Splashing dynamics of a drop impact onto a deep liquid pool with moving film interface

The impact of a drop onto a stagnant deep liquid pool results in jet formation in the splashing regime. The perturbations in the free surface alter the impact conditions and change the splash dynamics. We present the simulations of the water drop impact onto a deep liquid pool with a moving free surface. Occurrence of the asymmetric crater profile and bending of the central jet toward the flow direction of the free surface are observed. The inclination of the jet increased with an increase in inertia of the moving liquid surface. A secondary droplet pinched-off from the tip of the jet, and the volume of this droplet increased with an increase in the inclination of the jet.

### Impact of surfactant addition on non-Newtonian fluid behavior during viscous fingering in Hele-Shaw cell

We present an experimental study of viscous fingering caused by the displacement of an oil phase by non-Newtonian fluids such as Carbopol® 940 with and without surfactant (SDS) addition in a radial Hele-Shaw cell. When polymer solutions are injected, a variety of fingering patterns as a function of flow rate are observed, which differ from the classical Saffman-Taylor instability. We have shown that if the surfactant concentration locally decreases the interfacial tension, it also leads to a reduction of viscosity and hence results in an increasing impact on the capillary number. We found that surfactant-polymer solutions have wider fingers with increasing flow rates in contrast with Newtonian solutions. Our study also revealed that the relative finger width of both non-Newtonian experiments with and without the surfactant converge asymptotically to the same value. We think that this phenomenon is caused by the decrease in surfactant concentration in the vicinity of the tip as the finger is growing so that the shear-thinning features of polymer prevail at long time.

### Analysis of granular rheology in a quasi-two-dimensional slow flow by means of discrete element method based simulations

The steady flow of spherical particles in a rectangular bin is studied using the discrete element method for different flow rates of the particles from the bin in the slow flow regime. The flow has two nonzero velocity components and is more complex than the widely studied unidirectional shear flows. The objective of the study is to characterize, in detail, the local rheology of the flowing material. The flow is shown to be of nearly constant density, with a symmetric stress tensor and the principal directions of the stress and rate of strain tensors being nearly colinear. The local rheology is analyzed using a coordinate transformation which enables direct computation of the viscosity and components of the pressure assuming the granular material to be a generalized Newtonian fluid. The scaled viscosity, fluctuation velocity, and volume fraction are shown to follow power law relations with the inertial number, a scaled shear rate, and data for different flow rates collapse to a single curve in each case. Results for flow of the particles on an inclined surface, presented for comparison, are similar to those for the bin flow but with a lower viscosity and a higher solid fraction due to layering of the particles. The in plane normal stresses are nearly equal and slightly larger than the third component. All three normal stresses correlate well with the corresponding fluctuation velocity components. Based on the empirical correlations obtained, a continuum model is presented for computation of granular flows.

### On the transition behavior of laminar flow through and around a multi-cylinder array

We numerically investigated the transitional behavior of two-dimensional laminar flows through and around a square array of 100 circular cylinders. The solid fraction of the array ϕ ranged from 0.007 85 to 0.661 and the Reynolds number Re (based on the free-stream velocity and the side length of the array) varied from 40 to 200. Globally, the first transition appears at the onset of vortex shedding, where the critical Reynolds number Recr is estimated from the Stuart-Landau equation. The results show that Recr ranges from 40 to ∼45 for the investigated range of ϕ. It is found that Recr increases quadratically with [math] and the critical Reynolds number for an individual cylinder (Rdcr) increases linearly with [math]. The subsequent transitions largely depend on ϕ, as revealed from the total drag and lift coefficients, Strouhal number, and the instantaneous vorticity field. For sufficiently small ϕ at high Re, the global vortex shedding is suppressed due to the weakened interaction between cylinders in the array. Several more cases with ϕ of 0.007 85 for Re between 400 and 4000 are also calculated to visualize the suppression behavior. The global transition behaviors are closely related to the secondary frequency (SF) observed from the power spectra of the local velocity. It is highly possible that the SF results from the cylinder interaction in the array. The local instabilities induced by cylinder interactions would promote the onset of global vortex shedding at small Re. Also, the local instabilities still exist even though the global vortex shedding is suppressed at large Re.

### Transition to chaos in the cylinder wake through the Mode C flow

The evolution of Mode C wake characteristics with the Reynolds number (Re) for Re up to 400 is investigated numerically. The Mode C wake instability is generated by placing a small wire in the near wake of a main circular cylinder. This setup ensures that the wake is unstable to Mode C only (without potential mode interactions), as demonstrated by Floquet stability analysis. Based on three-dimensional direct numerical simulations, three evolution regimes are identified for the fully developed Mode C flow. In the uniform periodic regime (Re = 166.4–210), the Mode C structure is uniformly distributed along the spanwise direction. The flow structure is 2T-periodic (T being the vortex shedding period) but retains a spatiotemporal symmetry every 1T. In the nonuniform periodic regime (Re = 220–230), the slightly nonuniform Mode C structure remains 2T-periodic at Re = 220 but undergoes a period quadrupling to 4T-periodic at Re = 230 before transitioning to chaos. In the chaotic regime (Re ≥ 240), the flow loses periodicity and becomes increasingly chaotic with increasing Re. The progressive wake transition to chaos is found to originate from the instability in the braid shear layer region through the uneven growth in strength and the consequent nonuniformity of the Mode C streamwise vortices. The wake transitions to chaos through the routes of Mode C and Mode B (for an isolated circular/square cylinder) are compared.

### Invited contributions from outstanding early career researchers

### Special topic on food and fluids

### Identification of trapping in a peristaltic flow: A new approach using dynamical system theory

In this paper, we propose a new approach for the identification of characteristic peristaltic flow features such as “bolus” and “trapping.” Using dynamical system analysis, we relate the occurrence of a bolus to the existence of a center (an elliptic equilibrium point). Trapping occurs when centers exist under the wave crests along with a pair of saddles (hyperbolic equilibrium points) lying on the central line. For an augmented flow, centers form under the wave crests, whereas saddles lie above (below) the central line. The proposed approach works much better than the presently adopted approach in two ways: (1) it does not require random testing and (2) it characterizes the qualitative flow behavior for the complete range of parameter values. The literature is somewhat inconsistent with regard to the terminologies used for describing characteristic flow behaviors. We have addressed this issue by explicitly defining quantities such as “bolus,” “backward flow,” “trapping,” and “augmented flow.”