# Latest papers in fluid mechanics

### Defining Lagrangian coherent vortices from their trajectories

We study the transport properties of mesoscale eddies (i.e., vortices of 100–200 km in diameter) over a finite time duration. While these oceanic structures are well-known to stir and mix surrounding water, they can also carry and transport water properties in a coherent manner. In this paper, we are interested in dynamic transport properties of these coherent structures, despite their chaotic environment. Here, we reveal that such vortices can be identified based a simple decomposition of their Lagrangian trajectories. We identify and extract coherent vortices as material lines along which particles’ trajectories share similar polar rotations. The proposed method identifies coherent vortices and their centers in an automatic manner. We illustrate our new method by identifying and extracting Lagrangian coherent vortices in different two-dimensional flows.

### Characterizing three-dimensional features of vortex surfaces in the flow past a finite plate

We extend the vortex-surface field (VSF), a Lagrangian-based structure identification method, to investigate vortex dynamics in flows past a plate simulated by the immersed boundary method. As an example, the VSF evolution characterizes the three-dimensional features of vortex surfaces in the flow past a finite plate at the Reynolds number of 300, aspect ratio of 2, and angle of attack of 30°. The VSF isosurface displays that near-plate vortex surfaces first roll up from plate edges and then evolve into hairpinlike structures near the leading edge and semiring structures near plate tips and in the wake. We quantitatively distinguish two types of vortical structures by the vanishing streamwise vorticity on VSF isosurfaces and refer them to as the leading edge vortex (LEV) and the tip vortex (TIV). Based on circulations through cross sections of vortex surfaces, we demonstrate that the lift generated from the LEV is suppressed by the finite growth of TIVs. In the wake region, we quantify the geometry of helical vortex lines in TIVs and the contribution of the helical vorticity component to the streamwise vortical impulse.

### Influences of thermal effects on cavitation dynamics in liquid nitrogen through venturi tube

Investigation on cavitation features in cryogenic liquids is of great importance to rocket engine design due to their complicated physics. This paper experimentally investigates the characteristics of unsteady liquid nitrogen (LN2) cavitating flow through a transparent venturi tube with image processing techniques. The numerical simulations based on the computational fluid dynamic approach are also performed to help explain the mechanisms. A pressure ratio (Pr) associated with the inlet and the outlet subcooling is found to have a linear relationship with the cavitation number. The nondimensional thermal effect parameter derived from the single bubble dynamics is used to quantify thermal effect intensity. The cavity length derived from standard derivation results has an inversely linear relation with Pr, and there exists an inflection point of the pressure ratio (Prc) below which the cavity length growth rate is relatively larger. The effects of the bulk temperature on the magnitude of Prc are numerically investigated, which reveals that Prc increases as the liquid temperature increases. The oscillating frequencies of the sheet and cloud cavitating flow are also analyzed according to two Strouhal numbers based on cavity length (Stc) and venturi throat diameter (Std), respectively. For cloud cavitation, Stc lies in between 0.30 and 0.40 for all Pr values, while for sheet cavitation, it decreases to 0.04–0.08. Besides, in the cloud cavitation region, Std increases linearly with Pr but has a weak relation with [math]. It is also found that with increased values of [math], the transition point of Pr from sheet cavitation to cloud cavitation is delayed.

### Water exit dynamics of jumping archer fish: Integrating two-phase flow large-eddy simulation with experimental measurements

Archer fish jumping for prey capture are capable of achieving accelerations that can reach 12 times gravitational from a stationary start at the free surface. This behavior is associated with nontrivial production of hydrodynamic thrust. In this work, we numerically investigate the hydrodynamic and aerodynamic performance of a jumping smallscale archer fish (Toxotes microlepis) to elucidate the propulsive mechanisms that contribute to the rapid acceleration and the considerable jump accuracy. We conduct high-fidelity, two-phase flow, large-eddy simulation (LES) of an anatomically realistic archer fish using detailed jump kinematics in water, through the water/air interface, and in air. The complex fish body kinematics are reconstructed using high-speed imaging. The LES results during the water phase of the jump are compared with particle image velocimetry measurements of a live jumping archer fish, and excellent agreement is found. The numerical simulations further enable detailed analysis of the flow dynamics and elucidate for the first time the dynamics of the coherent vortical structures in both the water and air phases. In particular, the pectoral fins are shown to contribute to the initial spike in acceleration before water exit and to enhance the overall jumping performance of the fish.

### Application of spectral proper orthogonal decomposition to velocity and passive scalar fields in a swirling coaxial jet

Direct numerical simulation is used to study unconfined coaxial jets under the influence of strong swirl imparted to the outer jet. Spectral proper orthogonal decomposition is employed to elucidate the physically important structures or modes in the flow. The analysis is extended to the transport of passive scalars injected through each jet. A partially penetrated vortex breakdown bubble is formed as a result of the strong swirl. In the region upstream of the central stagnation point, the first two (most energetic) spatial modes of the velocity field at the cross-stream section reveal three pairs of counter-rotating vortical structures, while the succeeding two modes reveal four pairs of such structures. The centers of these vortical structures are found to lie in the inner mixing layer present between the two jets. The corresponding spatial modes of the scalars also exhibit organized lobelike structures in this region. These organized structures are subsequently disrupted in the downstream region. The significance of these pairs of counter-rotating vortical structures is demonstrated by reconstruction of various turbulence statistics, namely, the root mean square (rms) velocities, the rms scalar fluctuations, the covariance between the two scalars, and the radial turbulent fluxes of the scalars. The results show that the first four modes make a greater contribution to these statistics except for the covariance between two scalars, particularly in the inner mixing layer.

### Modification of turbulent boundary layer coherent structures with drag reducing polymer solution

The modification of dominant coherent structures that extend through the log-region of a drag reduced turbulent boundary layer is studied via examination of two-point correlations from time-resolved particle-image-velocimetry. Measurements were acquired in polymer oceans (uniform concentration) at drag reduction levels corresponding to the low drag reduction regime (<40%) and the high drag reduction (HDR) regime (>40%) and at an intermediate level (46%). The mean velocity profiles and two-point correlations were compared with those of water (Newtonian, DR = 0%). These results show that, with increasing drag reduction, the inclination of these dominant coherent structures decreases, their streamwise extent increases, and the fluctuations in the correlations are suppressed (especially at HDR). These observations are examined in comparison with the coherent structure literature (Newtonian and polymeric).

### Novel nonequilibrium steady states in multiple emulsions

We numerically investigate the rheological response of a noncoalescing multiple emulsion under a symmetric shear flow. We find that the dynamics significantly depends on the magnitude of the shear rate and on the number of the encapsulated droplets, two key parameters whose control is fundamental to accurately select the resulting nonequilibrium steady states. The double emulsion, for instance, attains a static steady state in which the external droplet stretches under flow and achieves an elliptical shape (closely resembling the one observed in a sheared isolated fluid droplet), while the internal one remains essentially unaffected. Novel nonequilibrium steady states arise in a multiple emulsion. Under low/moderate shear rates, for instance, the encapsulated droplets display a nontrivial planetarylike motion that considerably affects the shape of the external droplet. Some features of this dynamic behavior are partially captured by the Taylor deformation parameter and the stress tensor. Besides a theoretical interest on its own, our results can potentially stimulate further experiments, as most of the predictions could be tested in the lab by monitoring droplets’ shapes and position over time.

### High-Rayleigh-number thermal convection of compressed gases in inclined rectangular enclosures

High-Rayleigh-number convection is experimentally studied using compressed gases for a wide range of Rayleigh numbers (1.85 × 106 ≤ Ra ≤ 1.04 × 1011) and angles of inclination (θ = 0°, 30°, 60°, 90°, 120°, and 150°) with rectangular enclosures of varied aspect ratios (AR = 1, 3, 6, and 10). Experimental results reveal that the Nusselt number decreases monotonically with increasing angle of inclination. Furthermore, for any angle of inclination and a given Rayleigh number, the Nusselt number is observed to follow a decreasing trend with an increase in aspect ratio, which gradually amplifies as the angle of inclination is increased. Z-type shadowgraph flow visualization experiments, employed to characterize buoyant flow behavior at various angles of inclination, confirm the observed heat transfer trends.

### Turbulent flow interaction with a circular cylinder

This paper presents a comprehensive experimental study on the unsteady pressure exerted on the surface of a round cylinder in smooth and turbulent flows. A highly instrumented cylinder with several static pressure taps and dynamic pressure transducers at different spanwise and peripheral locations was used, enabling extensive dynamic surface pressure, coherence, and turbulence length-scale analysis. The effects of the free-stream turbulence and turbulent length scale are investigated by placing the turbulent-generating grids within the wind tunnel duct. For both the laminar and turbulent incident flows, the surface pressure results show the emergence of the fundamental, first and second harmonics at most peripheral angles, while at the cylinder base, the surface pressure spectra are dominated by the first harmonic. It has also been observed that an increase in the level of the turbulence intensity results in an increase in the energy level of unsteady pressure acting on the cylinder. An increase in the length scale of the incoming flow structures is shown to result in an increase in the energy level of the tonal frequencies and the broadband content of the surface pressure spectra. The spanwise coherence results have also shown that an increase in the length scale of the flow structures increases the spanwise correlation length of the flow structures at the vortex shedding frequency at the stagnation point, while at the cylinder base, the spanwise correlation length decreases at the vortex shedding frequency.

### Drag forces on nanoparticles in the free-molecule regime: Effect of the particle temperature

Author(s): Jun Wang, Junjie Su, and Guodong Xia

In the present paper, we theoretically study the drag force on nanoparticles in the free-molecule regime. It has been widely assumed that the particle temperature is equal to the gas media temperature in the open literature. However, this assumption can be invalid in some real applications. Based on...

[Phys. Rev. E 101, 013103] Published Wed Jan 08, 2020

### Study of the Hopf functional equation for turbulence: Duhamel principle and dynamical scaling

Author(s): Koji Ohkitani

We consider a formulation for the Hopf functional differential equation which governs statistical solutions of the Navier-Stokes equations. By introducing an exponential operator with a functional derivative, we recast the Hopf equation as an integro-differential functional equation by the Duhamel p...

[Phys. Rev. E 101, 013104] Published Wed Jan 08, 2020

### Asymmetric rectified electric fields generate flows that can dominate induced-charge electrokinetics

Author(s): S. M. H. Hashemi Amrei, Gregory H. Miller, and William D. Ristenpart

Extant theories for induced-charge electrokinetics (ICEK) sometimes fail to predict even the correct direction of flow. By combining the recently discovered phenomenon of asymmetric rectified electric fields with a generalized form of ICEK, this long-standing dilemma is explained.

[Phys. Rev. Fluids 5, 013702] Published Wed Jan 08, 2020

### Flow control over a square cylinder using attached rigid and flexible splitter plate at intermediate flow regime

A detailed flow field behind a stationary square cylinder with attached rigid and flexible splitter plates has been studied using particle image velocimetry, constant temperature anemometry, and flow visualization techniques. A wide range of lengths of the splitter plate (L/B = 0–8) are considered, and their respective wake interference is reported. The investigation is carried out at an intermediate flow regime at three Reynolds numbers 600, 1000, and 2000 (based on blocking width “B” of the cylinder). The literature seriously lacks the information on a passive flow control of bluff body wakes in this flow regime. This study shows that the wake frequency and mean drag coefficient vary nonmonotonically to splitter plate lengths. The length of the splitter plate is a critical parameter, which, apart from flow control, can also bring a significant wake transition. At L/B > 3 to L/B = 4, strong secondary vortices are shed from the trailing edge. The shedding of the secondary vortex leads to a sudden shrinkage in the recirculation bubble and an increase in the periodicity of the unsteady flow. The onset of high amplitude flapping occurs in a flexible splitter plate (L/B = 3) at Re = 2000. The vortex shedding frequency becomes higher than the first mode natural frequency of the flexible splitter plate for this length and remains in the same regime for L/B > 3. The amplitude of flapping increases up to L/B = 5 and then again recedes. The high amplitude flapping of the flexible splitter plate adversely affects the mean drag coefficient of the bluff body.

### Self-similar solutions of asymmetric Rayleigh-Taylor mixing

The late nonlinear phase of the Rayleigh-Taylor instability is characterized by the self-similar expansion of the instability mixing layer given at late times by h ≈ αAgt2. In this paper, we present a new model of this mixing layer, based on a piecewise step function approximation where the main constraint imposed is conservation of mass. This model is used to predict the structuring of the mean density of the layer and the asymmetry of the layer for a given Atwood number. By comparing experimental data and simulation results, we confirmed the predictions of the model for the asymmetry of the α values. Our model leads to a simple correction to the formulation of the expansion of the mixing layer which is consistent with α for a given system that is independent of the density difference for both immiscible fluids and miscible fluids with low mass diffusion. As the model predicts the mean density profile, it can be used to state the energy released by the instability.

### Coalescence dynamics of a droplet on a sessile droplet

The coalescence dynamics of an ethanol droplet freely falling on a sessile ethanol droplet is investigated experimentally using a high-speed imaging system. The regime maps showing the partial coalescence and spreading behaviors in the plane of the Weber number (We) and the volume of the sessile droplet (Vp) normalized with the volume of the impacting droplet (Vi) have been presented. The partial coalescence phenomenon is observed when the ratio of the volume of the sessile droplet to that of the impacting droplet (Vp/Vi) is greater than two. For Vp/Vi = 2, the size of the daughter droplet is found to be about 0.1 times as that of the impacting droplet, which increases with the increase in the We and normalized volume of the sessile droplet. In the present study, the negative curvature of the droplet coupled with the presence of the substrate leads to a different coalescence dynamics.

### Fingering regimes in unstable miscible displacements

We study the life-cycle of miscible fingering, from the early fingering initiation, through their growth and nonlinear interactions to their decay to a single finger at late times. Dimensionless analysis is used to relate the number of fingers, the nature of their nonlinear interactions (spreading, coalescence, tip splitting), and their eventual decay to the viscosity ratio, transverse Peclet number, and anisotropic dispersion. We show that the initial number of fingers that grow is approximately half that predicted by analytical solutions that neglect the impact of longitudinal diffusion smearing the interface between the injected solvent and the displaced fluid. The growth rates of these fingers are also approximately one quarter that predicted by these analyses. Nonetheless, we find that the dynamics of finger interactions over time can be scaled using the most dangerous wavenumber and associated growth rate determined from linear stability analysis. This subsequently allows us to provide a relationship that can be used to estimate when predict when the late time, single finger regime will occur.

### The particle stress in dilute suspensions of inertialess spheroids in turbulent channel flow

Particle stress is known to play a vital role in turbulence modulation. However, the earlier studies on particle stress were mostly confined to the cases of spherical and elongated particles. In the present study, we investigated the stress generated in dilute suspensions of inertialess spheroids with various shapes in wall-bounded turbulence. We performed direct numerical simulations of turbulent particle-laden channel flows utilizing a one-way coupled Eulerian-Lagrangian approach. The stress in the suspension of oblate spheroids was examined in detail and compared with prolate spheroid cases for the first time. The results show that particle stress is strongly dependent on particle shape and the stress of the oblate spheroid is qualitatively different from the case of prolate particles. However, we found that the fluctuating spanwise shear stress of flat oblate spheroids, which makes a significant contribution to turbulence dissipation, is in the same order of magnitude of the term generated by elongated prolate spheroids at a constant volume fraction. We also examined the effect of the Reynolds number on the particle stress in channel flows at Reτ = 180 and 1000. The results reveal a negligible influence on the mean stresses, but the fluctuating stresses are significantly Reynolds number dependent. In the buffer layer, we observed the correlations between the particle stress of spheroids and the fluctuating velocity of the fluid in the streamwise direction, which could be attributed to the different orientation of spheroids and fluid strain rate in low- and high-speed streaks of near-wall turbulence.

### A vortex identification method based on local fluid rotation

In this work, a vortex identification method is developed by analyzing the physical meaning of the local rotation of fluid elements. It is shown that a point is locally rotational when the velocity gradient tensor at the point has a pair of complex eigenvalues. The local rotation can be represented by a so called vortex vector. The direction of the vortex vector is defined as that of the local fluid rotation axis, which is parallel to the eigenvector of velocity gradient tensor corresponding to the real eigenvalue. The magnitude is evaluated as the twice of the minimum angular velocity around the point among all azimuth in the plane perpendicular to the vortex vector. Based on the local fluid rotation, a vortex is identified as a connected region where the vortex vector at each point is not equal to zero. The vortex identification method is validated by applying it to Reynolds-averaged Navier-Stokes data and direct numerical simulation data. The results reveal that the method can fully describe the complex structures of vortices.

### Erratum: “Quasi-classical trajectory-based non-equilibrium chemical reaction models for hypersonic air flows” [Phys. Fluids 31, 106102 (2019)]

### Flow induced by an oscillating sphere in probing complex viscosity of polymer solutions

Author(s): Yanzhen He, Lu Li, Takashi Taniguchi, Remco Tuinier, and Tai-Hsi Fan

Flow pattern and apparent complex viscosity are derived explicitly for viscoelastic flow induced by an oscillatory colloid in polymer solutions, with depletion effect taken into account. Within the linear regime, the model can be used to interpret active and passive microrheological measurements.

[Phys. Rev. Fluids 5, 013302] Published Tue Jan 07, 2020