The circular hydraulic jump commonly forms on a horizontal plate struck by a vertical jet of liquid. New observations of this phenomenon are described.

A previously unreported instability of the jump is examined. This is shown to arise when the local Reynolds number Rj just ahead of the jump exceeds a critical value of 147. Prior to this instability, the flow behind the jump contains a closed eddy, the length of which decreases to zero as Rj increases towards its critical value. Physical explanations for this flow structure and instability are proposed.

Accurate measurements of liquid depths were made using a light-absorption technique, in which a laser was shone through water containing a strong dye. Liquid depths ahead of and behind the jump were so determined and depth profiles of the jump in the stable regime were obtained.

As the outer depth was increased, the jump closed in on the jet and eventually disappeared: this extinction of the jump is also investigated.

The formation of solitary internal waves with trapped cores via shoaling is investigated numerically. For density fields for which the buoyancy frequency increases monotonically towards the surface, sufficiently large solitary waves break as they shoal and form solitary-like waves with trapped fluid cores. Properties of large-amplitude waves are shown to be sensitive to the near-surface stratification. For the monotonic stratifications considered, waves with open streamlines are limited in amplitude by the breaking limit (maximum horizontal velocity equals wave propagation speed). When an exponential density stratification is modified to include a thin surface mixed layer, wave amplitudes are limited by the conjugate flow limit, in which case waves become long and horizontally uniform in the centre. The maximum horizontal velocity in the limiting wave is much less than the wave's propagation speed and as a consequence, waves with trapped cores are not formed in the presence of the surface mixed layer.

We numerically calculate the drag on a sphere or a filament immersed in an incompressible viscous monolayer or membrane on one, or between two, viscous infinitely deep bulk phases. We show that contributions due to the Marangoni effect of the monolayer or membrane account for a significant part of the total drag. Effects of protrusion of objects into the three-dimensional fluids adjacent to the monolayer and membrane are investigated. Known analytical expressions in the limit of a very viscous membrane or monolayer are recovered by our numerics. A sphere in a membrane exhibits maximal drag when symmetrically immersed with the equator coinciding with the membrane plane. No discontinuity of the drag arises when the sphere is totally immersed into the subphase and detaches from the monolayer. Effects of protrusion are more important for objects moving in a membrane or monolayer of low surface viscosity. At large surface shear viscosity protrusions must be larger than the length defined by the ratio of surface to bulk viscosities to alter the drag on the object. Our calculations may be useful for the measurement of hydrodynamic radii of lipid rafts in membranes and for electrocapillary effects of spheres immersed in a surface.

Free convection has been studied in gaseous helium at low temperatures in a cylindrical vessel of aspect ratio (diameterlheight) 2·5. Compared with measurements in fluids at room temperature the present arrangement has the advantages of small size, a short time constant and improved accuracy. As the Rayleigh number was varied from 60 to 2 × 109, the Nusselt number rose from 1 to 69, obeying the relation Nu = 0·173Ra0·2800±0·0005 over the upper four decades of Ra. The critical Rayleigh number was 1630, but the conditions of the experiment did not allow reliable measurements at such low values of Ra. The very high sensitivity within a given experiment showed the presence of several ‘discrete transitions’, which were often step like and not merely a change of gradient as reported by other workers. The largest of these, at Ra = 3 · 105, involved a drop in heat flux of some 6% and was somewhat hysteretic. The temperature fluctuations increased markedly as the step was crossed.

Two problems representative of the gravity flow of granular materials are considered in the context of a theory presented by Goodman (1970). The problems consist of steady fully-developed flow of a granular material down an inclined plane and between vertical parallel plates. It is shown that the dynamical behaviour of these materials is quite different from that of a viscous fluid. For the inclined flow problem, the normal stresses are not only unequal but vary non-linearly with depth. Also the maximum value of the mass flux distribution does not necessarily occur at the upper surface. For the vertical channel-flow problem, the material behaves somewhat like a Bingham fluid in that a plug region exists in the central part of the channel. The interesting feature of this problem is that the concentration of material volume in the shearing region outside the plug may either increase or decrease from the plug to the channel wall, depending on the boundary conditions. Experimental evidence for these phenomena in real granular materials is cited.

The results of this investigation suggest that the gravity flow of granular materials is essentially governed by two factors-a material characteristic length, which is possibly related to the grain size, and the externally imposed constraints such as the gravity field or the pressure exerted upon the granular material from the confining plates.

The behaviour of concentric double emulsion droplets in linear flows is examined analytically, for the case when both fluid–fluid interfaces remain nearly spherical, and numerically, for the effect of finite interface deformation. The theoretical analysis is used to calculate the velocity fields interior and exterior to the particle, the first effects of flow-induced deformation, and the effective viscosity of a dilute emulsion of compound droplets. The numerical simulations allow for a complete investigation of the finite deformation of both the outer drop and the encapsulated particle. For concentric multiphase particles, there appear to be two distinct mechanisms of globule breakup: (i) continuous extension of the globule corresponding to non-existence of a steady particle shape or (ii) contact of the two interfaces at the globule centre, owing to incompatibility of the steady inner and outer interface shapes, even though the globule is only modestly deformed. Finally, the effect of different flow-types, i.e. uniaxial or biaxial extensional flows, is shown, in one example, to suggest breakup of the inner droplet even though the outer droplet maintains a steady shape.

The stability properties and stationary statistics of inviscid barotropic flow over topography are examined. Minimum enstrophy states have potential vorticity proportional to the streamfunction and are nonlinearly stable; correspondingly, canonical equilibrium based on energy and enstrophy conservation predicts mean potential vorticity is proportional to the mean streamfunction. It is demonstrated that in the limit of infinite resolution the canonical mean state is statistically sharp, that is, without any eddy energy on any scale, and is identical to the nonlinearly stable minimum enstrophy state. Special attention is given to the interaction between small scales and a dynamically evolving large-scale flow. On the β-plane, these stable flows have a westward large-scale component. Possibilities for a general relation between inviscid statistical equilibrium and nonlinear stability theory are examined.

The stirring and mixing properties of one-phase coaxial jets, with large outer (annular) to inner velocity ratio ru = u2/u1 are investigated. Mixing is contemplated according to its geometrical, statistical and spectral facets with particular attention paid to determining the relevant timescales of the evolution of, for example, the interface area generation between the streams, the emergence of its scale-dependent (fractal) properties and of the mixture composition after the mixing transition. The two key quantities are the vorticity thickness of the outer, fast stream velocity profile which determines the primary shear instability wavelength and the initial size of the lamellar structures peeled-off from the slow jet, and the elongation rate γ = (u2 − u1)/e constructed with the velocity difference between the streams and the gap thickness e of the annular jet. The kinetics of evolution of the interface corrugations, and the rate at which the mixture evolves from the initial segregation towards uniformity is prescribed by γ−1. The mixing time ts, that is the time needed to bring the initial scalar lamellae down to a transverse size where molecular diffusion becomes effective, and the corresponding dissipation scale s(ts) are

formula here

where Re and Sc denote the gap Reynolds number and the Schmidt number, respectively. The persistence of the large-scale straining motion is also apparent from the spectra of the scalar fluctuations which exhibit a k−1 shape on the inertial range of scales.

The role of particles heavier than the fluid (glass spheres in water) in a turbulent open channel flow over a smooth bed is examined at volume concentration about $10^{-3}$. The present work focuses on the dynamical interaction between the solid (particles) and the fluid phases in the near-wall region. Experimental measurements have been performed by means of phase Doppler anemometry to acquire two velocity components, particle size and concentration data simultaneously; the Reynolds number of the flow was close to 15 000. It is observed that in the particle-laden flow, the vertical profiles of the streamwise mean velocity (for both fluid and solid phases) are reduced in the outer layer ($y^{ + }\,{ >}\, 20$), but increased in the viscous sublayer ($y^{ + }\,{<}\,5$) in comparison to the clear-water conditions, leading to an apparent slip kinematic boundary condition close to the wall ($y^{ + } \,{\approx}\,2$). Moreover, in the presence of solid particles, the flow exhibits a velocity close to the wall ($y^{ + }\,{ <}\, 15$) which is smaller than that of the particles, while in the outer layer the opposite takes place. In particle-laden flow, turbulence intensities of the streamwise and especially of the vertical velocity are damped for $y^{ + }\,{>}\,10$–20 (depending on particle inertia) but enhanced in the very near-wall region ($y^{ + }\,{ <}\, 5$), as is the Reynolds stress. These findings can be explained if they are referred to the mechanism of particle entrainment and deposition, which takes place close to the wall. This mechanism is related to particle inertia and to the dynamic of the structure of near-wall turbulence, which connects the buffer and outer regions with the very near-wall region. A significant momentum exchange between the two phases, which is particularly effective in the buffer region, is revealed by the quadrant analysis of the Reynolds stresses.

Experiments with fluids whose viscosity depends strongly on temperature are used to study the effect of viscosity variations in the range 10−105 on the heat transfer and horizontally averaged temperature of a convecting layer between horizontal isothermal boundaries. At large viscosity variations (3 × 103 and 105) and Rayleigh numbers less than the critical value given by linear theory, the system can be either conductive or convective depending on whether the Rayleigh number is increased from an earlier conductive state or decreased from a preexisting convective state. At higher Rayleigh numbers and for the entire range of viscosity variation studied the heat transfer differs little (< 20%) from that of a uniform-viscosity fluid when the Rayleigh number is defined in terms of the viscosity corresponding to a temperature equal to the average of the boundary temperatures. The relationship between Nusselt number and supercriticality (Ra/Rc) is even more remarkable being independent of viscosity variation and indistinguishable from that of a uniform-viscosity fluid with appropriate Prandtl number. The horizontally averaged temperature becomes increasingly asymmetrical with increasing viscosity variation due to the relatively large temperature change across the cold, more-viscous boundary layer, and results in an isothermal interior temperature significantly hotter than the average of the boundary temperatures. The measured temperature and convective heat transfer as a function of depth show that for viscosity variations greater than about 100 most of the viscosity change occurs within a stagnant conductive layer that develops above the actively convecting part of the system.

The interference of passive thermal fields produced by two (and more) line sources in decaying grid turbulence is studied by using the inference method described by Warhaft (1981) to determine the cross-correlation coefficient ρ between the temperature fluctuations produced by the sources. The evolution of ρ as a function of downstream distance, for 0.075 < d/l < 10, where d is the wire spacing and l is the integral lengthscale of the turbulence, is determined for a pair of sources located at various distances from the grid. It is found that ρ may be positive or negative (thereby enhancing or diminishing the total temperature variance) depending on the line-source spacing, their location from the grid and the position of measurement. It is also shown that the effects of a mandoline (Warhaft & Lumley 1978) may be idealized as the interference of thermal fields produced by a number of line sources. Thus new light is shed on the rate of decay of scalar-variance dissipation. The thermal field of a single line source is also examined in detail, and these results are compared with other recent measurements.

The paper gives the result of a study on the efflux of gases through circular apertures. The problem is considered as an example of a transition from the gasdynamic to the gaskinetic régime.

The mass flow of helium, argon and nitrogen was measured for a range of upstream pressures corresponding to (mean free path)/(aperture diameter) from about 50 to 5 × 10−3; within this range the transition from molecular effusion to inviscid, transonic flow takes place. The theory for the two asymptotic limits is discussed and first-order corrections to the free molecular and inviscid limit formulae are given.

We study the evaporation rate from single drops as well as collections of drops on a solid substrate, both experimentally and theoretically. For a single isolated drop of water, in general the evaporative flux is limited by diffusion of water through the air, leading to an evaporation rate that is proportional to the linear dimension of the drop. Here, we test the limitations of this scaling law for several small drops and for very large drops. We find that both for simple arrangements of drops, as well as for complex drop size distributions found in sprays, cooperative effects between drops are significant. For large drops, we find that the onset of convection introduces a length scale of approximately 20 mm in radius, below which linear scaling is found. Above this length scale, the evaporation rate is proportional to the surface area.

Measured values of mean velocity, Reynolds stresses and probability density distributions of fluctuating velocity are reported for the turbulent coaxial jets, with and without swirl, emerging into stagnant surroundings from a long pipe and an annulus concentric with the pipe. They were obtained using hot-wire anemometry and on-line data processing with the aid of a mini-computer. The results show that non-swirling coaxial flow configurations approach a self-similar state in a much smaller distance than that of the round jet, for velocity ratios ranging between 0·65 and 1·5; this is due to the mixing layer and vortex shedding that occur in the region downstream of the separation wall between the two streams. In the presence of swirl, the coaxial jet was found to develop at a faster rate. An assessment of turbulence models, based on Reynolds stress closures, suggests that previous assumptions for turbulent diffusion of turbulent kinetic energy are in error.

The rheology of particulate dispersions which are strongly influenced by particular types of non-hydrodynamic forces is analysed within the framework of suspension mechanics. Interactions between particles in a homogeneous shear flow without inertia are governed by viscous, electrostatic, London-van der Waals and Brownian forces. The balance among these provides the fluid with a microstructure described quantitatively at dilute concentrations by a pair distribution function and qualitatively by a characteristic interaction length. The bulk rheology follows from the microstructural variables through suitable averaging.

In dilute electrostatically stabilized suspensions of small rigid spheres for which London-van der Waals attractions and hydrodynamic interactions can be ignored, the theory predicts a Newtonian low-shear limit. The analytic expression for the viscosity contains a ϕ2-coefficient which can be quite large and agrees well with experimental data. At higher flow strengths a scale analysis of the pair conservation equation indicates a shear-and strain-thinning rheology, representing a breakdown of the fluid microstructure. Without flow the interaction length attains a maximum determined by the balance between Brownian motion and electrostatic repulsion. A weak shear merely perturbs this balance but generates stresses proportional to the fifth power of the length. With increasing shear rate this length and consequently the shear viscosity are reduced until viscous interactions completely dominate. Asymptotic solutions for an intermediate regime in which Brownian motion and hydrodynamic interactions are both negligible reveal power-law extensional and shear viscosities with non-zero normal stresses.

It is shown experimentally that, in steady flow, transition to Mach reflection occurs at the von Neumann condition in the strong shock range (Mach numbers from 2.8 to 5). This criterion applies with both increasing and decreasing shock angle, so that the hysteresis effect predicted by Hornung, Oertel & Sandeman (1979) could not be observed. However, evidence of the effect is shown to be displayed in an unsteady experiment of Henderson & Lozzi (1979).

This work experimentally studies the behaviour of underwater explosion bubbles near different boundaries. The results are compared with theoretical and experimental data on cavitation bubbles. Although explosion and cavitation bubbles behave similarly on a macroscopic level, there are still some differences, most of which are from the explosive nature of the explosion bubble. The relationship between bubble migration and the Kelvin impulse, surface inertia m* and surface stiffness k* is investigated. We found that none of them comprehensively predicts the migration of both cavitation and explosion bubbles when boundary elasticity is considered. This elasticity should be considered as a relative value with respect to bubble size. On the other hand, the phase between local vibration of boundaries and the pulsation of bubbles could be a useful predictive index of bubble migration. When using research results developed for cavitation bubbles in relation to explosion bubbles, the material presented here may be useful for pointing out their similarities and differences.

A method is presented in this article for deriving higher-order correction terms to the well-known asymptotic results for laminar forced-convection heat and mass transfer, and a formula is obtained for computing under fairly general conditions the first correction term to the asymptotic Nusselt number at large Péclet numbers for flows with small or moderate Reynolds numbers. This result is then applied to the problem of heat transfer from a solid, isothermal sphere in Stokes flow, to yield the asymptotic expression for the average Nusselt number,

for Pe→ ∞, Re→ 0, where and Pe are based on the radius of the sphere.

The evolution of a vortex ring in an ideal fluid under self-induction from a flat and elliptic configuration is followed numerically using the cut-off approximation (Crow 1970) for the velocity at the vortex. Calculations are presented for four different axes ratios of the initial ellipse. A particular choice is made for the core size and vorticity distribution in the core of the vortex ring. When the initial axes ratio is close to 1, the vortex ring oscillates periodically. The periodicity is lost as more eccentric cases are considered. For initial axes ratio 0·2, the calculations suggest a break-up of the ring through the core at one portion of the ring touching that at another, initially distant, portion of the ring.

Results from quantitative experiments, conducted at moderate Reynolds number with the vortex rings produced by puffing air through elliptic orifices, are compared with the calculations. The agreement is fairly good and it is found that a vortex ring produced from an orifice of axes ratio 0·2 breaks up into two smaller rings. The relevance of the results to the vortex trail of an aircraft is discussed.

Turbulence suppression by use of screens was studied in a small wind tunnel especially designed and built for the purpose. Wide ranges of mesh sizes and wire-diameter Reynolds numbers were covered in the present investigation, enabling the study of sub- and super-critical screens under the same, well-controlled, flow conditions. For the latter type small-scale fluctuations, produced by the screen itself, interact with the incoming turbulence. In the immediate vicinity of the screen the turbulence was found to be highly anisotropic and the intensities were higher than on the upstream side. Downstream of a short initial decay region, where the intensities decrease rapidly, the return to isotropy was found to be much slower than for the unmanipulated turbulence. The latter was generated by a square rod grid, and was shown to become practically isotropic beyond a distance of roughly 20 mesh widths from the grid. The role of the turbulence scales for the overall reduction effectiveness, and for the optimization of screen combinations for application in low-turbulence wind tunnels was studied.