It is common knowledge that relatively small drops or bubbles have a tendency to stick to the surfaces of solids. Two specific problems are investigated: the shape of the largest drop or bubble that can remain attached to an inclined solid surface; and the shape and speed at which it moves along the surface when these conditions are exceeded. The slope of the fluid-fluid interface relative to the surface of the solid is assumed to be small, making it possible to obtain results using analytic techniques. It is shown that from both a physical and mathematical point of view contact-angle hysteresis, i.e. the ability of the position of the contact line to remain fixed as long as the value of the contact angle θ lies within the interval θR [les ] θ [les ] θA, where θA [nequiv ] θR, emerges as the single most important characteristic of the system.

The present paper is the first part of a two-part report on a detailed investigation of periodic turbulent pipe flow. In this investigation, experimental data on instantaneous velocity and wall shear stress were obtained at a mean Reynolds number of 50000 in a fully developed turbulent pipe flow in which the volumetric flow rate was varied sinusoidally with time around the mean. Two oscillation frequencies at significant levels of flow modulation were studied in detail. The higher of these frequencies was of the order of the turbulent bursting frequency in the flow, and the other can be regarded as an intermediate frequency at which the flow still departed significantly from quasi-steady behaviour. While a few similar experiments have been reported in the recent literature, the present study stands out from the others in respect of the flow regimes investigated, the magnitude of flow modulation, the detailed nature of the measurements and most importantly the identification of a relevant parameter to characterize unsteady shear flows. The present paper contains the main experimental results and comparisons of these results with the results of a numerical calculation procedure which employs a well-known quasi-steady turbulence closure model. The experimental data are used to study the manner in which the time-mean, the ensemble-averaged and the random flow properties are influenced by flow oscillation at moderate to high frequencies. In addition, the data are also used to bring out the capability and limitations of quasi-steady turbulence modelling in the prediction of unsteady shear flows. A further and more detailed analysis of the experimental data, results of some additional experiments and a discussion on the characterization of turbulent shear flows are provided in Part 2 (Ramaprian & Tu 1983).

The main experimental results of the study of periodic turbulent pipe flow have been described in Part 1 of this report. In this second part, these experimental data are examined in greater detail to understand the effect of imposed oscillation on the flow structure, at moderate to large oscillation frequencies. Data on phase and amplitude and energy spectrum are used to study the effect of the imposed oscillation on the turbulence structure at these interactive frequencies of oscillation. Additional experiments which were performed to study the effect of oscillation frequency on the flow structure are also reported. Based on the present observations as well as on the data from other sources, it is inferred that turbulent shear flows respond very differently from laminar shear flows to imposed unsteadiness. A turbulent Stokes number relevant for characterizing the unsteady turbulent shear flows is identified and used to classify such flows.

Flow in the separation bubble formed along the sides of a blunt flat plate with right-angled corners has been studied in terms of extensive single- and two-point measurements of velocity and surface-pressure fluctuations. The cross-correlations between the surface-pressure and velocity fluctuations are found to be useful for the study of large-scale vortex structure in the bubble. Large-scale vortices are shed downstream from the separation bubble with a frequency of about 0.6U∞/xR, where U∞ is the approaching velocity and xR is the time-mean length of the bubble. On top of this regular vortex shedding, there exists a large-scale unsteadiness in the bubble. Vortices which are much larger than the regular vortices are shed with frequencies less than about 0.2U∞/xR. The large-scale unsteadiness is accompanied by enlargement and shrinkage of the bubble and also by a flapping motion of the shear layer near the separation line. The intermittent nature of the flow in the bubble is clarified in some detail. The distributions of the cross-correlations between the pressure and velocity fluctuations demonstrate the vortex structure in the reattaching zone. The longitudinal distance between the vortices is estimated to be (0.7–0.8) xR and their convection velocity is about 0.5U∞ near the reattachment line. The cross-correlations also suggest the existence of a longitudinal counter-rotating system in the bubble. The distance between the axes of the rotation is of the order of 0.6xR. Variations of timescales, lengthscales and phase velocities of the vortices are presented and discussed.

Mean drift currents due to spatially periodic surface waves in a viscous rotating fluid are investigated theoretically. The analysis is based on the Lagrangian description of motion. The fluid is homogeneous, the depth is infinite, and there is no continuous energy input at the surface. Owing to viscosity the wave field and the associated mass transport will attenuate in time. For the non-rotating case the present approach yields the time-decaying Stokes drift in a slightly viscous ocean. The analysis shows that the drift velocities are finite everywhere. In a rotating fluid it is found that the effect of viscosity implies a non-zero net mass transport associated with the waves, as opposed to the result of no net transport obtained from inviscid theory (Ursell 1950).

A generalized energy stability analysis necessarily incorporating charge-diffusion effects is applied to an electrohydrodynamic equilibrium comprising a dielectric liquid confined between two planar electrodes and subjected to an injection of unipolar charge. Generalized energy, kinetic-charge and mixed-type functionals are considered. Using the physical constraint that the sign of space-charge density can never change, it is possible to bound the nonlinear terms in the functional evolution equations. Sufficient conditions to guarantee global monotonic stability in the mean are then derived. In the case of a strong injection of charge the mixed-type functional provides theoretical values of the stability parameter close to the experimental values. Sufficient conditional stability bounds are also obtained for the leading-order diffusion-free equilibrium.

The mechanism of boundary-layer transition and the behaviour of spiral vortices on spheres rotating in otherwise undisturbed fluid were investigated experimentally. Critical and transition Reynolds numbers which determine the laminar-turbulent transition regime on the sphere surface were measured. In addition the number of spiral vortices on the sphere and the direction of the vortex axis were clarified.

In a fully developed turbulent channel flow, measurements of the streamwise vorticity fluctuations ωx have been made. A newly designed probe provides simultaneously in addition to the vorticity signal all three velocity signals. The new probe bears a likeness to the Kovasznay-type vorticity probe, but consists of four electrically independent hot wires, each mounted separately on a total of eight supporting prongs. A new calibration technique had to be developed for this probe.

In addition to various statistical properties of the three velocity components, the distributions of vorticity fluctuations and of skewness and flatness factors are given up to wall distances as close as y+ = 19. A pronounced maximum of the streamwise vorticity fluctuations was found at y+ ≈ 20. Large values of the flatness factor characterize the outer flow region.

The principal aim of this paper is to derive constitutive equations describing a magnetic fluid. The fluid is modelled as a dilute suspension of small spheroidal magnetic particles in a non-magnetic solute. The conditions for stability of fluid (against coagulation) are discussed and upper and lower bounds for particle sizes are determined. For a stationary fluid, the bulk magnetization is calculated with allowance for particle—particle interactions. The full stress tensor is determined for a flowing fluid that experiences an externally applied magnetic field. Both the flow and field may have arbitrary spatial and time dependences provided only that the lengthscale of spatial variations is large compared with particle dimensions, and that the timescale is long compared with the particle relaxation time due to Brownian motion. These results are applied to shear and pipe flows, where comparison with experiment is made, and to flow induced by rotating magnetic fields. Finally the damping of ultrasound having a characteristic period of the same order as the particle relaxation time is considered.

The long-time t−5/2 behaviour of the angular-velocity autocorrelation function is determined by the diffusion of fluid motion to large distances, from where the particle appears a point singularity. From an examination of this flow, the coefficient of t−5/2 can be related to some effective aspect ratios which describe how the particle rotates in a simple shear flow.

In this paper we consider the problem of the concentration jump of a vapour in the vicinity of a plane wall, which consists of the condensed phase of the vapour, in a rarefied gas mixture of that vapour (A) and another ‘inert’ gas (B). The general formulation of the problem of determining the concentration-jump coefficient CdA is given. In the Knudsen layer the simplest model of Boley-Yip theory is used to simplify the Boltzmann equations for the binary gas mixture. The numerical calculation of the concentration jump coefficient CdA for various values of evaporation coefficient αA is illustrated for the case of nB [Gt ] nA for which experimental data are available.

An experimental study has been made of the concept of controlling boundary-layer transition by superimposing in the flow Tollmien–Schlichting waves that are of equal amplitude and antiphased to the disturbances that grow and lead to transition. The cases that have been considered are transition arising from a single-frequency two-dimensional disturbance and transition arising from a nonlinear interaction between two waves of different frequency. A feedback system for controlling transition has also been studied. In each case, both hot-wire surveys and flow visualization have shown that it is possible to delay transition but that the flow cannot be restored completely to its undisturbed state. This appears to be a consequence of interactions between the very weak three-dimensional background disturbances in the flow and the primary two-dimensional waves. The implications of these findings in an implementation of the concept are discussed.

A primary motivation for this work arises from the contradictory results obtained in some recent measurements of the zero-crossing frequency of turbulent fluctuations in shear flows. A systematic study of the various factors involved in zero-crossing measurements shows that the dynamic range of the signal, the discriminator characteristics, filter frequency and noise contamination have a strong bearing on the results obtained. These effects are analysed, and explicit corrections for noise contamination have been worked out. New measurements of the zero-crossing frequency N0 have been made for the longitudinal velocity fluctuation in boundary layers and a wake, for wall shear stress in a channel, and for temperature derivatives in a heated boundary layer. All these measurements show that a zero-crossing microscale, defined as Λ = (2πN0)−1, is always nearly equal to the well-known Taylor microscale λ (in time). These measurements, as well as a brief analysis, show that even strong departures from Gaussianity do not necessarily yield values appreciably different from unity for the ratio Λ/λ. Further, the variation of N0/N0 max across the boundary layer is found to correlate with the familiar wall and outer coordinates; the outer scaling for N0 max is totally inappropriate, and the inner scaling shows only a weak Reynolds-number dependence. It is also found that the distribution of the interval between successive zero-crossings can be approximated by a combination of a lognormal and an exponential, or (if the shortest intervals are ignored) even of two exponentials, one of which characterizes crossings whose duration is of the order of the wall-variable timescale ν/U2*, while the other characterizes crossings whose duration is of the order of the large-eddy timescale δ/U∞. The significance of these results is discussed, and it is particularly argued that the pulse frequency of Rao, Narasimha & Badri Narayanan (1971) is appreciably less than the zero-crossing rate.

We consider longshore motion generated within the surf zone by obliquely incident breaking waves, and seek to describe the effect on such motion of variations, caused by wave grouping, in the incident longshore momentum flux. The effects of associated variations in set-up are not considered.

We use the linear long-wave equations to describe the motion resulting from the longshore momentum contained in a wave group. This consists of a succession of edge waves which disperse along the beach, and, for the example considered, an eventual steady circulation cell at the position of the wave group. We suggest that such a cell is always likely to be formed if the wave group is sufficiently localized, and that higher-modenumber edge waves are more likely to be excited.

We find timescales for the dispersal of the edge waves, and for the decay, due to bottom friction, of the circulation cell: we suggest that the latter may more generally be used, as a timescale for the effect of friction on longshore motion.

The interaction of a rarefaction wave with a gradual monotonic area reduction of finite length in a duct, which produces transmitted and reflected rarefaction waves and other possible rarefaction and shock waves, was studied both analytically and numerically. A quasi-steady flow analysis which is analytical for an inviscid flow of a perfect gas was used first to determine the domains of and boundaries between four different wave patterns that occur at late times, after all local transient disturbances from the interaction process have subsided. These boundaries and the final constant strengths of the transmitted, reflected and other waves are shown as a function of both the incident rarefaction-wave strength and area-reduction ratio, for the case of diatomic gases and air with a specific-heat ratio of 7/5. The random-choice method was then used to solve numerically the conservation equations governing the one-dimensional non-stationary gas flow for many different combinations of rarefaction-wave strengths and area-reduction ratios. These numerical results show clearly how the transmitted, reflected and other waves develop and evolve with time, until they eventually attain constant strengths, in agreement with quasi-steady flow predictions for the asymptotic wave patterns. Note that in all of this work the gas in the area reduction is initially at rest.

This paper is a study of how external turbulence affects an initially turbulence-free region in which there is a mean-velocity gradient dU/dz. Rapid-distortion theory shows how external turbulence induces irrotational fluctuations in the sheared region, which interact with the shear to produce rotational velocity fluctuations and mean Reynolds stresses. These stresses extend into the sheared region over a distance of the order of the integral scale L∞. Since the actual front between the initial external turbulence and the shear flow is a randomly contorted surface, the turbulence of a fixed point near the front is intermittent. Intermittency is included in the present analysis by a simple statistical model.

Experiments were done in a wind tunnel with the flow divided by a plate extending from upstream to x = 0. Above the plate, turbulence was produced by a grid. Below the plate a low turbulence shear was produced by wire screens. The wake of the plate (x > 0) decayed downstream.

Turbulent shear stress was observed to grow from zero to significant values in the interaction region. The magnitude and extent of the observed stress agrees reasonably well with predictions. We conclude that turbulent stresses can be produced by irrotational fluctuations in a region of mean shear, and that this effect can be estimated using rapid-distortion theory.

There are two main effects of turbulence on the mean flow past rods of square cross-section aligned with the approaching flow. Small-scale turbulence increases the growth rate of the shear layer, while large-scale turbulence enhances the roll-up of the shear layer. The consequences of these depend on the length of a square rod. The mean base pressure of a square rod varies considerably with turbulence intensity and scale as well as with its length.

In this paper we present a linear stability analysis for an unbounded, vertically stratified fluid which has compensating horizontal temperature and salinity gradients, so there is no horizontal density gradient. We obtain the most unstable perturbation for given linear horizontal and vertical gradients and calculate the growth rates, the vertical lengthscale of the intrusion and the slope of the intrusion to the horizontal. We show that the system is most unstable to two-dimensional disturbances and that, except for a small region in which the temperature stratification is unstable and the salinity stratification is stable, the most-unstable disturbance is non-oscillatory. We also obtain a solution to the fully nonlinear equations and calculate the fluxes of heat and salt. The nonlinear solution shows that alternating interfaces of salt-finger and diffusive interfaces will eventually appear on the intrusion when the vertical stratifications are both stable.

A nonlinear analysis, based on lubrication theory, is presented for the adjustment under surface tension of an initially uniform annular film of viscous fluid confined within a circular cylindrical pipe. The film surrounds a thread of another viscous fluid. Small axisymmetric interfacial disturbances of sufficiently long wavelength are found to grow, leading to the break-up of the initially continuous outer film into a number of isolated rings of fixed length on the pipe wall. The implications for the rupture of fluid threads surrounded by moderately thin films in confined geometries are discussed.

Experiments are described which show the steady streaming of fluid under a flexible membrane, located near the bottom of a wave basin in shallow water. Circulation of fluid in a closed circuit was thus obtained, and measurements were made of the pressure head and total flow. The phenomenon might be used to extract power from waves at very low efficiency, but the theoretical basis is not yet understood.