Volume 25, Issue 10, October 2013

The topological and dynamical features of small scales are studied in the context of decaying magnetohydrodynamic turbulent flows using direct numerical simulations. Joint probability density functions (PDFs) of the invariants of gradient quantities related to the velocity and the magnetic fields demonstrate that structures and dynamics at the time of maximum dissipation depend on the large scale initial conditions at the examined Reynolds numbers. This is evident in particular from the fact that each flow has a different shape for the joint PDF of the invariants of the velocity gradient in contrast to the universal teardrop shape of hydrodynamic turbulence. The general picture that emerges from the analysis of the invariants is that regions of high vorticity are correlated with regions of high strain rate S also in contrast to hydrodynamic turbulent flows. Magnetic strain dominated regions are also well correlated with region of high current density j . Viscous dissipation ( ) as well as Ohmic dissipation ( ) resides in regions where strain and rotation are locally almost in balance. The structures related to the velocity gradient possess different characteristics than those associated with the magnetic field gradient with the latter being locally more quasitwo dimensional.
 AWARD AND INVITED PAPERS


Circulation based models for Boussinesq gravity currents
View Description Hide DescriptionIn addition to the conservation of mass and horizontal momentum, existing analytical models of gravity currents traditionally require an assumption about the conservation or loss of energy along specific streamlines for closure. Here, we show that the front velocity of gravity currents can be predicted as a function of their height from mass and momentum balances alone by considering the evolution of interfacial vorticity. This approach does not require information on the pressure field and therefore avoids the need for the energy conservation arguments invoked by earlier models. Predictions by the new theory are shown to be in close agreement with results from numerical simulations. We also discuss the influence of downstream mixing on the front velocity predicted by this theory.

Nearwall turbulence
View Description Hide DescriptionThe current state of knowledge about the structure of wallbounded turbulent flows is reviewed, with emphasis on the layers near the wall in which shear is dominant, and particularly on the logarithmic layer. It is shown that the shear interacts with scales whose size is larger than about one third of their distance to the wall, but that smaller ones, and in particular the vorticity, decouple from the shear and become roughly isotropic away from the wall. In the buffer and viscous layers, the dominant structures carrying turbulent energy are the streamwise velocity streaks, and the vortices organize both the dissipation and the momentum transfer. Farther from the wall, the velocity remains organized in streaks, although much larger ones than in the buffer layer, but the vortices lose their role regarding the Reynolds stresses. That function is taken over by wallattached turbulent eddies with sizes and lifetimes proportional to their heights. Two kinds of eddies have been studied in some detail: vortex clusters, and ejections and sweeps. Both can be classified into a detached background, and a geometrically selfsimilar wallattached family. The latter is responsible for most of the momentum transfer, and is organized into composite structures that can be used as models for the attachededdy hierarchy hypothesized by Townsend [“Equilibrium layers and wall turbulence,” J. Fluid Mech.11, 97–120 (1961)]. The detached component seems to be common to many turbulent flows, and is roughly isotropic. Using a variety of techniques, including direct tracking of the structures, it is shown that an important characteristic of wallbounded turbulence is temporally intermittent bursting, which is present at all distances from the wall, and in other shear flows. Its properties and time scales are reviewed, and it is shown that bursting is an important part of the production of turbulent energy from the mean shear. It is also shown that a linearized model captures many of its characteristics.

Simulation based planning of surgical interventions in pediatric cardiology
View Description Hide DescriptionHemodynamics plays an essential role in the progression and treatment of cardiovascular disease. However, while medical imaging provides increasingly detailed anatomical information, clinicians often have limited access to hemodynamic data that may be crucial to patient risk assessment and treatment planning. Computational simulations can now provide detailed hemodynamic data to augment clinical knowledge in both adult and pediatric applications. There is a particular need for simulation tools in pediatric cardiology, due to the wide variation in anatomy and physiology in congenital heart disease patients, necessitating individualized treatment plans. Despite great strides in medical imaging, enabling extraction of flow information from magnetic resonance and ultrasound imaging, simulations offer predictive capabilities that imaging alone cannot provide. Patient specific simulations can be used for in silico testing of new surgical designs, treatment planning, device testing, and patient risk stratification. Furthermore, simulations can be performed at no direct risk to the patient. In this paper, we outline the current state of the art in methods for cardiovascular blood flow simulation and virtual surgery. We then step through pressing challenges in the field, including multiscale modeling, boundary condition selection, optimization, and uncertainty quantification. Finally, we summarize simulation results of two representative examples from pediatric cardiology: single ventricle physiology, and coronary aneurysms caused by Kawasaki disease. These examples illustrate the potential impact of computational modeling tools in the clinical setting.

Numerical simulations of spatially developing, accelerating boundary layers
View Description Hide DescriptionWe present the results of direct and largeeddy simulations of spatially developing boundary layers subjected to favorable pressure gradient, strong enough to cause reversion of the flow towards a quasilaminar state. The numerical results compare well with experimental data. Visualization of the flow structures shows the wellknown stabilization of the streaks, the reorientation of outer layer vortices in the streamwise direction, and the appearance of turbulent spots in the retransition region. Both instantaneous visualizations and turbulent statistics highlight the significant damping of wallnormal and spanwise fluctuations. The fast component of the pressure fluctuations appears to be the main driver of this process, contributing to reduce pressure fluctuations and, as a consequence, the energy redistribution term in the Reynolds stress budgets. The streamwise stresses, in whose budget a separate production term plays a role, do not decay but remain frozen at their upstream value. The decrease of wallnormal and spanwise fluctuations appears to be the main cause of the innerlayer stabilization, by disrupting the generation and subsequent growth of streaks, consistent with various models of the turbulencegeneration cycle proposed in the literature. The outer layer seems to play a passive role in this process. The stretching and reorientation of the outerlayer vortices results in a more orderly and organized structure; since fewer ejections occur, the inner layer does not break this reorganization, which is maintained until retransition begins.
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 LETTERS


Inertial coalescence of droplets on a partially wetting substrate
View Description Hide DescriptionWe consider the growth rate of the height of the connecting bridge in rapid surfacetensiondriven coalescence of two identical droplets attached on a partially wetting substrate. For a wide range of contact angle values, the height of the bridge grows with time following a power law with a universal exponent of 2/3, up to a threshold time, beyond which a 1/2 exponent results, that is known for coalescence of freelysuspended droplets. In a narrow range of contact angle values close to 90°, this threshold time rapidly vanishes and a 1/2 exponent results for a 90° contact angle. The argument is confirmed by threedimensional numerical simulations based on a diffuse interface method with adaptive mesh refinement and a volumeoffluid method.

Do we understand the bubble formation by a single drop impacting upon liquid surface?
View Description Hide DescriptionLarge bubble formation by a single drop impacting upon a liquid surface with low impact energy is conventionally considered to be unimportant and not a cause for small bubble(s) generation. Our experiments contradict three widely accepted concepts about bubble formation. First, this paper presents results that give evidence of much wider existence of large bubble entrainment. Second, there is no closed characteristic regime for regular large bubble generation. Third, for the first time, there are results of bubble pair generation in sequence that show the direct formation of smaller bubble(s) due to a single large bubble rupturing without external disturbances. Additionally, this work demonstrates that the shape of an oscillating prolate drop at impact is the missing factor that helps predict large bubble formation. At the end, this paper presents a new characteristic map for large bubble formation that is based on the theoretical oscillation model.

Evolution of a hairpin vortex in a shearthinning fluid governed by a powerlaw model
View Description Hide DescriptionThe effect of a shearthinning fluid governed by a powerlaw model on the evolution of a hairpin vortex in a wallbounded flow was studied by means of direct numerical simulation. With a fixed Reynolds number and hairpin vortex strength, the effect of shearthinning on vortex evolution could be isolated. The primary observation is that very early in time shearthinning has the effect of reducing the production of vortex kinetic energy and dramatically increasing viscous dissipation. This leads to a delay in the transition of the flow to a turbulent state. Threedimensional flow visualizations reveal that the increased dissipation is associated with an instability in which the hairpin vortex is broken down into smallscale structures. It is suggested that the finite amplitude of the hairpin creates a lowering of viscosity near the hairpin vortex core which leads to this instability.

Experiments on windperturbed rogue wave hydrodynamics using the Peregrine breather model
View Description Hide DescriptionBeing considered as a prototype for description of oceanic rogue waves, the Peregrine breather solution of the nonlinear Schrödinger equation has been recently observed and intensely investigated experimentally in particular within the context of water waves. Here, we report the experimental results showing the evolution of the Peregrine solution in the presence of wind forcing in the direction of wave propagation. The results show the persistence of the breather evolution dynamics even in the presence of strong wind and chaotic wave field generated by it. Furthermore, we have shown that characteristic spectrum of the Peregrine breather persists even at the highest values of the generated wind velocities thus making it a viable characteristic for prediction of rogue waves.

Similarity theory of lubricated Hertzian contacts
View Description Hide DescriptionWe consider a heavily loaded, lubricated contact between two elastic bodies at relative speed U, such that there is substantial elastic deformation. As a result of the interplay between hydrodynamics and nonlocal elasticity, a fluid film develops between the two solids, whose thickness scales as U ^{3/5}. The film profile h is selected by a universal similarity solution along the upstream inlet. Another similarity solution is valid at the outlet, which exhibits a local minimum in the film thickness. The two solutions are connected by a hyperbolic problem underneath the contact. Our asymptotic results for a soft sphere pressed against a hard wall are shown to agree with both experiment and numerical simulations.

From the circular cylinder to the flat plate wake: The variation of Strouhal number with Reynolds number for elliptical cylinders
View Description Hide DescriptionThe variation of Strouhal number with Reynolds number is quantified experimentally for a series of elliptical cylinders spanning aspect ratios between , corresponding to a circular cylinder, and , corresponding to a flat plate, over the Reynolds number range . The widths of the spectral peaks in Fourier space at each Reynolds number, together with changes in the shape or continuity of the Strouhal number curves, provide information of underlying threedimensional transitions. Whilst modified versions of the mode A and B transitions of a circular cylinder wake occur at aspect ratios above , one major difference is observed for . In a limited range of Reynolds numbers, the wake appears to relaminarize after it has already undergone threedimensional transition. This flow regime is characterized by a strictly periodic vortex shedding.
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 ARTICLES

 Biofluid Mechanics

Swimming near deformable membranes at low Reynolds number
View Description Hide DescriptionMicroorganisms are rarely found in nature swimming freely in an unbounded fluid. Instead, they typically encounter other organisms, hard walls, or deformable boundaries, such as free interfaces or membranes. Hydrodynamic interactions between the swimmer and nearby objects lead to many interesting phenomena, such as changes in swimming speed, tendencies to accumulate or turn, and coordinated flagellar beating. Inspired by this class of problems, we investigate locomotion of microorganisms near deformable boundaries. We calculate the speed of an infinitely long swimmer close to a flexible surface separating two fluids; we also calculate the deformation and swimming speed of the flexible surface. When the viscosities on either side of the flexible interface differ, we find that fluid is pumped along or against the swimming direction, depending on which viscosity is greater.
 Micro and Nanofluid Mechanics

Mixing by chaotic advection in a magnetohydrodynamic driven flow
View Description Hide DescriptionA new device containing three circular electrodes and where very small quantities of a weakly electrically conductive liquid are propelled and mixed by chaotic advection is designed and constructed. The liquid, a copper sulfate solution, is propelled by the Lorentz body force, i.e., a magnetic field perpendicular to an electrical current. When the potentials of the electrodes are constant and the Lorentz force is small enough so that at the free surface the vertical velocity is practically zero, the flow field exhibits there a saddle point when the three circular electrodes are not in a concentric position. By modulating the electrical potential between the electrodes, the position of the saddle point changes. This slowly varying system is far from integrable and exhibits largescale chaos, the nonintegrability is due to the slow continuous modulation of the position of the saddle stagnation point and the two streamlines stagnating on it. Dye advection experiments are compared successfully to a numerical solution of the 3D equations of motion under these assumptions. We have also defined a potential mixing zone to predict the location of the chaotic region and calculated Poincaré sections. These two tools give results which are in excellent agreement, they are used, with others, to adjust the mixing protocol parameters and the geometry in order to improve mixing.
 Interfacial Flows

Experimental study on the evolution of traveling waves over an undulated incline
View Description Hide DescriptionWe present experimental results on the evolution of traveling waves over a strongly undulated incline. In order to investigate the difference between waves in the linearly stable and unstable region, we set the Reynolds number near the neutral curve. That way, we were able to cross the neutral curve by increasing the frequency of excitation, without changing the velocity field of the basic flow. The amplitude of excitation was also varied, to analyze the evolution of both linear and nonlinear waves. We report on a rich variety of phenomena, including: (a) energy transfer from the excitation frequency to its higher harmonics, (b) the growth rate of the traveling waves, (c) the stability of traveling waves depending on its amplitude, and (d) the amplitude of saturation depending on the excitation frequency. We compare our results to those so far available in the literature. To our knowledge, this is the first experimental work on the development of traveling waves over strongly undulated substrate geometries.

Stokes flow in a drop evaporating from a liquid subphase
View Description Hide DescriptionThe evaporation of a drop from a liquid subphase is investigated. The two liquids are immiscible, and the contact angles between them are given by the Neumann construction. The evaporation of the drop gives rise to flows in both liquids, which are coupled by the continuity of velocity and shearstress conditions. We derive selfsimilar solutions to the velocity fields in both liquids close to the threephase contact line, where the drop geometry can be approximated by a wedge. We focus on the case where Marangoni stresses are negligible, for which the flow field consists of three contributions: flow driven by the evaporative flux from the drop surface, flow induced by the receding motion of the contact line, and an eigenmode flow that is due to the stirring of the fluid in the corner by the largescale flow in the drop. The eigenmode flow is asymptotically subdominant for all contact angles. The moving contactline flow dominates when the angle between the liquid drop and the horizontal surface of the liquid subphase is smaller than 90°, while the evaporativeflux driven flow dominates for larger angles. A parametric study is performed to show how the velocity fields in the two liquids depend on the contact angles between the liquids and their viscosity ratio.

On the mechanism of wetting failure during fluid displacement along a moving substrate
View Description Hide DescriptionThis work investigates the onset of wetting failure for displacement of Newtonian fluids in parallel channels. A hydrodynamic model is developed for planar geometries where an advancing fluid displaces a receding fluid along a moving substrate. The model is evaluated with three distinct approaches: (i) the lowspeed asymptotic theory of Cox [J. Fluid Mech.168, 169–194 (1986)], (ii) a onedimensional (1D) lubrication approach, and (iii) a twodimensional (2D) flow model solved with the Galerkin finite element method (FEM). Approaches (ii) and (iii) predict the onset of wetting failure at a critical capillary number Ca ^{ crit }, which coincides with a turning point in the steadystate solution family for a given set of system parameters. The 1D model fails to accurately describe interface shapes near the threephase contact line when air is the receding fluid, producing large errors in estimates of Ca ^{ crit } for these systems. Analysis of the 2D flow solution reveals that strong pressure gradients are needed to pump the receding fluid away from the contact line. A mechanism is proposed in which wetting failure results when capillary forces can no longer support the pressure gradients necessary to steadily displace the receding fluid. The effects of viscosity ratio, substrate wettability, and fluid inertia are then investigated through comparisons of Ca ^{ crit } values and characteristics of the interface shape. Surprisingly, the lowspeed asymptotic theory (i) matches trends computed from (iii) throughout the entire investigated parameter space. Furthermore, predictions of Ca ^{ crit } from the 2D flow model compare favorably to values measured in experimental airentrainment studies, supporting the proposed wettingfailure mechanism.

Numerical simulations of bubble formation from submerged needles under nonuniform direct current electric field
View Description Hide DescriptionIn several chemical and space industries, small bubbles are desired for efficient interaction between the liquid and gas phases. In the present study, we show that nonuniform electric field with appropriate electrode configurations can reduce the volume of the bubbles forming at submerged needles by up to three orders of magnitude. We show that localized high electric stresses at the base of the bubbles result in slipping of the contact line on the inner surface of the needle and subsequent bubble formation occurs with contact line inside the needle. We also show that for bubble formation in the presence of highly nonuniform electric field, due to high detachment frequency, the bubbles go through multiple coalescences and thus increase the apparent volume of the detached bubbles.

On selfsimilar thermal rupture of thin liquid sheets
View Description Hide DescriptionWe consider the dynamics of a symmetrically heated thin incompressible viscous fluid sheet. We take surface tension to be temperature dependent and consequently the streamwise momentum equation includes the effects of thermocapillarity, inertia, viscous stresses, and capillarity. Energy transport to the surrounding environment is also included. We use a longwave analysis to derive a single nondimensional system which, with appropriate choices of Reynolds number, recovers two previously studied cases. In both cases, we find conditions under which sufficiently largeamplitude initial temperature profiles induce film rupture in finite time, notably without the inclusion of disjoining pressures from van der Waals effects. When the Reynolds number is large, the similarity solution is governed by a balance of inertia and capillarity near the rupture location, analogous to the isothermal case. When the Reynolds number is small, the thermocapillary transients induce the same similarity solution over intermediate times that is found for the drainage of lamellae in foams. For O(1) Reynolds numbers, the dynamics are governed initially by the large Reynolds number evolution, and then a transition over several orders of magnitude in the sheet thickness needs to take place before the small Reynolds number similarity solution is observed.

Effect of ambient air on liquid jet impingement on a moving substrate
View Description Hide DescriptionAn experimental investigation into the effect of surrounding air pressure on liquid jet impingement on a moving substrate was performed. The study was carried out with Newtonian liquids impacting dry substrates. A variety of jet speeds, substrate speeds, and liquid viscosities were studied. It was observed that, as is the case for Newtonian droplet impact, the surrounding air pressure plays a crucial role in the splashing behaviour of jet impingement. There exists a threshold pressure below which splash does not occur. It is proposed that for certain impingement conditions lamella detachment from the substrate occurs due to aerodynamic forces acting on the leading edge of the lamella, which destabilizes the balance between surface tension and fluid pressure forces.

Stability of a moving radial liquid sheet: Timedependent equations
View Description Hide DescriptionWe study the stability of a radial liquid sheet produced by headon impingement of two equal laminar liquid jets. Linear stability equations are derived from the inviscid flow equations for a radially expanding sheet that govern the timedependent evolution of the two liquid interfaces. The analysis accounts for the varying liquid sheet thickness while the inertial effects due to the surrounding gas phase are ignored. The analysis results in stability equations for the sinuous and the varicose modes of sheet deformation that are decoupled at the lowest order of approximation. When the sheet is excited at a fixed frequency, a small sinuous displacement introduced at the point of impingement grows as it is convected downstream suggesting that the sheet is unstable at all Weber numbers (We ≡ ρ l U ^{2} h/σ) in the absence of the gas phase. Here, ρ l is the density of the liquid, U is the speed of the liquid jet, h is the local sheet thickness, and σ is the surface tension. The sinuous disturbance diverges at We = 2 which sets the size of the sheet, in agreement with the results of Taylor [“The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets,” Proc. R. Soc. London, Ser. A253, 313 (1959)]. Asymptotic analysis of the sinuous mode for all frequencies shows that the disturbance amplitude diverges inversely with the distance from the edge of the sheet. The varicose waves, on the other hand, are neutrally stable at all frequencies and are convected at the speed of the liquid jet.

Inertial effects at moderate Reynolds number in thinfilm rimming flows driven by surface shear
View Description Hide DescriptionIn this paper, we study twodimensional thinfilm flow inside a stationary circular cylinder driven by an imposed surface shear stress. Modelling is motivated by a need to understand the cooling and film dynamics provided by oil films in an aeroengine bearing chamber characterised by conditions of very high surface shear and additional film mass flux from oil droplets entering the film through the surface. In typical highspeed operation, film inertial effects can provide a significant leadingorder mechanism neglected in existing lubrication theory models. Inertia at leadingorder is included within a depthaveraged formulation where wall friction is evaluated similar to hydraulic models. This allows key nonlinear inertial effects to be included while retaining the ability to analyse the problem in a mathematically tractable formulation and compare with other approaches. In constructing this model, a set of simplified mass and momentum equations are integrated through the depth of the film yielding a spatially onedimensional depthaveraged formulation of the problem. An a priori assumed form of velocity profile is needed to complete the system. In a local Stokes flow analysis, a quadratic profile is the exact solution for the velocity field though it must be modified when inertial effects become important. Extension of the velocity profile to a cubic profile is selected enabling specification of a wall friction model to include the roughness of the cylinder wall. A modelling advantage of including the inertia term, relevant to the applications considered, is that a smooth progression in solution can be obtained between cases of low Reynolds number corresponding to lubrication theory, and high Reynolds number corresponding to uniform rimmingflow. Importantly, we also investigate the effect of inertia on some typical solutions from other studies and present a greater insight to existing and new film solutions which arise from including inertia effects.