Long axisymmetric liquid zones are subject to axial temperature gradients which induce steady viscous flows driven by thermocapillarity. The approximately parallel flow in a cylindrical zone is examined for linearized instabilities. Capillary, surfacewave and thermal modes are found. Capillary breakup can be retarded or even suppressed for small Prandtl number and large Biot number B, which measures heat transfer from the liquid to the surrounding atmosphere. In the limiting case B → ∞ the zone becomes an isothermal jet subject to axial ‘wind stress’ on its interface. It is then possible to suppress capillary breakup entirely so that one can maintain long coherent jets.

The Stokes wave is generalized to progressive waves in deep water which are periodic in two orthogonal directions, and are steady relative to a frame of reference moving in one of these directions. These doubly periodic waves are nonlinear at their lowest approximation, and are calculated from the nonlinear equations for irrotational motion in deep water. It is shown how doubly periodic waves of small but finite wave slope may be calculated also from the nonlinear Schrödinger equation. The three-dimensional paths of particles on the free surface of a doubly periodic wave are found, and the interesting property is demonstrated that the mean particle paths differ from the direction of advance of the wave crests. The upper boundary of occurrence of doubly periodic waves at the smaller wavelength ratios is identified with the stability boundary for Stokes waves. The investigation aims to provide a closer approximation than Stokes waves to local wave structures on the ocean.

Two-dimensional burner-flame stability is discussed with arbitrary gas expansion. Density variations are allowed for by fully coupling the continuity and momentum equations. The flame is assumed to be close to a porous-plug-type flameholder so that the conventional hydrodynamic zone upstream of the flame cannot be included. Instead, the flow is assumed to obey a Darcy-type law within the holder, relating pressure gradient and velocity. It is shown that the influence of the holder and the acceleration due to gravity are important factors governing the onset of cellularity in porous-plug burner flames. Further, the balance of the transverse and longitudinal Darcy constants used to describe the upstream hydrodynamic zone within the holder have a vital effect on stability predictions. Experimental observations are confirmed by the theory presented.

We study the spectral statistics of the fluctuations of a passive scalar convected by a two-dimensional homogeneous isotropic turbulence using the eddy-damped quasinormal Markovian (EDQNM) theory, and – in certain cases – the near-equivalent test-field model (TFM). For zero correlation between scalar and vorticity fields it is known that these closures lead to inertial–convective ranges following respectively a k−1 law in the enstrophy-cascade range and a k−5/3 law in the inverse-energy-cascade range. We show that the scalar cascade in the latter range is direct, and is characterized by a positive eddy diffusivity. For forced flows in which correlation between vorticity and scalar forcing is prescribed, the k−5/3 range is replaced by a k1/3 range if the correlation is perfect, and for imperfect correlation we describe an analysis that bridges the ranges k1/3, k−1.

We also examine the infrared (k → 0) behaviour of the energy and scalar spectra. Statistically steady injection of energy and scalar variance at a wavenumber kI produces an energy spectrum E(k) ∼ k3, and a scalar spectrum E0(k) ∼ k. In the unforced case, for any initial conditions, the energy spectrum develops a k3 range for k less than the wavenumber characteristic of the energy-containing eddies and a k−3 range for larger k. This allows a demonstration – via closure – that this energy-bearing wavenumber decreases as t−1 and the enstrophy as t−2 (modulo logarithmic corrections), as predicted by Batchelor (1969). Finally we show the scalar-fluctuation variance decays as the enstrophy, if the enstrophy spectrum is considered as a passive scalar. If not, the decay exponent is proportional to the ratio of the characteristic eddy-damping rates of the velocity and scalar third-order moments.

Experiments have been performed to study the hydrodynamic stability of unsteady circular Couette flow generated by monotonic time-dependent inner-cylinder motions. The onset of instability was determined by measuring the axial component of velocity using laser-Doppler velocimetry; deviations from the pure-swirl value of zero are indicative of the initiation of Taylor vortices. The measurement technique was found to have an ‘intrusive’ effect on the flow stability, which was eliminated by the design of the experimental procedure. Significant enhancement of stability was found, in qualitative, but not quantitative, agreement with earlier theoretical predictions.

The axisymmetric withdrawal of fluid from a linearly stratified container is studied over the full parameter range. When only buoyancy and inertia are important the flow in the withdrawal layer is influenced by a virtual control point and is not analogous to that observed in the two-dimensional withdrawal problem. Two further flow regimes are shown to exist in which viscous forces are important: one in which convection of species is important, and a second in which diffusion of species is important. Theoretical arguments and laboratory experiments are used to show that $S = (Q^2N/\nu^3)^{\frac{1}{15}}$ is the appropriate flow parameter to differentiate between these possibilities. It is also argued that these results may be generalized to describe the features of several related flows: axisymmetric drawdown (or drawup) in withdrawal from a layered density structure, axisymmetric inflow into a linearly stratified environment and the axisymmetric spreading of density currents.

Flush-mounted hot-film gauges have proved very effective in measuring skin friction in steady laminar and turbulent boundary-layer flows. Their use is based on the analogy between momentum and heat transfer in the boundary layer. An extension of this technique for use with unsteady flows is presented, through the formulation of a more general relationship between the rates of heat and momentum transfer at the wall. The accuracy of the new formula and the range of its applicability are examined for the case of a periodic boundary layer, both in the laminar and turbulent regimes. This is accomplished by comparing the formula against exact numerical solutions of the differential equations. The present extension allows one to apply the hot-film technique to general unsteady-flow situations, including the measurement of the spectral density of wall-shear-stress fluctuations in steady turbulent flows.

Stability of convective motion generated by a lateral temperature difference in a variable-viscosity fluid contained in a vertical slot was studied experimentally. The experiments were carried out in a narrow tank 30 cm high × 11.5 cm deep × 2 cm wide with glycerin–water solutions of 70, 80 and 90% glycerine. The onset of instabilities was detected by means of shadowgraphs. As the critical temperature difference was exceeded, a regular array of convection cells appeared. The critical Rayleigh number showed a slight decreasing trend as the Prandtl number of the fluid was increased, with a concomitant increase in the viscosity variation. The critical wavenumber remained practically constant for the three solutions used. At large Rayleigh numbers, approximately seven times the critical value, boundary layers along the walls became unstable and the cellular convection pattern became disrupted.

Numerical solutions of the Navier–Stokes equations for fully developed, sinusoidal and pulsatile flows in curved tubes are presented for conditions not accessible to analytical perturbation methods. Simulations of physiological pulsatile flows in the aortic arch reveal a wide variety of interesting flow phenomena, including: (1) complex secondary flows with up to seven vortices in the half-tube; (2) cascaded vortex structures with vortices embedded within vortices; (3) strong secondary flows with associated wall shear stress nearly as large as the axial component; (4) reversal of axial-flow direction at the inside wall; (5) peak axial wall shear stress at the inside wall; (6) highest r.m.s. wall shear stress at the inside wall; and (7) oscillatory impedance, which is accurately described by straight-tube theory.

The generation and growth of gravity–capillary waves (λ ≈ 1 cm) by wind are reconsidered using linear instability theory to describe the process. For all friction velocities we solve the resulting Orr–Sommerfeld equation using asymptotic methods. New elements in our theory, compared with the work of Benjamin (1959) and Miles (1962), are more stress on mathematical rigour and the incorporation of the wind-induced shear current. We find that the growth rate of the initial wavelets, the first waves to be generated by the wind, is proportional to u*3.

We also study the effect of changes in the shape of the profiles of wind and wind-induced current. In doing this we compare results of Miles (1962), Larson & Wright (1975), Valenzuela (1976), Kawai (1979), Plant & Wright (1980) and our study. We find that the growth rate is very sensitive to the shape of the wind profile while the influence of changes in the current profile is much smaller. To determine correctly the phase velocity, the value of current and current shear at the interface are very important, much more so than the shape of either wind or current profile.

The influence of a transverse sound wave on vortex shedding from a rigid circular cylinder in a duct has been explored at Reynolds numbers from 20000 to 40000. In the absence of sound, the vortex shedding is found to consist of strings of coherent cyclic events which have frequencies that wander randomly about the nominal vortex-shedding frequency. Application of sound at the vortex-shedding frequency eliminates this wander and correlates the shedding along the cylinder axis. The frequency of vortex shedding can be shifted by sound applied either above or below the nominal vortex-shedding frequency. This entrainment is produced by the velocity induced by the sound wave rather than by the sound pressure. These phenomena are also observed in tube rows.

Vortical-pattern visualization for the starting flow behind airfoils is extended from a chordwise or two-dimensional mode to a spanwise or three-dimensional mode. We demonstrate the capabilities and limits of the extended method by means of selected photographic frames and sequences.

A laterally confined horizontal liquid layer is heated from below and cooled from above so that the single-component liquid is frozen in the upper part of the layer. When the imposed temperature difference is such that the Rayleigh number across the liquid is supercritical, there is Bénard convection in the liquid layer coupled with the dynamics of the solidification interface. Experimental results are presented for quasi-steady temperature variations at the horizontal boundaries. When the solidified layer is thick compared with the liquid layer a hysteresis loop is found for the heights of the liquid layer in a range of subcritical Rayleigh numbers. The interfacial corrugations exhibit a polygonal structure in this case. At Rayleigh numbers far above the critical value ‘bimodal patterns’ are observed with two distinct lengthscales. Finally a stability chart is given for the various interfacial patterns observed.

Measurements of rotating equilibrium bubble shapes in the low-gravity environment of a free-falling aircraft are presented. Emphasis is placed on bubbles which intersect the container boundaries. These data are compared with theoretical profiles derived from Laplace's formula and are in good agreement with the measurements. The interface shape depends on the contact angle, the radius of intersection with the container, and the parameter F, which is a measure of the relative importance of centrifugal force to surface tension. For isolated bubbles F has a maximum value of½. A further increase in F causes the bubble to break contact with the axis of rotation. For large values of F the bubble becomes more cylindrical and the capillary rise occurs over a thinner layer in order that the small radius of curvature can generate a sufficient pressure drop to account for the increased hydrostatic contribution.

As a uniformly coiled pipe is wound progressively tighter, centrifugal acceleration would be expected to drive the axial flow increasingly towards the outer wall of the pipe bend. Instead, the effect of bend curvature R is found experimentally to become fully expressed at small curvature ratios (a/R < 0.02), where a is the pipe radius. No further increase in the axial skew is observed in more tightly coiled pipe sections (0.02 [les ] a/R [les ] 0.20). In this ‘asymptotic’ regime where pipe curvature is unimportant, the developing axial skew intensifies as ≈ [(Re − 100) L/a]¼, where $Re = 2\overline{W}a/\nu $ and L is the entrance length. These results suggest that the action of centrifugal force remains balanced by swirl as flow develops in tightly coiled pipes, while in loosely coiled pipes the development of centrifugal effects lags the growth of swirl.

Plane stagnation flow is known to be linearly stable to three-dimensional perturbations. The purpose of this theoretical study is to show that the same flow can be destabilized if fluctuation levels are sufficiently high. In the present formulation, finite-amplitude disturbances are expanded in terms of the eigenfunctions pertaining to the linear stability of potential stagnation flow and a Galerkin method is used to derive the nonlinear amplitude equations coupling the different modes. Two- and three-mode interaction models based on the least-damped eigenfunctions of linear theory indicate that three-dimensional fluctuations can be triggered to grow exponentially above a certain critical intensity. The existence of such a threshold is in qualitative agreement with experimental studies of the secondary vortices arising in flows past blunt bodies.

Experimental results are presented for the instantaneous release of a constant volume of air into water in a long horizontal tube of square cross-section. The tube is closed at both ends and the volume of air is confined at one of the ends before it is released. The resulting motion, after the rapid formation of an air-cavity front, may be divided into three phases: initially the front of the air cavity moves at constant speed, later its speed decreases monotonically, and finally its speed executes a long series of erratic stops and starts before coming entirely to rest. The transition from the first to the second phase is observed to occur when a disturbance due to the tube end overtakes the cavity front. The final phase is dominated by surface-tension effects, complicated by surface contaminants. A simple model of the flow, based on Benjamin's (1968) theory of steady cavity flow and the classical theory of hydraulic jumps, is developed. With correction for surface tension, the model results compare well with the experimental results for the first two phases.

This paper describes a fundamental study of evaporation of volatile-liquid lenses due to the heat supply from the substrate of an immiscible, less-volatile liquid under the atmosphere of the common vapours of the two fluid substances. Experiments were performed with single n-pentane lenses placed on the surface of an otherwise quiescent pool of water. The behaviour of each lens throughout its life was observed in detail using laser shadowgraphy. It was found that the time required for complete evaporation of each lens and the behaviour of the lenses change, in a peculiar but rather regular way, with the age of the water surface. This ageing effect is more significant when fluids of higher purities are used, and it is thought to be due to the quantity of contaminants at the surface increasing with its age.

The response of a well-developed turbulent boundary layer to suddenly applied convex surface curvature is investigated, using conditional-sampling techniques so that the turbulent and non-turbulent regions of the flow can be clearly distinguished. The conclusion of this and the companion paper by Hoffmann, Muck & Bradshaw (1985) is that the effects of convex (stabilizing) and concave (destabilizing) curvature on boundary layers – and presumably on other shear layers – are totally different, even qualitatively: mild convex curvature, with a radius of curvature of the order of 100 times the boundary-layer thickness, tends to attenuate the pre-existing turbulence, apparently without producing large changes in statistical-average eddy shape, while concave curvature results in the quasi-inviscid generation of longitudinal (‘Taylor-Görtler’) vortices, together with significant changes in the turbulence structure induced directly by the curvature and indirectly by the vortices.

From the point of view of calculation methods, the implication is that, although stabilizing and destabilizing curvature are connected by a common dimensional analysis, the differences are such that the one cannot be regarded as a useful guide to the treatment of the other. Specifically, rates of change of turbulence-structure parameters with curvature parameter are likely to be nearly discontinuous at zero curvature, and in particular the time of response of a turbulent boundary layer to convex curvature, implying mere attenuation, is very much less than the time of response to concave curvature, implying reorganization of the eddy structure.

The response of a turbulent boundary layer to suddenly applied concave surface curvature with δ/R = 0.01–0.02 is investigated. The main conclusion of this and the companion paper by Muck, Hoffmann & Bradshaw (1985) is that the effects of concave (destabilizing) and convex (stabilizing) curvature on boundary layers – and presumably on other shear layers – are totally different, even qualitatively. As shown in Muck, Hoffmann & Bradshaw (1985), convex curvature tends to attenuate the pre-existing turbulence and, at least in the case of mild curvature, there are no large changes in statistical average eddy shape. Concave curvature, on the other hand, can lead to the quasi-inviscid generation of longitudinal (‘Taylor–Görtler’) vortices, and we show that significant changes in the turbulence structure are induced both directly by the curvature and indirectly by the vortices.