Focus on Fluids
Microplumes for nanovelocimetry
 Todd M. Squires

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 26 October 2017, pp. 14

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Fluid flows through nanoscale channels depend sensitively on the physical and chemical properties of the walls that surround them. The submicron dimensions of such channels, however, are impossible to resolve optically, which rules out most methods for flow visualization. Classic calculations by Squire (Q. J. Mech. Appl. Maths, vol. IV, 1951, pp. 321–329) and Landau & Lifshitz (Fluid Mechanics, vol. 6, 1959, Pergamon) showed that the laminar flow driven outside a capillary, by fluid emerging from the end of the capillary, is identical to the flow driven by a point force proportional to the average velocity in the capillary. Secchi et al. (J. Fluid Mech. 826, R3) analyze the dispersion of a solute that is injected along with the fluid, whose concentration decays slowly with distance but with a strong angular dependence that encodes the intracapillary velocity. Fluorescence micrographs of the concentration profile emerging from the nanocapillary can be related directly to the average fluid velocity within the nanocapillary. Beyond their remarkable capacity for nanovelocimetry, Landau–Squire plumes will likely appear throughout micro and nanofluidic systems.
Papers
Lagrangian transport in a class of threedimensional buoyancydriven flows
 P. S. Contreras, M. F. M. Speetjens, H. J. H. Clercx

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 26 October 2017, pp. 540

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The present study concerns the Lagrangian dynamics of threedimensional (3D) buoyancydriven cavity flows under steady and laminar conditions due to a global temperature gradient imposed via an opposite hot and cold sidewall. This serves as the archetypal configuration for naturalconvection flows in which (contrary to the wellknown Rayleigh–Bénard flow) gravity is perpendicular (instead of parallel) to the global temperature gradient. Limited insight into the Lagrangian properties of this class of flows, despite its relevance to observed flow phenomena as well as scalar transport, motivates this study. The 3D Lagrangian dynamics are investigated in terms of the generic structure and associated transport properties of the global streamline pattern (‘Lagrangian flow topology’) by both theoretical and computational analyses. The Grashof number $Gr$ is the principal control parameter for the flow topology: limit $Gr=0$ yields a trivial state of closed streamlines; $Gr>0$ induces symmetry breaking by fluid inertia and buoyancy and thus causes formation of toroidal coherent structures (‘primary tori’) embedded in chaotic streamlines governed by Hamiltonian mechanisms. Fluid inertia prevails for ‘smaller’ $Gr$ and gives behaviour that is dynamically entirely analogous to 3D liddriven cavity flows. Buoyancyinduced bifurcation of the flow topology occurs for ‘larger’ $Gr$ and underlies the emergence of ‘secondary rolls’ observed in the literature and to date unreported secondary tori for ‘larger’ Prandtl numbers $Pr$. Key to these dynamics are stagnation points and corresponding heteroclinic manifold interactions.
Symmetry breaking and instabilities of conical vortex pairs over slender delta wings
 BaoFeng Ma, Zhijin Wang, Ismet Gursul

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 26 October 2017, pp. 4172

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An investigation of symmetry breaking and naturally occurring instabilities over thin slender delta wings with sharp leading edges was carried out in a water tunnel using particle image velocimetry (PIV) measurements. Timeaveraged location, strength and core radius of conical vortices vary almost linearly with chordwise distance for three delta wings with $75^{\circ }$, $80^{\circ }$ and $85^{\circ }$ sweep angles over a wide range of angles of attack. Properties of the timeaveraged vortex pairs depend only on the similarity parameter, which is a function of the angle of attack and the sweep angle. It is shown that timeaveraged vortex pairs develop asymmetry gradually with increasing values of the similarity parameter. Vortex asymmetry can develop in the absence of vortex breakdown on the wing. Instantaneous PIV snapshots were analysed using proper orthogonal decomposition and dynamic mode decomposition, revealing the shear layer and vortex instabilities. The shear layer mode is the most periodic and more dominant for lower values of the similarity parameter. The Strouhal number based on the free stream velocity component in the crossflow plane is a function of only the similarity parameter. The dominant frequency of the shear layer mode decreases with the increasing similarity parameter. The vortex modes reveal the fluctuations of the vorticity magnitude and helical displacement of the cores, but with little periodicity. There is little correlation between the fluctuations in the cores of the vortices.
On the critical freesurface flow over localised topography
 J. S. Keeler, B. J. Binder, M. G. Blyth

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 26 October 2017, pp. 7396

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Flow over bottom topography at critical Froude number is examined with a focus on steady, forced solitary wave solutions with algebraic decay in the far field, and their stability. Using the forced Korteweg–de Vries (fKdV) equation the weakly nonlinear steady solution space is examined in detail for the particular case of a Gaussian dip using a combination of asymptotic analysis and numerical computations. Nonuniqueness is established and a seemingly infinite set of steady solutions is uncovered. Nonuniqueness is also demonstrated for the fully nonlinear problem via boundaryintegral calculations. It is shown analytically that critical flow solutions have algebraic decay in the far field both for the fKdV equation and for the fully nonlinear problem and, moreover, that the leadingorder form of the decay is the same in both cases. The linear stability of the steady fKdV solutions is examined via eigenvalue computations and by a numerical study of the initial value fKdV problem. It is shown that there exists a linearly stable steady solution in which the deflection from the otherwise uniform surface level is everywhere negative.
Global instability analysis and experiments on buoyant plumes
 Kuchimanchi K. Bharadwaj, Debopam Das

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 26 October 2017, pp. 97145

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The present work investigates the puffing instability of circular buoyant plumes by performing global linear stability analysis and experiments. In the nondimensional parameter space investigated, plumes exhibit global instability only for axisymmetric perturbations with two unstable modes, which are of oscillatory type. The frequencies of these two unstable global modes agree well with the experiments which suggest that puffing occurs in buoyant plumes as a result of linear global instability. A comprehensive investigation on the effect of various nondimensional parameters and inlet velocity profiles on frequency and growth rates of the global modes is carried out. The results are used to delineate the stability boundaries for these global modes and to obtain scaling laws for the associated oscillation frequencies. The analysis demonstrates that the two buoyancy parameters, Froude number and sourcetoambient density ratio, play dominant roles in impacting plume transition and oscillation frequencies. Results from global linear stability analysis and earlier experiments have majorly differed in two aspects. The earlier experiments reported a switch in puffing frequency scaling in Richardson number range 100–500, while the instability analysis predicts this switch at around 6000. Also, the instability analysis predicts the occurrence of puffing at density ratios higher than the critical value 0.5–0.6 reported in earlier experiments. To address these differences and validate the results obtained from global linear stability analysis, experiments are performed in a setup that has been carefully designed to minimize the settling chamber disturbances. The present experiments corroborate the findings of global linear stability analysis. The mechanisms responsible for global instability in plumes have been identified using perturbation vorticity transport equation.
Modes of synchronisation in the wake of a streamwise oscillatory cylinder
 Guoqiang Tang, Liang Cheng, Feifei Tong, Lin Lu, Ming Zhao

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 26 October 2017, pp. 146169

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A numerical analysis of flow around a circular cylinder oscillating inline with a steady flow is carried out over a range of driving frequencies $(f_{d})$ at relatively low amplitudes $(A)$ and a constant Reynolds number of 175 (based on the freestream velocity). The vortex shedding is investigated, especially when the shedding frequency $(f_{s})$ synchronises with the driving frequency. A series of modes of synchronisation are presented, which are referred to as the $p/q$ modes, where $p$ and $q$ are natural numbers. When a $p/q$ mode occurs, $f_{s}$ is detuned to $(p/q)f_{d}$, representing the shedding of $p$ pairs of vortices over $q$ cycles of cylinder oscillation. The $p/q$ modes are further characterised by the periodicity of the transverse force over every $q$ cycles of oscillation and a spatial–temporal symmetry possessed by the global wake. The synchronisation modes $(p/q)$ with relatively small natural numbers are less sensitive to the change of external control parameters than those with large natural numbers, while the latter is featured with a narrow space of occurrence. Although the mode of synchronisation can be almost any rational ratio (as shown for $p$ and $q$ smaller than 10), the probability of occurrence of synchronisation modes with $q$ being an even number is much higher than $q$ being an odd number, which is believed to be influenced by the natural even distribution of vortices in the wake of a stationary cylinder.
Strouhal–Reynolds number relationship for flow past a circular cylinder
 Hongyi Jiang, Liang Cheng

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 26 October 2017, pp. 170188

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The Strouhal–Reynolds number ($St{}Re$) relationship for flow past a circular cylinder in the low $Re$ range of $Re\leqslant 1000$ is investigated through two (2D) and threedimensional (3D) direct numerical simulations (DNS). An improved method is proposed for the determination of the separating velocity and the wake width to allow for a better estimation of the wake Strouhal number $St^{\ast }$. For $Re$ in the extended laminar regime calculated by 2D DNS, the $St^{\ast }$ values are found to be more uniform than the original $St$ for the 2D flow. It is also found that the $St^{\ast }$ values for the 2D and 3D flows agree well in the laminar regime of $Re$ up to approximately 270. In addition, uniform $St^{\ast }$ values are also obtained for different mode A and mode B flow structures triggered artificially by using different cylinder span lengths in DNS. It is demonstrated that the drop in $St$ (with respect to its 2D counterpart) with the development of different 3D wake structures is due to the decrease in the separating velocity and the increase in the wake width for a 3D flow, rather than the existence of a particular wake structure such as pure mode A or vortex dislocation. However, as the wake flow becomes increasingly turbulent with further increase in $Re$, the $St^{\ast }$ value for the 3D flow increases gradually and deviates from its 2D counterpart, since for turbulent 3D flows the vortex shedding frequency scales on a length smaller than the wake width.
Dynamics of falling films on the outside of a vertical rotating cylinder: waves, rivulets and dripping transitions
 Manuel Rietz, Benoit Scheid, François Gallaire, Nicolas Kofman, Reinhold Kneer, Wilko Rohlfs

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 26 October 2017, pp. 189211

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Falling liquid films on the underside of a plate or on the outside of a rotating cylinder are subject to a destabilizing body force. The evolution of the film topology is determined by interactions between the Kapitza and the Rayleigh–Taylor instability, leading to complex patterning of the film surface and eventually fluid detachment from the substrate. This study experimentally investigates the evolution of the surface topology for a film on the outside of a vertical rotating cylinder of large radius. Shear at the liquid/air interface is suppressed through an outer, corotating cylinder. The film evolution is captured through high speed visualization in dependence of the control parameters, namely Reynolds number and rotation frequency. An increasing influence of the Rayleigh–Taylor instability for an increasing destabilizing body force (increasing rotational speed of the cylinder) is most notably observed in the form of a decreasing inception length of rivulet structures dominating the film topology. Wavelength as well as inception length of rivulets match the predictions from linear stability analysis of the classical Rayleigh–Taylor problem. In this context, experimental and supporting numerical results suggest that the emergence of rivulets occurs for any nonzero value of the destabilizing body force after a given evolution length that decreases with increasing body force. Fluid detachment from the substrate is found to be intimately related to the existence of rivulet structures. In dependence of the control parameters, detaching droplets are either observed as a result of interactions of solitary pulses of varying phase speed on rivulets, directly after destabilization of twodimensional waves into rivulets or immediately at the fluid inlet. By comparison to the convective/absolute instability transition predicted by linear stability analysis of an integral boundary layer formulation of the problem in question, it is shown that the prediction of a predominant dripping mechanism lies beyond the scope of linear analysis.
Shock–boundary layer interaction and energetics in transonic flutter
 Pradeepa T. Karnick, Kartik Venkatraman

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 26 October 2017, pp. 212240

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We study the influence of shock and boundary layer interactions in transonic flutter of an aeroelastic system using a Reynoldsaveraged Navier–Stokes (RANS) solver together with the Spalart–Allmaras turbulence model. We show that the transonic flutter boundary computed using a viscous flow solver can be divided into three distinct regimes: a low transonic Mach number range wherein viscosity mimics increasing airfoil thickness thereby mildly influencing the flutter boundary; an intermediate region of drastic change in the flutter boundary due to shockinduced separation; and a high transonic Mach number zone of no viscous effects when the shock moves close to the trailing edge. Inviscid transonic flutter simulations are a very good approximation of the aeroelastic system in predicting flutter in the first and third regions: that is when the shock is not strong enough to cause separation, and in regions where the shockinduced separated region is confined to a small region near the trailing edge of the airfoil. However, in the second interval of intermediate transonic Mach numbers, the power distribution on the airfoil surface is significantly influenced by shockinduced flow separation on the upper and lower surfaces leading to oscillations about a new equilibrium position. Though power contribution by viscous forces are three orders of magnitude less than the power due to pressure forces, these viscous effects manipulate the flow by influencing the strength and location of the shock such that the power contribution by pressure forces change significantly. Multiple flutter points that were part of the inviscid solution in this regime are now eliminated by viscous effects. Shock motion on the airfoil, shock reversal due to separation, and separation and reattachment of flow on the airfoil upper surface, also lead to multiple aerodynamic forcing frequencies. These flow features make the flutter boundary quantitatively sensitive to the turbulence model and numerical method adopted, but qualitatively they capture the essence of the physical phenomena.
Mechanism of aeroacoustic sound generation and reduction in a flow past oscillating and fixed cylinders
 Yuji Hattori, Ryu Komatsu

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 26 October 2017, pp. 241268

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The aeroacoustic sound generated in a flow past two cylinders, one of which is oscillating and the other is fixed, is studied by direct numerical simulation. This problem involves key ingredients of the aeroacoustic noise generated from wind turbines, helicopters, axial flow fans and other turbomachinery: flow, a moving body and a fixed body. The corrected volume penalization method is successfully applied to resolve the sound pressure of aeroacoustic waves as a solution of the compressible Navier–Stokes equations. The sound pressure was shown to be in good agreement with the prediction by the Ffowcs Williams–Hawkings aeroacoustic analogy, which takes account of the cylinder motion, confirming the accuracy of the corrected volume penalization method. Prior to the case of two cylinders, sound generation in flow past a single oscillating cylinder is considered. The fluid motion can be either periodic or nonperiodic depending on the frequency and the amplitude of cylinder oscillation. The acoustic power is significantly reduced when the fluid motion locks in to a frequency lower than the natural frequency of vortex shedding from a fixed cylinder. When a fixed cylinder is added, the acoustic power depends strongly on the distance between the cylinders, since that determines whether synchronization occurs and the phase difference between the three forces: the lift forces exerted on the two cylinders and the inertial force due to volume displacement effect of the oscillating cylinder. In particular, significant sound reduction is observed when the fixed cylinder is placed upstream and the frequency of the cylinder oscillation is set to the frequency for which the acoustic power is minimized in the singlecylinder case.
Optimal transient growth on a vortex ring and its transition via cascade of ringlets
 X. Mao, F. Hussain

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 26 October 2017, pp. 269286

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Linear and nonlinear transient growths of perturbations on a vortex ring up to Reynolds number ($\equiv$ circulation/viscosity) $Re=27\,000$ are studied. For short time intervals, perturbations around the ring axis undergo the strongest linear transient growth and lead to secondary structures in the form of ringlets, owing to the Orr mechanism and an inviscid vorticityamplification mechanism: in contrast to the wellreported instabilities and lobe structures along the vortex ring core. These secondary ringlet structures induce a tertiary group of ringlets through similar transient perturbation growth. This cascade of ringlets lead to the breakup of the main ring even before activation of the vortexcore instabilities. Such a cascade scenario is also observed in the development of a vortex ring perturbed by random disturbance in the axis region. These new modes and mechanisms for the generation and breakup of vortex ring structures bring insights into the dynamics and control of vortex ring flows.
The aeroacoustics of finite wallmounted square cylinders
 Ric Porteous, Danielle J. Moreau, Con J. Doolan

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 26 October 2017, pp. 287328

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This paper presents the results of an experimental study that relates the flow structures in the wake of a square finite wallmounted cylinder with the radiated noise. Acoustic and hotwire measurements were taken in an anechoic wind tunnel. The cylinder was immersed in a nearzeropressure gradient boundary layer whose thickness was 130 % of the cylinder width, $W$. Aspect ratios were in the range $0.29\leqslant L/W\leqslant 22.9$ (where $L$ is the cylinder span), and the Reynolds number, based on width, was $1.4\times 10^{4}$. Four shedding regimes were identified, namely R0 ($L/W<2$), RI ($2<L/W<10$), RII ($10<L/W<18$) and RIII ($L/W>18$), with each shedding regime displaying an additional acoustic tone as the aspect ratio was increased. At low aspect ratios (R0 and RI), downwash dominated the wake, creating a highly threedimensional shedding environment with maximum downwash at $L/W\approx 7$. Looping vortex structures were visualised using a phase eduction technique. The principal core of the loops generated the most noise perpendicular to the cylinder. For higher aspect ratios in RII and RIII, the main noise producing structures consisted of a series of inclined vortex filaments, where the angle of inclination varied between vortex cells.
Global stability of axisymmetric flow focusing
 F. CruzMazo, M. A. Herrada, A. M. GañánCalvo, J. M. Montanero

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 26 October 2017, pp. 329344

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In this paper, we analyse numerically the stability of the steady jetting regime of gaseous flow focusing. The base flows are calculated by solving the full Navier–Stokes equations and boundary conditions for a wide range of liquid viscosities and gas speeds. The axisymmetric modes characterizing the asymptotic stability of those flows are obtained from the linearized Navier–Stokes equations and boundary conditions. We determine the flow rates leading to marginally stable states, and compare them with the experimental values at the jettingtodripping transition. The theoretical predictions satisfactorily agree with the experimental results for large gas speeds. However, they do not capture the trend of the jettingtodripping transition curve for small gas velocities, and considerably underestimate the minimum flow rate in this case. To explain this discrepancy, the Navier–Stokes equations are integrated over time after introducing a small perturbation in the tapering liquid meniscus. There is a transient growth of the perturbation before the asymptotic exponential regime is reached, which leads to dripping. Our work shows that flow focusing stability can be explained in terms of the combination of asymptotic global stability and the system shortterm response for large and small gas velocities, respectively.
Continuum theory for rapid cohesiveparticle flows: general balance equations and discreteelementmethodbased closure of cohesionspecific quantities
 Kevin M. Kellogg, Peiyuan Liu, Casey Q. LaMarche, Christine M. Hrenya

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 26 October 2017, pp. 345382

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The continuum description of rapid cohesiveparticle flows comprises the population balance, which tracks various agglomerate sizes in space and time, and kinetictheorybased balances for momentum and granular energy. Here, fundamental closures are provided in their most general form. In previous population balances, the probability (‘success factor’) that a given collision results in agglomeration or breakage has been set to a constant even though it is well established that the outcome of a collision depends on the impact (relative) velocity. Here, physically based closures that relate the success factors to the granular temperature, a (continuum) measure of the impact velocity, are derived. A key aspect of this derivation is the recognition that the normal component of the impact velocity dictates whether agglomeration occurs. With regard to the kinetictheory balances, cohesion between particles makes the collisions more dissipative, thereby decreasing the granular temperature. The extra dissipation due to cohesion is accounted for using an effective coefficient of restitution, again determined using the derived distribution of normal impact velocities. This collective treatment of the population and kinetictheory balances results in a general set of equations that contain several parameters (e.g. critical velocities of agglomeration) that are cohesionspecific (van der Waals, liquid bridging, etc.). The determination of these cohesionspecific quantities using simple discrete element method simulations, as well as validation of the resulting theory, is also presented.
The nearfield pressure radiated by planar highspeed freeshearflow turbulence
 David A. Buchta, Jonathan B. Freund

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 26 October 2017, pp. 383408

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Jets with Mach numbers $M\gtrsim 1.5$ are well known to emit an intense, fricative, socalled crackle sound, having steep compressions interspersed with weaker expansions that together yield a positive pressure skewness $S_{k}>0$. Its shocklike features are obvious hallmarks of nonlinearity, although a full explanation of the skewness is lacking, and wave steepening alone is understood to be insufficient to describe its genesis. Direct numerical simulations of highspeed freeshear flows for Mach numbers $M=0.9$, $1.5$, $2.5$ and $3.5$ in the Reynolds number range $60\leqslant Re_{\unicode[STIX]{x1D6FF}_{m}}\leqslant 4200$ are used to examine the mechanisms leading to such pressure signals, especially the pressure skewness. For $M=2.5$ and $3.5$, the pressure immediately adjacent the turbulence already has the large $S_{k}\gtrsim 0.4$ associated with jet crackle. It also has a surprisingly complex threedimensional structure, with locally high pressures at compressionwave intersections. This structure is transient, and it simplifies as radiating waves subsequently merge through nonlinear mechanisms to form the relatively distinct and approximately twodimensional Machlike waves deduced from laboratory visualizations. A transport equation for $S_{k}$ is analysed to quantify factors affecting its development. The viscous dissipation that decreases $S_{k}$ is balanced by a particular nonlinear flux, which is (of course) absent in linear acoustic propagation and confirmed to be independent of the simulated Reynolds numbers. Together these effects maintain an approximately constant $S_{k}$ in the near acoustic field.
Layer formation in horizontally forced stratified turbulence: connecting exact coherent structures to linear instabilities
 Dan Lucas, C. P. Caulfield, Rich R. Kerswell

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 26 October 2017, pp. 409437

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We consider turbulence in a stratified ‘Kolmogorov’ flow, driven by horizontal shear in the form of sinusoidal body forcing in the presence of an imposed background linear stable stratification in the third direction. This flow configuration allows the controlled investigation of the formation of coherent structures, which here organise the flow into horizontal layers by inclining the background shear as the strength of the stratification is increased. By numerically converging exact steady states from direct numerical simulations of chaotic flow, we show, for the first time, a robust connection between linear theory predicting instabilities from infinitesimal perturbations to the robust finiteamplitude nonlinear layered state observed in the turbulence. We investigate how the observed vertical length scales are related to the primary linear instabilities and compare to previously considered examples of shear instability leading to layer formation in other horizontally sheared flows.
Direct numerical simulation of turbulence modulation by particles in compressible isotropic turbulence
 Qi Dai, Kun Luo, Tai Jin, Jianren Fan

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 26 October 2017, pp. 438482

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In this paper, a systematic investigation of turbulence modulation by particles and its underlying physical mechanisms in decaying compressible isotropic turbulence is performed by using direct numerical simulations with the Eulerian–Lagrangian pointsource approach. Particles interact with turbulence through twoway coupling and the initial turbulent Mach number is 1.2. Five simulations with different particle diameters (or initial Stokes numbers, $St_{0}$) are conducted while fixing both their volume fraction and particle densities. The underlying physical mechanisms responsible for turbulence modulation are analysed through investigating the particle motion in the different cases and the transport equations of turbulent kinetic energy, vorticity and dilatation, especially the twoway coupling terms. Our results show that microparticles ($St_{0}\leqslant 0.5$) augment turbulent kinetic energy and the rotational motion of fluid, critical particles ($St_{0}\approx 1.0$) enhance the rotational motion of fluid, and large particles ($St_{0}\geqslant 5.0$) attenuate turbulent kinetic energy and the rotational motion of fluid. The compressibility of the turbulence field is suppressed for all the cases, and the suppression is more significant if the Stokes number of particles is close to 1. The modifications of turbulent kinetic energy, the rotational motion and the compressibility are all related with the particle inertia and distributions, and the suppression of the compressibility is attributed to the preferential concentration and the inertia of particles.
Streak instability in turbulent channel flow: the seeding mechanism of largescale motions
 Matteo de Giovanetti, Hyung Jin Sung, Yongyun Hwang

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 26 October 2017, pp. 483513

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It has often been proposed that the formation of largescale motion (or bulges) is a consequence of successive mergers and/or growth of nearwall hairpin vortices. In the present study, we report our direct observation that largescale motion is generated by an instability of an ‘amplified’ streaky motion in the outer region (i.e. verylargescale motion). We design a numerical experiment in turbulent channel flow up to $Re_{\unicode[STIX]{x1D70F}}\simeq 2000$ where a streamwiseuniform streaky motion is artificially driven by body forcing in the outer region computed from the previous linear theory (Hwang & Cossu, J. Fluid Mech., vol. 664, 2015, pp. 51–73). As the forcing amplitude is increased, it is found that an energetic streamwise vortical structure emerges at a streamwise wavelength of $\unicode[STIX]{x1D706}_{x}/h\simeq 1{}5$ ($h$ is the halfheight of the channel). The application of dynamic mode decomposition and the examination of turbulence statistics reveal that this structure is a consequence of the sinuousmode instability of the streak, a subprocess of the selfsustaining mechanism of the largescale outer structures. It is also found that the statistical features of the vortical structure are remarkably similar to those of the largescale motion in the outer region. Finally, it is proposed that the largest streamwise length of the streak instability determines the streamwise length scale of verylargescale motion.
Separation control and drag reduction for boattailed axisymmetric bodies through contoured transverse grooves
 A. Mariotti, G. Buresti, G. Gaggini, M. V. Salvetti

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 26 October 2017, pp. 514549

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We describe the results of a numerical and experimental investigation aimed at assessing the performance of a control method to delay boundary layer separation consisting of the introduction on the surface of contoured transverse grooves, i.e. of small cavities with an appropriate shape orientated transverse to the incoming flow. The shape of the grooves and their depth – which must be significantly smaller than the thickness of the incoming boundary layer – are chosen so that the flow recirculations present within the grooves are steady and stable. This passive control strategy is applied to an axisymmetric bluff body with various rear boat tails, which are characterized by different degrees of flow separation. Variational multiscale large eddy simulations and wind tunnel tests are carried out. The Reynolds number, for both experiments and simulations, is $Re=u_{\infty }D/\unicode[STIX]{x1D708}=9.6\times 10^{4}$; due to the different incoming flow turbulence level, the boundary layer conditions before the boat tails are fully developed turbulent in the experiments and transitional in the simulations. In all cases, the introduction of one single axisymmetric groove in the lateral surface of the boat tails produces significant delay of the boundary layer separation, with consequent reduction of the pressure drag. Nonetheless, the wake dynamical structure remains qualitatively similar to the one typical of a bluntbased axisymmetric body, with quantitative variations that are consistent with the reduction in wake width caused by boat tailing and by the grooves. A few supplementary simulations show that the effect of the grooves is also robust to the variation of the geometrical parameters defining their shape. All the obtained data support the interpretation that the relaxation of the noslip boundary condition for the flow surrounding the recirculation regions, with an appreciable velocity along their borders, is the physical mechanism responsible for the effectiveness of the present separationcontrol method.
Twophase gravity currents resulting from the release of a fixed volume of fluid in a porous medium
 Madeleine J. Golding, Herbert E. Huppert, Jerome A. Neufeld

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 26 October 2017, pp. 550577

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We consider the instantaneous release of a finite volume of fluid in a porous medium saturated with a second, immiscible fluid of different density. The resulting twophase gravity current exhibits a rich array of behaviours due to both the residual trapping of fluid as the current recedes and the differing effects of surface tension between advancing and receding regions of the current. We develop a framework for the evolution of such a current with particular focus on the largescale implications of the form of the constitutive relation between residual trapping and initial saturation. Porescale hysteresis within the current is represented by families of scanning curves relating capillary pressure and relative permeability to saturation. In the resulting vertically integrated model, all capillary effects are incorporated within specially defined saturation and flux functions specific to each region. In the longtime limit, when the height of the current and the saturations within it are low, the saturation and flux functions can be approximated by mathematically convenient power laws. If the trapping model is approximately linear at low saturations, the equations admit a similarity solution for the propagation rate and height profile of the latetime gravity current. We also solve the governing partial differential equation numerically for the nonlinear Land’s trapping model, which is commonly used in studies of twophase flows. Our investigation suggests that for trapping relations for which the proportion of trapped to initial fluid saturation increases and tends to unity as the initial saturation decreases, both of which are properties of Land’s model, a gravity current slows and eventually stops. This trapping behaviour has important applications, for example to the ultimate distance contaminants or stored carbon dioxide may travel in the subsurface.