Hot-wire and flow-visualization studies have been carried out in three air jets subjected to pure-tone acoustic excitation, and the instability, vortex roll-up and transition as well as jet response to the controlled excitation have been investigated. The centreline fluctuation intensity can be enhanced by inducing stable vortex pairing to a level much higher than even that at the ‘preferred mode’, but can also be suppressed below the unexcited level under certain conditions of excitation. The conditions most favourable to vortex pairing were determined as a function of the excitation Strouhal number, the Reynolds number (ReD), and the initial shear-layer state, i.e. laminar or turbulent. It is shown that the rolled-up vortex rings undergo pairing under two distinct conditions of excitation: ‘the shear layer mode’ when the Strouhal number based on the initial shear-layer momentum thickness (Stθ) is about 0·012, and ‘the jet column mode’ when the Strouhal number based on the jet diameter (StD) is about 0·85. The former involves pairing of the near-exit thin vortex rings when the initial boundary layer is laminar, irrespective of the value of StD. The latter involves pairing of the thick vortex rings at x/D ≅ 1·75, irrespective of Stθ or whether the initial boundary layer is laminar or turbulent. For laminar exit boundary layer, pairing is found to be stable, i.e., occurring regularly in space and time, for ReD < 5 × 104, but becomes intermittent with increasing ReD or fluctuation intensity in the initial boundary layer.

The trajectories of the vortex centres and their convection velocities during a pairing event have been recorded through phase-locked measurements. In the presence of stable vortex pairing, the time average profiles of fluctuation intensities and Reynolds stress show noticeable deviations from those in the unexcited jet. The vortex pairing phenomenon produce considerably larger excursions of the $\widetilde{uv}(t)$ signal than the time-average Reynolds stress reveals, suggesting that only certain phases of the pairing process may be important in entrainment, and production of Reynolds stress and jet noise.

The coherent structure dynamics in the near field of a circular jet has been experimentally explored by inducing ‘stable’ vortex pairing through controlled excitation (see Zaman & Hussain 1980) and applying phase-averaging techniques. Hot-wire measurements were made in a 7·62 cm air jet with laminar exit boundary layer at the Reynolds number ReD = 3·2 × 104, excited at the Strouhal number StD = 0·85. At a particular phase during the pairing process, spatial distributions of the phase-average longitudinal and lateral velocity perturbations (〈u)〉, 〈v〉), vorticity, streamlines, the coherent and background Reynolds stresses and turbulence intensities have been educed. These data have been obtained for four different locations occupied by the vortices at the same phase (preceding, during, and following the pairing event), in the region 0 < x/D < 5. Spatial distributions of these measures at four successive phases during the pairing process are also educed in an attempt to further understand the vortex-pairing dynamics. The flow physics is discussed on the basis of measurements over the physical extent of the vortical structures, phase-locked to specific phases of the pairing event and thus do not involve use of the Taylor hypothesis.

The computed pseudostream functions at particular phases are compared with the corresponding streamlines drawn by the method of isoclines. Transition of the vortices is examined on the basis of vorticity diffusion, the superimposed random fluctuation field intensities and Reynolds stress and phase-locked circumferential correlation measurements. The peak vorticity drops rapidly owing to transition and interaction of the vortices during pairing but, farther downstream, the decay can be attributed to destruction of the coherent vorticity by the background turbulence Reynolds stress, especially at the locations of the latter's ‘saddle points’. Controlled excitation enhances the initial circumferential coherence of the vortical structures, but is ineffective in delaying turbulent breakdown near the end of the potential core; the breakdown appears to occur through evolution of the circumferential lobe structures. The coherent structure Reynolds stress is found to be much larger than the background turbulence Reynolds stress for 0 < x/D [lsim ] 3, but these two are comparable near the end of the jet potential core. The zone average of the coherent structure Reynolds stress over the cross-section of the merging vortex pair is much larger than that over a single vortical structure either before or after the completion of pairing. During the pairing process, such average correlations are found to be the largest at an early phase of the process while entrainment, turbulent breakdown as well as rapid diffusion of vorticity occur at a later phase. The regions of alternate positive and negative coherent Reynolds stresses associated with the structures and their interactions help explain ‘negative production’.

The evolution of the shape of a slender inviscid drop in an axisymmetric straining motion is studied at low Reynolds numbers. It is found that the shape equation can be solved by polynommals with time-dependent coefficients. A global stability result can be used to show simply that only one possible equilibrium is stable. It is further shown that if the slender drop starts with a long-wavelength waist then it cannot go to this stable equilibrium and must either extend indefinitely or burst. In the class of trinomial shapes, it is shown that the drop either bursts or goes to the stable equilibrium, depending on whether or not the initial shape has a waist.

The authors consider an homogeneous non-isotropic turbulence which develops without mean velocity gradient so that it should return to isotropy. This turbulence has been obtained by application of two successive plane strains to a grid-generated turbulence, and this configuration has already been described in a preceding paper. It is shown in particular that the nonlinear effects make no significant contribution to the rotation of the principal axes of the Reynolds stress tensor. In the case of the return to isotropy, an important parameter connected with the turbulent energy distribution between three directions comes into play. In the present experiment it has a positive sign whereas in previous experiments this sign was negative. In particular, the authors conclude that, when this parameter is positive, the return to isotropy is slower than in the opposite case.

Conditions are found for the appearance of non-uniform progressive waves of permanent form from a long-wave modulation of a finite-amplitude Stokes wave on deep water. The waveheight at which the modulated waves can occur is a very slowly decreasing function of the modulation wavelength for values up to 150 times the original wavelength. Some qualitative remarks are made about the problem of determining the stability of the new waves.

The time development of the symmetrical standing zone of recirculation, which is formed in the early stage of the flow due to a circular cylinder impulsively set in motion perpendicular to its generators, has been studied using a flow visualization technique. The Reynolds numbers (based upon the diameter) range from 40 to 104. Some new phenomena indicated in the flow patterns are revealed, and several different regimes are differentiated by a detailed analysis of the evolution of the main flow characteristics. A correlation with some theoretical results is established.

Previous studies of the distortion of the electric double layer around a charged sphere have assumed that the electric stresses are small compared with the viscous stresses. The flow around the particle is therefore changed only slightly by the presence of the charge cloud. This change is measured by the Hartmann number, and in § 6 we remove the restriction that it should be small. It is found that the previous linearized theory is sufficiently accurate for typical experimental values of the Hartmann number. Previous studies have also assumed that the potential at the surface of the particle is small. This assumption is removed in § 7 of this paper. For values of the non-dimensional surface potential smaller than 2 the predictions are altered by less than 10 %. For higher values the differences between linear and nonlinear theory are not negligible, especially when the charge cloud is thin compared with the radius of the charged sphere.

The steady movement of a fluid meniscus in a circular capillary tube is analysed by means of finite-element numerical simulation for a range of values of contact angles and contact-line velocities with minute slippage of the fluid on the tube wall, thus relaxing the conventional no-slip boundary condition. The resulting flow field does not produce unbounded forces at contact line, contrary to that with the no-slip condition. The unknown meniscus shape is determined by an iterative scheme in which the imbalance in the normal-stress boundary condition is the basis for improving the shape. Comparison of the numerical results found here and the experimental results of a number of investigators suggests the possibility that the contact angle does not vary with contact-line velocity.

A rational asymptotic theory describing the perturbed flow in a turbulent boundary layer encountering a small two-dimensional hump is presented. The theory is valid in the limit of very high Reynolds number in the case of an aerodynamically smooth surface, or in the limit of small drag coefficient in the case of a rough surface. The method of matched asymptotic expansions is used to obtain a multiple-structured flow, along the general lines of earlier laminar studies. The leading-order velocity perturbations are shown to be precisely the inviscid, irrotational, potential flow solutions over most of the domain. The Reynolds stresses are found to vary across a thin layer adjacent to the surface, and display a singular behaviour near the surface which needs to be resolved by an even thinner wall layer. The Reynolds stress perturbations are calculated by means of a second-order closure model, which is shown to be the minimum level of sophistication capable of describing these variations. The perturbation force on the hump is also calculated, and its order of magnitude is shown to depend on the level of turbulence closure; a cruder turbulence model gives rise to spuriously large forces.