We study the pressure-driven transient motion of a periodic file of deformable liquid drops through a cylindrical tube with circular cross-section, at vanishing Reynolds number. The investigations are based on numerical solutions of the equations of Stokes flow obtained by the boundary-integral method. It is assumed that the viscosity and density of the drops are equal to those of the suspending fluid, and the interfaces have constant tension. The mathematical formulation uses the periodic Green's function of the equations of Stokes flow in a domain that is bounded externally by a cylindrical tube, which is computed by tabulation and interpolation. The surface of each drop is discretized into quadratic triangular elements that form an unstructured interfacial grid, and the tangential velocity of the grid-points is adjusted so that the mesh remains regular for an extended but limited period of time. The results illustrate the nature of drop motion and deformation, and thereby extend previous studies for axisymmetric flow and small-drop small-deformation theories. It is found that when the capillary number is sufficiently small, the drops start deforming from a spherical shape, and then reach slowly evolving quasi-steady shapes. In all cases, the drops migrate radially toward the centreline after an initial period of rapid deformation. The apparent viscosity of the periodic suspension is expressed in terms of the effective pressure gradient necessary to drive the flow at constant flow rate. For a fixed period of separation, the apparent viscosity of a non-axisymmetric file is found to be higher than that of an axisymmetric file. In the case of non-axisymmetric motion, the apparent viscosity reaches a minimum at a certain ratio of the drop separation to tube radius. Drops with large effective radii to tube radius ratios develop slipper shapes, similar to those assumed by red blood cells in flow through capillaries, but only for capillary numbers in excess of a critical value.

Laboratory experiments were carried out to investigate the properties of a collapsing turbulent patch generated within a linearly stratified fluid by a sustained energy source and its long-time evolution in the presence of lateral boundaries. An oscillating grid spanning the width of the experimental tank was used as the turbulence source. Initially, the patch grows rapidly, as in an unstratified fluid, until the buoyancy forces arrest its vertical growth. Thereafter, the patch collapses to form horizontally propagating intrusions at its equilibrium density level. The fluid lost from the patch into the intrusion is replenished by return currents generated at the top and bottom edges of the patch. The nose of the intrusion propagates with a constant average speed (‘initial spreading regime’) determined mainly by the horizontal pressure gradient forces and the resistance induced by upstream propagating, low-frequency, columnar internal waves. Although the intrusion propagation speed is independent of viscous effects, they cause the development of a slug of fluid pushed ahead of the intrusion. When this slug reaches the endwall, strong upstream blocking occurs, causing the intrusion to decelerate (‘blocked regime’); the intrusion nose, however, eventually reaches the endwall. The thickness of the patch is found to be approximately constant during the initial spreading regime and slowly growing in the blocked regime. At large times (t) both the patch and the ‘fully blocked’ intrusion begin to grow vertically with a power law of the form t1/5. A simple mixing model is advanced to explain this observation. Various turbulent and internal-wave parameters pertinent to collapsing patches were also measured, and their properties were compared with those of non-collapsing patches.

The three-dimensional mixing layer is characterized by both two-dimensional and streamwise large-scale structures. Understanding the effects of those large-scale structures on the dispersion of particles is very important. Using a pseudospectral method, the large-scale structures of a three-dimensional temporally developing mixing layer and the associated dispersion patterns of particles were simulated. The Fourier expansion was used for spatial derivatives due to the periodic boundary conditions in the streamwise and the spanwise directions and the free-slip boundary condition in the transverse direction. A second-order Adam–Bashforth scheme was used in the time integration. Both a two-dimensional perturbation, which was based on the unstable wavenumbers of the streamwise direction, and a three-dimensional perturbation, derived from an isotropic energy spectrum, were imposed initially. Particles with different Stokes numbers were traced by the Lagrangian approach based on one-way coupling between the continuous and the dispersed phases.

The time scale and length scale for the pairing were found to be twice those for the rollup. The streamwise large-scale structures develop from the initial perturbation and the most unstable wavelength in the spanwise direction was found to be about two thirds of that in the streamwise direction. The pairing of the spanwise vortices was also found to have a suppressing effect on the development of the three-dimensionality. Particles with Stokes number of the order of unity were found to have the largest concentration on the circumference of the two-dimensional large-scale structures. The presence of the streamwise large-scale structures causes the variation of the particle concentrations along the spanwise and the transverse directions. The extent of variation also increases with the development of the three-dimensionality, which results in the ‘mushroom’ shape of the particle distribution.

Experiments are conducted to study the solidification from below of aqueous ammonium chloride. Thermochromic liquid crystal paints are used to visualize the temperature field simultaneously in both the liquid and the mushy layers. In a quasi-two-dimensional cell (thickness 10 mm), mushy-layer and boundary-layer convection are revealed as bumps in isotherms within and above the mushy layer, respectively. The onset, growth and decay of these convective modes are measured by monitoring the progression of the bumps during an experiment. The small-wavelength boundary-layer mode is short-lived (approximately 20–30 min), whereas the larger-wavelength mushy-layer mode survives for several hours, dominating the flow even long after the growth has stopped. Experiments in a Hele-Shaw cell (thickness 2.0 mm) enable simultaneous visualization of both the temperature field and the solid fraction. A coarsening mechanism is observed in which the flow spontaneously changes, reducing the strength of plume convection in one of the channels, and leading to growth of dendrites into the channel. An oscillatory convective mode is also observed, perhaps an indication of one of the oscillatory modes recently predicted by Chen, Lu & Yang (1994) and by Anderson & Worster (1995).

Using a barotropic model in spherical geometry, we construct new solutions for steadily travelling vortex pairs and study their stability properties. We consider pairs composed of both point and finite-area vortices, and we represent the rotating background with a set of zonal strips of uniform vorticity. After constructing the solution for a single point-vortex pair, we embed it in a rotating background, and determine the equilibrium configurations that travel at constant speed without changing shape. For equilibrium solutions, we find that the stability depends on the relative strength (which may be positive or negative) of the vortex pair to the rotating background: eastward-travelling pairs are always stable, while westward-travelling pairs are unstable when their speeds approach that of the linear Rossby–Haurwitz waves. This finding also applies (with minor differences) to the case when the vortices are of finite area; in that case we find that, in addition to the point-vortex-like instabilities, the rotating background excites some finite-area instabilities for vortex pairs that would otherwise be stable. As for practical applications to blocking events, for which the slow westward pairs are relevant, our results indicate that free barotropic solutions are highly unstable, and thus suggest that forcing mechanisms must play an important role in maintaining atmospheric blocking events.

The statistics of a turbulent passive scalar (temperature) and their Reynolds number dependence are studied in decaying grid turbulence for the Taylor-microscale Reynolds number, Rλ, varying from 30 to 731 (21[les ]Peλ[les ]512). A principal objective is, using a single (and simple) flow, to bridge the gap between the existing passive grid-generated low-Péclet-number laboratory experiments and those done at high Péclet number in the atmosphere and oceans. The turbulence is generated by means of an active grid and the passive temperature fluctuations are generated by a mean transverse temperature gradient, formed at the entrance to the wind tunnel plenum chamber by an array of differentially heated elements. A well-defined inertial–convective scaling range for the scalar with a slope, nθ, close to the Obukhov–Corrsin value of 5/3, is observed for all Reynolds numbers. This is in sharp contrast with the velocity field, in which a 5/3 slope is only approached at high Rλ. The Obukhov–Corrsin constant, Cθ, is estimated to be 0.45–0.55. Unlike the velocity spectrum, a bump occurs in the spectrum of the scalar at the dissipation scales, with increasing prominence as the Reynolds number is increased. A scaling range for the heat flux cospectrum was also observed, but with a slope around 2, less than the 7/3 expected from scaling theory. Transverse structure functions of temperature exist at the third and fifth orders, and, as for even-order structure functions, the width of their inertial subranges dilates with Reynolds number in a systematic way. As previously shown for shear flows, the existence of these odd-order structure functions is a violation of local isotropy for the scalar differences, as is the existence of non-zero values of the transverse temperature derivative skewness (of order unity) and hyperskewness (of order 100). The ratio of the temperature derivative standard deviation along and normal to the gradient is 1.2±0.1, and is independent of Reynolds number. The refined similarity hypothesis for the passive scalar was found to hold for all Rλ, which was not the case for the velocity field. The intermittency exponent for the scalar, μθ, was found to be 0.25±0.05 with a possible weak Rλ dependence, unlike the velocity field, where μ was a strong function of Reynolds number. New, higher-Reynolds-number results for the velocity field, which smoothly follow the trends of Mydlarski & Warhaft (1996), are also presented.

Interactions of oblique waves have recently been investigated theoretically and numerically and found to give rise to rapid transition in flows subcritical to linear wave disturbances. The transition scenario consists of the formation and transient growth of streamwise streaks of high and low velocity and later a rapid growth of high-frequency disturbances leading to breakdown. The present study is the first extensive experimental investigation of oblique transition. The experiments were carried out in a plane Poiseuille flow air channel in which the oblique waves were generated, one at each wall, by vibrating ribbons and the development of the flow was mapped with hot-wire anemometry. The experiments consist both of low- and high-amplitude wave disturbances; in both cases streaky structures are created. For the low-amplitude case these structures decay, whereas for the high amplitude the flow goes towards breakdown. This study has confirmed and extended previous theoretical and numerical results showing that oblique transition may be an important transition scenario.

The shape of liquid surfaces in regular N-pods in the absence of gravity is considered. A liquid volume in the vertex of a regular N-pod wets the adjacent faces if the sum of the liquid's contact angle γ with the faces and half the dihedral angle α between adjacent faces is smaller than π/2. A suggestion for why the surface shape in the wedge approaches its cylindrical shape at infinity exponentially is given. The range of this exponential decrease is related to the curvature of the meniscus and the angles α and γ: The decrement of the decrease generally shows a weak dependence on α+γ, predominantly depending on the liquid volume. Extremely close to the wetting limit, when α+γ approaches π/2, the decrement vanishes. The exponential meniscus shape leads to a similarity relation and allows small relative liquid volumes in polyhedrons to be split up into partial volumes ascribed to the corners and others ascribed to the wedges. The respective relations among volume, curvature, contact angle and corner geometry are obtained by numerical simulation and the limits of applicability are discussed. This greatly simplifies the calculation of liquid surfaces in the limit of small liquid volumes. The results obtained apply to liquid surfaces in a Space environment, e.g. to metallic melts in crucibles and to propellants and other technical fluids in tanks and reservoirs, as well as to liquid surfaces on Earth, e.g. to liquids trapped in polyhedral pores and to liquid foams, provided their characteristic length is sufficiently small compared to the capillary length.

Transversely homogeneous, uniformly sheared, turbulent flow was allowed to reach its asymptotic structure in a straight wind tunnel section and then it was passed through a sequence of two curved sections and a final straight section. The cross-sectional shape of the entire wind tunnel was rectangular, while the two curved sections had circular centrelines with the same radius but opposing curvatures. In all cases, the mean strain rate due to curvature was relatively weak (±5%), compared to the mean shear rate, but its effects on the turbulence kinetic energy and structure were substantial; streamwise pressure gradient effects were negligible. The turbulence structure approached approximately self-similar states towards the downstream ends of each curved section but the main interest of the present study was the rate of adjustment of the turbulence following a stepwise change in curvature. It has been shown that the adjustment of the shear stress anisotropy, which is a sensitive indicator of structural changes, can be approximated by a first-order system response, whose time constant scales with the inverse mean shear and is independent of the curvature parameter. Uniformly sheared flow results were used for an interpretation of the structure of curved turbulent boundary layers, both during adjustment and in a fully developed state.

Two simple feedback control laws for drag reduction are derived by applying a suboptimal control theory to a turbulent channel flow. These new feedback control laws require pressure or shear-stress information only at the wall, and when applied to a turbulent channel flow at Reτ=110, they result in 16–22% reduction in the skin-friction drag. More practical control laws requiring only the local distribution of the wall pressure or one component of the wall shear stress are also derived and are shown to work equally well.

The purpose of the paper is to demonstrate the effectiveness of the matched asymptotic expansions (MAE) method for the planing flow problem. The matched asymptotics, taking into account the flow nonlinearities in those regions where they are most pronounced (i.e. in the vicinity of the edges), are shown to significantly extend the range where the linear theory gives good results. Two model problems are used: the planing flat plate with a spoiler on the trailing edge and the curved planing foil. Asymptotic solutions obtained by the MAE method are compared with those obtained using linear and exact nonlinear theories. Based on the results, the asymptotic solution to the planing problem under the gravity is proposed.

Steady incompressible flow past an aerofoil with a cavity in its upper surface is considered. The aerofoil and cavity shape is constructed to ensure that the high-Reynolds-number asymptotics of the flow is described by the Batchelor model.

The transformation of initially isotropic turbulent flow of electrically conducting incompressible viscous fluid under the influence of an imposed homogeneous magnetic field is investigated using direct numerical simulation. Under the assumption of large kinetic and small magnetic Reynolds numbers (magnetic Prandtl number Pm[Lt ]1) the quasi-static approximation is applied for the computation of the magnetic field fluctuations. The flow is assumed to be homogeneous and contained in a three-dimensional cubic box with periodic boundary conditions. Large-scale forcing is applied to maintain a statistically steady level of the flow energy. It is found that the pathway traversed by the flow transformation depends decisively on the magnetic interaction parameter (Stuart number). If the magnetic interaction number is small the flow remains three-dimensional and turbulent and no detectable deviation from isotropy is observed. In the case of a strong magnetic field (large magnetic interaction parameter) a rapid transformation to a purely two-dimensional steady state is obtained in agreement with earlier analytical and numerical results for decaying MHD turbulence. At intermediate values of the magnetic interaction parameter the system exhibits intermittent behaviour, characterized by organized quasi-two-dimensional evolution lasting several eddy-turnover times, which is interrupted by strong three-dimensional turbulent bursts. This result implies that the conventional picture of steady angular energy transfer in MHD turbulence must be refined. The spatial structure of the steady two-dimensional final flow obtained in the case of large magnetic interaction parameter is examined. It is found that due to the type of forcing and boundary conditions applied, this state always occurs in the form of a square periodic lattice of alternating vortices occupying the largest possible scale. The stability of this flow to three-dimensional perturbations is analysed using the energy stability method.

The turbulent fountain that results from the injection of a dense fluid upwards into a large tank of stably stratified fluid of lower density is studied experimentally and theoretically. For both axisymmetric and line fountains, we have used a combination of dimensional arguments and laboratory experiments to determine the initial height above the source at which the flow first comes to rest. Depending on the strength of the stratification and the fluxes of momentum and buoyancy at the source, the subsequent down flow may either spread along the base of the tank or intrude at an intermediate height in the environment. We determine both the height of intermediate intrusion and the critical condition for spreading along the base. We also relate numerical solutions of the entrainment equations to our experimental observations, and obtain effective entrainment coefficients for both axisymmetric and line fountains. Finally, we discuss the quantitative application of our results to the replenishment of magma chambers and to the heating or cooling of a room.

The stability of nonlinear tertiary solutions in rotating plane Couette flow is examined numerically. It is found that the tertiary flows, which bifurcate from two-dimensional streamwise vortex flows, are stable within a certain range of the rotation rate when the Reynolds number is relatively small. The stability boundary is determined by perturbations which are subharmonic in the streamwise direction. As the Reynolds number is increased, the rotation range for the stable tertiary motions is destroyed gradually by oscillatory instabilities. We expect that the tertiary flow is overtaken by time-dependent motions for large Reynolds numbers. The results are compared with the recent experimental observation by Tillmark & Alfredsson (1996).