We investigate the instability and nonlinear saturation of temperature-stratified Taylor–Couette flows in a finite height cylindrical gap and calculate angular momentum transport in the nonlinear regime. The model is based on an incompressible fluid in Boussinesq approximation with a positive axial temperature gradient applied. While both ingredients, the differential rotation as well as the stratification due to the temperature gradient, are stable themselves, together the system becomes subject of the stratorotational instability and a non-axisymmetric flow pattern evolves. This flow configuration transports angular momentum outwards and will therefore be relevant for astrophysical applications. The belonging coefficient of β viscosity is of the order of unity if the results are adapted to the size of an accretion disk. The strength of the stratification, the fluid's Prandtl number and the boundary conditions applied in the simulations are well suited too for a laboratory experiment using water and a small temperature gradient around 5 K. With such a set-up the stratorotational instability and its angular momentum transport could be measured in an experiment.

The linear stability of the impulsively started flow through a pipe of circular cross-section is studied at high Reynolds number R. A crucial non-dimensional time of O(R7/9) is identified at which the disturbance acquires internal flow characteristics. It is shown that even if the disturbance amplitude at this time is as small as O(R−22/27) the subsequent evolution of the perturbation is nonlinear, although it can still be followed analytically using a multiple-scales approach. The amplitude and wave speed of the nonlinear disturbance are calculated as functions of time and we show that as t → ∞, the disturbance evolves into the long-wave limit of the neutral mode structure found by Smith & Bodonyi in the fully developed Hagen–Poiseuille flow, into which our basic flow ultimately evolves. It is proposed that the critical amplitude found here forms a stability boundary between the decay of linear disturbances and ‘bypass’ transition, in which the fully developed state is never attained.

We investigate in detail the dynamics of bouncing of a fluid-immersed solid sphere onto a textured wall at moderate Reynolds and Stokes numbers. Using high-frequency interferometric measurements, the dynamics of the sphere is resolved in time and space, before, during and after collision with the wall. The critical Stokes number for bouncing is shown to be significantly influenced by the geometry of the texture, i.e. the surface fraction and the height of the micro-pillars. A modified Hertz model is developed to take into account the influence of this texture geometry on the collision dynamics. The predicted scaling for the collision time and penetration depth of the sphere into the textured wall is found to be in good agreement with the experimental measurements.

The dynamical behaviour of a system of parallel line vortices in an inviscid fluid is studied numerically. The initial configuration of the system is assumed to be such that the points of intersection of the line vortices with a plane normal to the vorticity form a regular polygon. The numerical experiments show that the vortex polygon is rearranged due to non-linear interactions among the line vortices in such a way as to produce a more or less uniform distribution of vortices inside the fluid with an approximately constant mean separation. The average angular velocity of the rotation of the vortex lines about the instantaneous centroid of the vortex system remains approximately constant. These results agree with the conjecture of Raja Gopal (1964). The results may prove to be of some value in a macroscopic model of liquid helium based on hydrodynamical principles.

The stability of forward and rearward slug flows due to the motion of a body through a perfectly conducting liquid with an embedded magnetic field aligned to the direction of motion is studied. It is found that, for sub-Alfvénic flows, the forward and rearward slug flows predicted by Stewartson, Leibovich and Ludford are stable. For super-Alfvénic flows, if at all meaningful, both the forward and the rearward slug flows are stable also.

The dynamics of a near-surface vortex are examined in a two-layer setting on the beta-plane. Initially, the vortex is radially symmetric and localized in the upper layer. Two non-dimensional parameters govern its evolution and translation: the ratio δ of the thickness of the vortex to the total depth of the fluid, and the non-dimensional beta-effect number α = βL/f (f and β are the Coriolis parameter and its meridional gradient respectively, L is the radius of the vortex). We assume, as suggested by oceanic observations, that α < δ < 1: A simple set of asymptotic equations is derived, which describes the beta-induced translation of the vortex and a dipolar perturbation developing on and under the vortex (in both layers).

This set was solved numerically for oceanic lenses, and the following features were observed: (i) The meridional (southward) component of the translation speed of the lens rapidly ‘overtakes’ the zonal (westward) component. The former grows approximately linearly, whereas the latter oscillates about the Nof (1981) value (i.e. about the speed of translation of a vortex in a one-layer reduce-gravity fluid). (ii) Vortices of the same shape, but different radii and amplitudes, follow the same trajectory. The amplitude and radius affect only the absolute value, but not the direction, of the translation speed. (iii) In the lower layer below the vortex, a ‘region’ is generated where the velocity of the fluid is growing linearly with time. The velocity field in the region becomes more and more homogeneous (and equal to the translation speed of the vortex).

The steady plane boundary-layer flows of velocity field {u(x, y), v(x, y)} induced by continuous moving surfaces are revisited in this paper. It is shown that the governing balance equations, as well as the asymptotic condition u(x, ∞) = 0 at the outer edge of the boundary layer are invariant under arbitrary translations y → y + y0(x) of the transverse coordinate y. The wall conditions, i.e. the prescribed stretching velocity u(x, 0) ≡ Uw(x) and the transpiration velocity v(x, 0) ≡ Vw(x) distributions, however, undergo in general substantial changes. The consequences of this basic symmetry property on the structure of the solution space are investigated. It is found that starting with a primary solution which describes the boundary-layer flow induced by an impermeable surface, infinitely many translated solutions can be generated which form a continuous group, the translation group of the given primary solution. The elements of this group describe boundary-layer flows induced by permeable surfaces stretching under transformed wall conditions, Uw(x) → Ũw(x) = u[x, y0(x)] and Vw(x) → Ṽw(x) = v[x, y0(x)] − y′0(x)u[x, y0(x)], respectively. In this way, starting with a known solution {u(x, y), v(x, y)} so that the inverse y0(x) = u−1(x, Ũw) of u[x, y0(x)] exists, a new solution {ũ(x, y), ṽ(x, y)} corresponding to any desired stretching velocity distribution Ũw(x) can be prepared. It also turns out that several exact solutions discovered during the latter decades are not basically new solutions, but translated counterparts of some formerly reported primary solutions. A few specific examples are discussed in detail.

Euromech 98 was held in Eindhoven inNovember 1977 with the authors as chairmen. The Colloquium was attended by 48 participants from a number of European countries. Bubbles play an important role in many areas of technology: propeller-induced cavitation in ship building, cavitation in fluid machinery, nucleate boiling in reactorsand similar devices, and many processes (centrifuges, mixers) in the chemical process industry. A wide variety of research, both of fundamental and of more applied nature, is going on in universities and in industrial laboratories. Representatives from all theabove areas were included among the participants and consequently the topics raised in the presentations and discussions covered a very broad field.

This paper investigates theoretically the vertical evolution of a turbulent plume into a linearly stratified ambient fluid, by regarding it as composed of two distinct regions. In the first region, called the positive buoyant region, the plume buoyancy and the plume momentum act in the same upward direction, whereas in the second region, called the negative buoyant region, they act in opposite directions. In a first step, analytical expressions for the plume variables at the transition height (i.e. between the two regions) are obtained from one-dimensional conservation equations, using the plume entrainment model and under the Boussinesq approximation. In a second step, these variables are used in order to determine analytically the buoyancy and volume fluxes as well as the density deficit of the plume at its top. In this investigation, the transition height (denoted ${z}_{t} $) and the total plume height (denoted ${z}_{p} $) are obtained in the form of two integrals. These integrals are evaluated asymptotically in three different cases associated with particular flow regimes. Finally, the limit of the Boussinesq assumption for such flows is discussed.

We consider pressure-driven flow of an ion-carrying viscous Newtonian fluid through a non-uniformly shaped channel coated with a charged deformable porous layer, as a model for blood flow through microvessels that are lined with an endothelial glycocalyx layer (EGL). The EGL is negatively charged and electrically interacts with ions dissolved in the blood plasma. The focus here is on the interplay between electrochemical effects, and the pressure-driven flow through the microvessel. To analyse these effects we use triphasic mixture theory (TMT) which describes the coupled dynamics of the fluid phase, the elastic EGL, ion transport within the fluid and electric fields within the microvessel. The resulting equations are solved numerically using a coupled boundary–finite element method (BEM-FEM) scheme. However, in the physiological regime considered here, ion concentrations and electric potentials vary rapidly over a thin transitional region (Debye layer) that straddles the lumen–EGL interface, which is difficult to resolve numerically. Accordingly we analyse this region asymptotically, to determine effective jump conditions across the interface for BEM-FEM computations within the bulk EGL/lumen. Our results demonstrate that ion–EGL electrical interactions can influence the near-wall flow, causing it to become reversed. This alters the stresses exerted upon the vessel wall, which has implications for the hypothesised role of the EGL as a transmitter of mechanical signals from the blood flow to the endothelial vessel surface.

In a previous study we investigated three-scalar mixing in a turbulent coaxial jet (Cai et al. J. Fluid Mech., vol. 685, 2011, pp. 495–531). In this flow a centre jet and a co-flow are separated by an annular flow; therefore, the resulting mixing process approximates that in a turbulent non-premixed flame. In the present study, we investigate the effects of the velocity and length scale ratios of the annular flow to the centre jet, which determine the relative mean shear rates between the streams and the degree of separation between the centre jet and the co-flow, respectively. Simultaneous planar laser-induced fluorescence and Rayleigh scattering are employed to obtain the mass fractions of the centre jet scalar (acetone-doped air) and the annular flow scalar (ethylene). The results show that varying the velocity ratio and the annulus width modifies the scalar fields through mean-flow advection, turbulent transport and small-scale mixing. While the evolution of the mean scalar profiles is dominated by the mean-flow advection, the shape of the joint probability density function (JPDF) was found to be largely determined by the turbulent transport and molecular diffusion. Increasing the velocity ratio results in stronger turbulent transport, making the initial scalar evolution faster. However, further downstream the evolution is delayed due to slower small-scale mixing. The JPDF for the higher velocity ratio cases is bimodal at some locations while it is always unimodal for the lower velocity ratio cases. Increasing the annulus width delays the progression of mixing, and makes the effects of the velocity ratio more pronounced. For all cases the diffusion velocity streamlines in the scalar space representing the effects of molecular diffusion generally converge quickly to a curved manifold, whose curvature is reduced as mixing progresses. The curvature of the manifold increases significantly with the velocity and length scale ratios. Predicting the observed mixing path along the manifold as well as its dependence on the velocity and length scale ratios presents a challenge for mixing models. The results in the present study have implications for understanding and modelling multiscalar mixing in turbulent reactive flows.

The flow of a viscous gravity current over a lubricating layer of fluid is modelled using lubrication theory. We study the case of an axisymmetric current with constant influx which allows for a similarity solution, which depends on three parameters: a non-dimensional influx rate ${\mathcal{Q}}$; a viscosity ratio $m$ between the lower and upper layer fluid; and a relative density difference $\unicode[STIX]{x1D700}$. The limit of equal densities $\unicode[STIX]{x1D700}=0$ is singular, as the interfacial evolution equation changes nature from parabolic to hyperbolic. Theoretical analysis of this limit reveals that a discontinuity, or shock, in the interfacial height forms above a critical viscosity ratio $m_{crit}=3/2$, i.e. for a sufficiently less viscous upper-layer fluid. The physical mechanism for shock formation is described, which is based on advective steepening of the interface between the two fluids and relies on the lack of a contribution to the pressure gradient from the interfacial slope for equal-density fluids. In the limit of small but non-zero density differences, local travelling-wave solutions are found which regularise the singular structure of a potential shock and lead to a constraint on the possible shock heights in the form of an Oleinik entropy condition. Calculation of a simplified time-dependent system reveals the appropriate boundary conditions for the late-time similarity solution, which includes a shock at the nose of the current for $m>3/2$. The numerically calculated similarity solutions compare well to experimental measurements with respect to the predictions of self-similarity, the radial extent and the self-similar top-surface shapes of the current.