Highlights of 2017

Small drops impinging obliquely on thin flowing soap films frequently demonstrate the rare emergence of bulk elastic effects working in-tandem with the more commonplace hydrodynamic interactions. Three collision regimes are observable: (a) drop piercing through the film, (b) it coalescing with the flow, and (c) it bouncing off the film surface. During impact, the drop deforms along with a bulk elastic deformation of the film. For impacts that are close-to-tangential, the bounce-off regime predominates. We outline a reduced order analytical framework assuming a deformable drop and a deformable three-dimensional film, and the idealization invokes a phase-based parametric study. Angular inclination of the film and the ratio of post and pre-impact drop sizes entail the phase parameters. We also perform experiments with vertically descending droplets (constituted from deionized water) impacting against an inclined soap film, flowing under constant pressure head. Model-predicted phase domain for bounce-off compares well to our experimental findings. Additionally, the experiments exhibit momentum transfer to the film in the form of shed vortex dipoles, along with propagation of free surface waves. On consulting prior published work, we note that for locomotion of water-walking insects using an impulsive action, the momentum distribution to the shed vortices and waves are both significant, taking up respectively 2/3 and 1/3 of the imparted streamwise momentum. Considering the visually similar impulse actions, this theory, despite its assumption of a quiescent liquid bath of infinite depth, is applied to the drop bounce-off experiments, and the resultant shed vortex dipole momenta are compared to the momenta of the coherent vortex structures computed from particle imaging velocimetry data. The magnitudes reveal identical order (10⁻⁷ N s), suggesting that notwithstanding the disparities, the bounce-off regime may be tapped as a toy analog for impulse-based interfacial biolocomotion.

We present a novel vortex identification method based on structured vorticity (ω_s) of the direction field of flow (velocity vectors set to unit magnitude). As a direct measure of streamline curvature is insensitive to vortex strength, ω_s is effective in detecting vortices of various strengths. The effectiveness has been tested against both analytical flows (pure shear flow, Oseen vortex flow, strong outward spiraling motion, straining flow, Taylor–Green flow) and experimental flows (closed cavity flow, closed and open channel flow). Comparison of the new method with the swirling-strength method indicates that the new method shows promise as being a simple and effective criterion for vortex identification.

Friction drag reduction effect by superhydrophobic surfaces in a turbulent channel flow is investigated by means of direct numerical simulation. The simulations are performed under a constant pressure gradient at the friction Reynolds number of 180. A special focus is laid upon the influence of the angle of microridge structure to flow direction, while the gas area fraction on the surface is kept at 50% and the groove width is kept constant at 33.75 wall units. Larger drag reduction effect is observed for a smaller angle: the bulk-mean velocity is increased about 15% when the microridge is parallel to the flow. The drag reduction effect is found to deteriorate rapidly with the microridge angle due to a decrease in the slip velocity. The Reynolds stress budgets show that the modification in each physical effect is qualitatively similar but more pronounced when the microridge is aligned with the stream.

Inertia–gravity wave (IGW) radiation from the elliptical vortex is investigated in the f-plane shallow water system. The far field of IGW is analytically derived for the case of an almost circular Kirchhoff vortex with a small aspect ratio. Cyclone–anticyclone asymmetry appears at finite values of the Rossby number (Ro) caused by the source originating in the Coriolis acceleration. While the intensity of IGWs from the cyclone monotonically decreases as f increases, that from the anticyclone increases as f increases for relatively smaller f and has a local maximum at intermediate f. A numerical experiment is conducted on a model using a spectral method in an unbounded domain. The numerical results agree quite well with the analytical ones for elliptical vortices with small aspect ratios, implying that the derived analytical forms are useful for the verification of the numerical model. For elliptical vortices with larger aspect ratios, however, significant deviation from the analytical estimates appears. The intensity of IGWs radiated in the numerical simulation is larger than that estimated analytically. The reason is that the source of IGWs is amplified during the time evolution because the shape of the vortex changes from ideal ellipse to elongated with filaments. Nevertheless, cyclone–anticyclone asymmetry similar to the analytical estimate appears in all the range of aspect ratios, suggesting that this asymmetry is a robust feature.

A dispersion relation for gravity waves in water covered by disk-like impurities embedded in a viscous matrix is derived. The macroscopic equations are obtained by ensemble-averaging the fluid equations at the disk scale in the asymptotic limit of long waves and low disk surface fraction. Various regimes are identified depending on the disk radii and the thickness and viscosity of the top layer. Semi-quantitative analysis in the close-packing regime suggests dramatic modification of the dynamics, with orders of magnitude increase in wave damping and wave dispersion. A simplified model working in this regime is proposed. Possible applications to wave propagation in an ice-covered ocean are discussed and comparison with field data is provided.

Soft microcapsules moving in a cylindrical capillary deform from quasi-spherical shapes to elongated shapes with an inversion of curvature at the rear. We investigated the perturbation of the flow by particle tracking velocimetry around deformed microcapsules in confined flow. These experiments are completed by numerical simulations. Microcapsules are made of a thin membrane of polymerized human albumin and their shear elastic moduli are previously characterized in a cross flow chamber. Firstly, the velocity of the microcapsule can be calculated by theoretical predictions for rigid spheres, even for large deformations as 'parachute-like' shapes, if a relevant definition of the ratio of confinement is chosen. Secondly, at the rear and the front of the microcapsule, the existence of multiple recirculation regions is governed by the local curvature of the membrane. The amplitudes of these perturbations increase with the microcapsule deformation, whereas their axial extents are comparable to the radius of the capillary whatever the confinement and the capillary number. We conclude that whereas the motion of microcapsules in confined flow has quantitative similitudes with rigid spheres in terms of velocity and axial extent of the perturbation, their presence induces variations in the flow field that are related to the local deformation of the membrane as in droplets.

Turbulence and edge states are investigated numerically in a plane Poiseuille flow driven by a fixed pressure gradient. Simulations are carried out within the minimal flow unit, a concept introduced by Jiménez and Moin (1991 J. Fluid Mech. 225 213–40) to unravel the dynamics of near-wall structures in the absence of outer large-scale motions. For both turbulent and edge regimes the activity appears to be localised near only one wall at a time, and the long term dynamics features abrupt reversals. The dynamics along one reversal is structured around the transient visit to a subspace of symmetric flow fields. An exact travelling wave solution is found to exist very close to this subspace. Additionally the self-similarity of the asymmetric states is addressed. Contrary to most studies focusing on symmetric solutions, the present study suggests that edge states, when localised near one wall, do not scale in outer units. The current study suggests a composite scaling.

Multiphase flow simulation serves a vital purpose in applications as diverse as engineering design, natural disaster prediction, and even study of astrophysical phenomena. In these scenarios, it can be very difficult, expensive, or even impossible to fully represent the physical system under consideration. Even still, many such real-world applications can be modeled as a two-phase flow containing both continuous and dispersed phases. Consequentially, the continuous phase is thought of as a fluid and the dispersed phase as particles. The continuous phase is typically treated in the Eulerian frame of reference and represented on a fixed grid, while the dispersed phase is treated in the Lagrangian frame and represented by a sample distribution of Lagrangian particles that approximate a cloud. Coupling between the phases requires interpolation of the continuous phase properties at the locations of the Lagrangian particles. This interpolation step is straightforward and can be performed at higher order accuracy. The reverse process of projecting the Lagrangian particle properties from the sample points to the Eulerian grid is complicated by the time-dependent non-uniform distribution of the Lagrangian particles. In this paper we numerically examine three reconstruction, or projection, methods: (i) direct summation (DS), (ii) least-squares, and (iii) sparse approximation. We choose a continuous representation of the dispersed phase property that is systematically varied from a simple single mode periodic signal to a more complex artificially constructed turbulent signal to see how each method performs in reconstruction. In these experiments, we show that there is a link between the number of dispersed Lagrangian sample points and the number of structured grid points to accurately represent the underlying functional representation to machine accuracy. The least-squares method outperforms the other methods in most cases, while the sparse approximation method is able to capture physically important flow features when under-sampled but at an increased cost. Interestingly, the DS method has been used in the past but in comparison to the other two methods it offers only first order convergence. The above three methods were also compared against standard linear and cubic interpolation techniques from non-uniform Lagrangian points to the Eulerian grid. The performance of these standard interpolation methods were only of the order of DS.

Axisymmetric flow in a cylindrical tank over a rotating bottom is investigated and its approximate solution with an analytic expression is obtained. The interior region, comprising the majority of the fluid, consists of two sub-regions. It is easily shown that a rigid-body rotational flow with the same rotation rate as that of the bottom is formed in the inner interior and that a potential flow with constant angular momentum occurs in the outer interior sub-region. However, the radius that divides these two sub-regions has not been determined. To determine this radius, the structures of the boundary layers are investigated in detail. These boundary layers surround the interior regions, and include the boundaries between the interior region and the side wall of the tank, between the interior and the bottom, and between the inner and outer interior sub-regions. By connecting the flows in the boundary layers, the vertical circulation as a whole is established, and consequently the radius dividing the two interior sub-regions is successfully determined as a function of the aspect ratio of the water layer region. This axisymmetric flow will be utilized as the basic state for investigating theoretically various non-axisymmetric phenomena observed in laboratory experiments.