A completely non-intrusive technique, utilizing synchronized flow visualization and one-point, two-component laser-Doppler velocimetry, has been developed to examine the vortical structure of a homogeneous plane shear layer at a moderate Reynolds number. Results include ensemble-averaged velocity and vorticity maps and, derived from these data, zone-averaged statistics of the basic structure, at 6.2 initial wavelengths downstream of the splitter-plate trailing edge. The velocity field data paint a clear picture of the processes involved in the engulfment or entrainment of free-stream irrotational fluid by the vortices, and the evolution of the material interface separating fluid from the two free streams. The ensemble-averaged vorticity distribution is seen to be of an elliptical cross-section, closely resembling that of the Stuart vortex for a vorticity distribution parameter of 0.4. The effect of jitter which, in the case of zone averages is effectively removed, is assessed by comparison to conventional mean flow properties. It is found that vortex jitter greatly influences u′ and Ruu and, in confirmation of previous results, that a passive vortex does not contribute to the production of large-scale Reynolds stress.

Simultaneous measurements have been made of large-scale approximations of the three components of the vorticity vector in the far wake of a slightly heated cylinder. Analysis of the results is directed towards the properties of large-scale spanwise vortices and shear-aligned double-roller vortices and the relationship between them. The relationship between vorticity and temperature is also studied. The probability density function of the inclination of the vorticity vector in the (x, y)-plane exhibits a maximum at about 45° in the central part of the wake. The p.d.f. of the inclination of the vorticity vector in the (x, z)-plane supports the existence of a concentration of spanwise vorticity near the outer part of the wake. In this region, there is significant correlation between vorticity and temperature. Conditional averages of velocity and temperature fluctuations and vorticity components are presented with respect to two types of detection, the first focusing on peaks in the ωx and ωy signals, and the second focusing on aspects of the large spanwise structures. Results from the two procedures are consistent, although different in emphasis, and are interpreted in terms of the downstream development of the wake. The upstream ends of large structures stretch and shear-align smaller, probably older, vortices while transporting heat and momentum defect outwards. Near the centreplane, the downstream ends of large structures transport colder, high-speed, spanwise-vortical fluid towards the centreplane, but ωx and ωy are not correlated with either temperature or the large structure. In (x, z)-planes, cuts through the shear-aligned vortices would appear to show double rollers.

In this paper we calculate the streaming induced by gravity waves passing over a thin fluid layer, one side of which is rigid while the other is a flexible, inextensible membrane. The problem is relevant to some recent laboratory experiments by Allison (1983) on the pumping action of water waves.

On the assumption that the flow is laminar and that the lateral displacement b of the membrane is small compared with the thickness Δ of the fluid layer, we calculate the velocity profile of the streaming U within the layer. This depends on the ratio Δ/δ, where δ is the thickness of the Stokes layers at the upper and lower boundaries. When 0 < Δ/δ > 6 the boundary layers interact strongly and the velocity profile is unimodal. At large values of Δ/δ the profile of U exhibits thin ‘jets’ near the boundaries.

The calculated drift velocities agree as regards order of magnitude with those observed. However, the pressure gradients observed were larger than those calculated, due possibly to turbulence, but probably also to finite-amplitude and end-effects.

The theory given here can be considered as an extension of the theory of peristaltic pumping to flows at higher Reynolds number.

Many studies of fragmentation of liquid drops at supersonic Mach numbers report the appearance of large amounts of mist. Photographs from other studies, which do not mention mist at all, strongly suggest that copious amounts of mist are formed at the earliest stages of fragmentation. In this paper, we present arguments and calculations which indicate that this mist is formed from condensed vapour arising from the flash vaporization of the hot and low-pressure liquid on the leeside of the drop. Low leeside pressures are produced by the rarefaction of the gas, the acceleration of the drop, and the high tensions generated by rapid stretching of the stripped liquid. The droplet temperature may rise because of heat transfer from the hot gas to thin drop filaments, and by viscous heating due to rapid deformation.

A two-dimensional vortex pair is commonly generated by pushing fluid down a semi-infinite channel by means of an impulsively started piston. The strength and separation of the two fully developed vortices strongly depend upon the time history of the piston motion. When the piston is impulsively stopped, two secondary vortices are formed downstream of the channel ends and interact with the primary pair in a fairly complicated way.

In the present work we attempt to provide a discrete-vortex model of the process of pair formation. The effects of viscosity are assumed to affect only the separation process, having negligible influence on the overall flow. In the limit of infinite Reynolds number, the problem becomes one of inviscid flow, and the separation at the sharp edges is approximated by a Kutta–Joukowski condition, large vortex regions being replaced by simple concentrated vortices. The growing vortex sheets shed from the edge are represented by a simplified model due to Brown and Michael.

Present results are able to account for the failure of the ‘puffing’ technique as well as the success of Barker and Crow's ‘downwash’ technique in producing vortex pairs.

Flow-visualization experiments are also reported, and good qualitative agreement is found between numerical and experimental results.

The present model also shows that the presence of secondary vortices drastically modifies the trajectories of free vortices as obtained in a previous work due to Sheffield.

Natural convection in a rectangular cavity is examined, utilizing the second law of thermodynamics. Through an application of the second law the rate of entropy generation associated with the convective pattern changes is evaluated for the onset of natural convection in a cavity with free boundaries, for which an exact solution is sought, as well as with rigid boundaries which is studied numerically. Entropy to be generated from the perturbed temperature and velocity fields is shown to depend on AR (aspect ratio of the cavity), Rac (the critical Rayleigh number) and a non-dimensional parameter, Ω, which is related to the ratio of entropy generation by viscous friction to that by thermal transport. The convective pattern change is related to a change in the spatial distributions of the rate of entropy generation due to heat transfer and due to dissipation, demonstrating that an application of the second law helps examine convective pattern changes quantitatively by dealing with temperature and velocity fields in a unified manner.

A Janus swimmer is any force-free, torque-free organism, particle or micro-robot operating at low Reynolds numbers and having contiguous regions of its boundary on which different boundary conditions are in play. In this paper we study a ‘slip–stick’ Janus swimmer theoretically within a two-dimensional model. The boundary of the swimmer is split into two zones: its motion is driven by an imposed tangential stress on a portion of the boundary with the complement taken to be a no-slip surface. The Stokes flow generated by the swimmer, and its swimming speed, are determined in closed analytical form as a function of the angle over which the stress actuation is active.

We consider the stability of a planar gas–liquid foam with low liquid fraction, in the absence of surfactants and stabilizing particles. We adopt a network modelling approach introduced by Stewart & Davis (J. Rheol., vol. 56, 2012, p. 543), treating the gas bubbles as polygons, the accumulation of liquid at the bubble vertices (Plateau borders) as dynamic nodes and the liquid bridges separating the bubbles as uniformly thinning free films; these films can rupture due to van der Waals intermolecular attractions. The system is initialized as a periodic array of equally pressurized bubbles, with the initial film thicknesses sampled from a normal distribution. After an initial transient, the first film rupture initiates a phase of dynamic rearrangement where the bubbles rapidly coalesce, evolving toward a new quasi-equilibrium. We present Monte Carlo simulations of this coalescence process, examining the time intervals over which large-scale rearrangement occurs as a function of the model parameters. In addition, we show that when this time interval is rescaled appropriately, the evolution of the normalized number of bubbles is approximately self-similar.

We note that the mirror-symmetric solution in plane Couette flow, found recently by Gibson, Halcrow & Cvitanović (J. Fluid Mech., vol. 611, 2009, pp. 107–130) and Itano & Generalis (Phys. Rev. Lett., vol. 102, 2009, p. 114501), belongs to the solution group classified as ‘ribbon’ in rotating-plane Couette flow (RPCF). It represents a subcritical (in terms of the system rotation) solution at zero rotation rate on the three-dimensional tertiary flow branch which bifurcates from the second streamwise-independent flow in RPCF. The way of its appearance is similar to that of the Nagata solution (J. Fluid Mech., vol. 217, 1990, pp. 519–527), which lies on the subcritical three-dimensional tertiary flow branch bifurcating from the first streamwise-independent flow in RPCF.

When a contact line moves with a sufficiently large speed, liquid or gas films can be entrained on a solid depending on the direction of contact-line movement. In this work, the contact-line dynamics in the situation of a generic two-fluid system is investigated. We demonstrate that the hydrodynamics of a contact line, no matter whether advancing or receding, can formally reduce to that of a receding one with small interfacial slopes. Since the latter can be well treated under the classical lubrication approximation, this analogy allows us to derive an asymptotic solution of the interfacial profiles for arbitrary values of contact angle and viscosity ratio. For the dip-coating geometry, we obtain, with no adjustable parameters, an analytical formula for the critical speed of wetting transition, which in particular predicts the onset of both liquid and gas entrainment. Moreover, the present analysis also builds a novel connection between the Cox–Voinov law and classical lubrication theory for moving contact lines.

The effects of density variation and body force on the stability of a heterogeneous horizontal shear layer are investigated. The density is assumed to decrease exponentially with height, and the body force is assumed to be derivable from a potential; the velocity distribution in the shear layer is taken to be U(y) = tanh y. The method of small disturbances is employed to obtain a family of neutral stability curves depending on the choice of the Richardson number. It is demonstrated, furthermore, that the value of the critical Richardson number depends on the magnitude of the non-dimensional density gradient.

We investigate the dynamics of the buoyancy-driven rise of a bubble inside a viscoplastic material when it is subjected to an acoustic pressure field. To this end, we develop a simplified model based on the Lagrangian formalism assuming a pulsating bubble with a spherical shape. Moreover, to account for the effects of a deformable bubble, we also perform detailed two-dimensional axisymmetric simulations. Qualitative agreement is found between the simplified approach and the detailed numerical simulations. Our results reveal that the acoustic excitation enhances the mobility of the bubble, by increasing the size of the yielded region that surrounds the bubble, thereby decreasing the effective viscosity of the liquid and accelerating the motion of the bubble. This effect is significantly more pronounced at the resonance frequency, and it is shown that bubble motion takes place even for Bingham numbers (Bn) that can be orders of magnitude higher than the critical Bn for bubble entrapment in the case of a static pressure field.

We study the transient dynamics of a viscous liquid contained in a narrow gap between a rigid surface and a parallel elastic plate. The elastic plate is deformed due to an externally applied time-varying pressure field. We model the flow field via the lubrication approximation and the plate deformation by the Kirchhoff–Love plate theory. We obtain a self-similarity solution for the case of an external point force acting on the elastic plate. The pressure and deformation field during and after the application of the external force are derived and presented by closed-form expressions. We examine a distributed external pressure, spatially uniform and linearly increasing with time, acting on the elastic plate over a finite region and during a finite time period, similar to the viscous–elastic interaction time-scale. The interaction between elasticity and viscosity is shown to reduce by an order of magnitude the pressure within the Hele-Shaw cell compared with the externally applied pressure. The results thus suggest that elastic Hele-Shaw configurations may be used to achieve significant impact mitigation.

Effects of random bathymetric irregularities on wave generation by transcritical ship motion in a shallow channel are investigated. Invoking Boussinesq approximation in shallow waters, it is shown that the wave evolution is governed by an integro-differential equation combining features of Korteweg–deVries and Burgers equations. For an isolated ship, the bottom roughness weakens the transient waves radiated both fore and aft. When many ships advance in tandem, a steady mount of high water can be formed in front and a depression behind. Wave forces on both an isolated ship and a ship in a caravan are obtained as functions of the mean-square roughness, ship speed and the blockage coefficient.

We use direct numerical simulations to study a steady bathtub vortex in a cylindrical tank with a central drain-hole, a flat stress-free surface and velocity prescribed at the inlet. We find that the qualitative structure of the meridional flow does not depend on the radial Reynolds number, whereas we observe a weak overall rotation at a low radial Reynolds number and a concentrated vortex above the drain-hole at a high radial Reynolds number. We introduce a simple analytically integrable model that shows the same qualitative dependence on the radial Reynolds number as the simulations and compares favourably with the results for the radial velocity and the azimuthal velocity at the surface. Finally, we describe the height dependence of the radius of the vortex core and the maximum of the azimuthal velocity at a high radial Reynolds number, and we show that the data on the radius of the vortex core and the maximum of the azimuthal velocity as functions of height collapse on single curves by appropriate scaling.

Based on amplitude expansions developed in Part 1 (Suslov & Paolucci 1999), we examine the mean flow characteristics of non-Boussinesq mixed convection flow of air in a vertical channel in the vicinity of bifurcation points for a wide range of temperature differences between the walls, and Grashof and Reynolds numbers. The constant mass flux and constant pressure gradient formulations are shown to lead to qualitatively similar, but quantitatively different, results. The physical nature of the distinct shear and buoyancy disturbances is investigated, and detailed mean flow and energy analyses are presented. The variation of the total mass of fluid in a flow domain as disturbances develop is discussed. The average Nusselt number and mass flux are estimated for supercritical regimes for a wide range of governing parameters.

Surfaces with filamentous structures are ubiquitous in nature on many different scales, ranging from forests to micrometre-sized cilia in organs. Hairy surfaces are elastic and porous, and it is not fully understood how they modify turbulence near a wall. The interaction between hairy surfaces and turbulent flows is here investigated numerically in a turbulent channel flow configuration at friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}\approx 180$. We show that a filamentous bed of a given geometry can modify a turbulent flow very differently depending on the resonance frequency of the surface, which is determined by the elasticity and mass of the filaments. Filaments having resonance frequencies lower than the main frequency content of the turbulent wall-shear stress conform to slowly travelling elongated streaky structures, since they are too slow to adapt to fluid forces of higher frequencies. On the other hand, a bed consisting of stiff and low-mass filaments has a high resonance frequency and shows local regions of increased permeability, which results in large entrainment and a vast increase in drag.