Strongly turbulent Taylor–Couette flow with independently rotating inner and outer cylinders with a radius ratio of is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux as a function of the Taylor number and the angular velocity ratio in the large-Taylor-number regime and well off the inviscid stability borders (Rayleigh lines) for co-rotation and for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux , with an amplitude and an exponent . The data are consistent with one effective exponent for all , but we discuss a possible dependence in the co- and weakly counter-rotating regimes. The amplitude of the angular velocity flux is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of , i.e. along the line . This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and in particular identify the radial position of the neutral line, defined by for fixed height . For these large values, the ratio , which is close to , is distinguished by a zero angular velocity gradient in the bulk. While for moderate counter-rotation , the neutral line still remains close to the outer cylinder and the probability distribution function of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the probability distribution function of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view and consistent interpretation for all these various results.

The present investigation is oriented towards a better understanding of the turbulent structure in the core region of fully developed and completely wall-bounded flows. In view of the already existing results concerning the bursting process in boundary layers (which are semi-bounded flows), an amplitude analysis of the Reynolds shear stress fluctuation u1u2, sorted into four quadrants of the u1, u2 plane, was carried out in a turbulent pipe flow. For the wall side of the core region, in which the correlation coefficient u1u2/u’1u’2 does not change appreciably with the distance from the wall, the structure of the Reynolds stress is found to be similar to that obtained in boundary layers: bursts, i.e. ejections of low speed fluid, make the dominant contribution to the Reynolds stress; the regions of violent Reynolds stress are small fractions of the overall flow; and the mean time interval between bursts is found to be almost constant across the flow. For the core region, the large cross-stream evolution of the correlation coefficient u1u2/u’1u’2 is associated with a new structure of the Reynolds stress induced by the completely wall-bounded nature of the flow. Very large amplitudes of u1u2 are still observed, but two distinct burst-like patterns are now identified and related to ejections originating from the two opposite halves of the flow. In addition to this interaction, a focusing effect caused by the circular section of the pipe is observed. As a result of these two effects, the mean time interval between the bursts decreases significantly in the core region and reaches a minimum on the pipe axis. Investigation of specific space-time velocity correlations reveals the possible existence of rotating structures similar to those observed at the outer edge of turbulent boundary layers. These coherent motions are found to have a scale noticeably larger than that of the bursts.

A direct numerical simulation of spatially periodic wavy core flows is carried out under the assumption that the densities of the two fluids are identical and that the viscosity of the oil core is so large that it moves as a rigid solid which may nevertheless be deformed by pressure forces in the water. The waves which develop are asymmetric with steep slopes in the high-pressure region at the front face of the wave crest and shallower slopes at the low-pressure region at the lee side of the crest. The simulation gives excellent agreement with the experiments of Bai, Chen & Joseph (1992) on up flow in vertical core flow where axisymmetric bamboo waves are observed. We define a threshold Reynolds number and explore its utility; the pressure force of the water on the core relative to a fixed reference pressure is negative for Reynolds numbers below the threshold and is positive above. The wave length increases with the hold-up ratio when the Reynolds number is smaller than a second threshold and decreases for larger Reynolds numbers. We verify that very high pressures are generated at stagnation points on the wavefront. It is suggested that a positive pressure force is required to levitate the core off the wall when the densities are not matched and to centre the core when they are. A further conjecture is that the principal features which govern wavy core flows cannot be obtained from any theory in which inertia is neglected.

The internal gravity wave (IGW) field emitted by a stably stratified, initially turbulent, wake of a towed sphere in a linearly stratified fluid is studied using fully nonlinear numerical simulations. A wide range of Reynolds numbers, $\mathit{Re}= UD/ \nu \in [5\times 1{0}^{3} , 1{0}^{5} ] $ and internal Froude numbers, $\mathit{Fr}= 2U/ (ND)\in [4, 16, 64] $ ($U$, $D$ are characteristic body velocity and length scales, and $N$ is the buoyancy frequency) is examined. At the higher $\mathit{Re}$ examined, secondary Kelvin–Helmholtz instabilities and the resulting turbulent events, directly linked to a prolonged non-equilibrium (NEQ) regime in wake evolution, are responsible for IGW emission that persists up to $Nt\approx 100$. In contrast, IGW emission at the lower $\mathit{Re}$ investigated does not continue beyond $Nt\approx 50$ for the three $\mathit{Fr}$ values considered. The horizontal wavelengths of the most energetic IGWs, obtained by continuous wavelet transforms, increase with $\mathit{Fr}$ and appear to be smaller at the higher $\mathit{Re}$, especially at late times. The initial value of these wavelengths is set by the wake height at the beginning of the NEQ regime. At the lower $\mathit{Re}$, consistent with a recently proposed model, the waves propagate over a narrow range of angles that minimize viscous decay along their path. At the higher $\mathit{Re}$, wave motion is much less affected by viscosity, at least initially, and early-time wave propagation angles extend over a broader range of values which are linked to increased efficiency in momentum extraction from the turbulent wake source.

The results are reported of velocity measurements in oscillatory flow over rippled beds. Velocities were measured with a laser-doppler anemometer in both an oscillating tray rig and an oscillatory flow water channel. Both self-formed and artificial ripples were examined. In addition, some measurements were made with an apparently plane bed with intense sediment motion.

The experimental results were compared with the predictions of Kalkanis (1964), Kajiura (1968), Bakker (1973, 1974) and Sleath (1974). The closest agreement between theory and experiment was obtained with the method of Sleath.

Measurements of the Eulerian drift velocities showed drift towards the adjacent ripple crest in the immediate vicinity of the bed and away from the crest further out.

The effect of small particles on decaying grid-generated turbulence is studied experimentally. Using a two-camera system, instantaneous fluid-phase and particle-phase measurements can be obtained simultaneously. The data obtained with this system are used to study the decay behaviour of the turbulent flow. The role of particle size, particle density and volume load is studied in a number of different cases. These cases are chosen so that the individual role of these parameters can systematically be evaluated. Addition of particles to the flow has significant effects on the decaying turbulence: first, the onset of the turbulent decay appears to shift upstream; second, the flow becomes anisotropic as it develops downstream. The latter is observed as an increase in integral length scale in the vertical direction. The rate at which the flow becomes anisotropic can be predicted using a new parameter: the product of the non-dimensional number density and the Stokes number (referred to as the ‘Stokes load’). This parameter, combining the relevant fluid and particle characteristics, is a measure for the energy redistribution leading to anisotropy. In addition to redistributing energy, the particles also produce turbulence. However, this only becomes evident when the grid-generated turbulence has decayed sufficiently, relatively far downstream of the grid. The turbulence production by particles can also account for the observed decrease in slope of the power spectrum, which leads to a ‘cross-over’ effect. The production of turbulence by the particles can be predicted using a model for the momentum deficit of the particle wakes. The validity of this approach is confirmed using conditional sampling of the fluid velocity field around the particles.

The two dominant, linearly independent surface-wave modes in a circular cylinder, which differ only by an azimuthal rotation of ½π and have equal natural frequencies, are nonlinearly coupled, both directly and through secondary modes. The corresponding, weakly nonlinear free oscillations are described by a pair of slowly modulated sinusoids, the amplitudes and phases of which are governed by a four-dimensional Hamiltonian system that is integrable by virtue of conservation of energy and angular momentum. The resulting solutions are harmonic in a particular, slowly rotating reference frame. Harmonic oscillations in the laboratory reference frame are realized for three special sets of initial conditions and correspond to a standing wave with a fixed nodal diameter and to two azimuthally rotating waves with opposite senses of rotation. The finite-amplitude corrections to the natural frequencies of these harmonic oscillations are calculated as functions of the aspect ratio d/a (depth/radius). A small neighbourhood of d/a = 0.1523, in which the natural frequency of the dominant axisymmetric mode approximates twice that of the two dominant antisymmetric modes, is excluded. Weak, linear damping is incorporated through a transformation that renders the evolution equations for the damped system isomorphic to those for the undamped system.

Laser-Doppler velocity measurements were obtained in water between finite rotating disks, with and without throughflow, in four cases: ω1 = ω2 = 0; ω2/ω1 = −1; ω2/ω1 = 0; ω2/ω1 = 1. The equilibrium flows are unique, and at mid-radius they show a high degree of independence from boundary conditions in r. With one disk rotating and the other stationary, this mid-radius ‘limiting flow’ is recognized as the Batchelor profile of infinite-disk theory. Other profiles, predicted by this theory to coexist with the Batchelor profile, were neither observed experimentally nor were they calculated numerically by the finite-disk solutions, obtained here via a Galerkin, B-spline formulation. Agreement on velocity between numerical results and experimental data is good at large values of the ratio RQ/Re, where RQ = Q/2πνs is the throughflow Reynolds number and Re = R22ω/ν is the rotational Reynolds number.

The influence of periodic perturbations on the development of two-dimensional free shear layers generated by a splitter plate was investigated in cases where the ratios of the two velocities u1 and u2 either side of the splitter plate were such that 0 < u1/u2 < 1. Investigations were carried out in both a suction and a blower wind tunnel. Results show that even very weak periodic perturbations caused by the wind tunnel may cause significant nonlinear spreading in the downstream development of the shear layer, a behaviour which is also observed when the shear layer is deliberately excited. Other things being equal, the effect of the disturbance is greater when flow separation at the splitter plate is turbulent than when it is laminar.

No self-induced feedback frequencies were measured in the test section. All tonal components that were detected in the flow could be traced to external sources.

The influence of trailing-edge thickness on the shear-layer development is found to become significant when it exceeds 50% of the sum of boundary-layer displacement thickness at the point of separation. As the trailing edge becomes thicker, the range over which the shear layer is self-similar is shifted farther downstream. This behaviour may be crucial for predicting the evolution of shear layers in high-speed flows having thin boundary layers at separation.

The momentum thickness criterion for estimating the development length of the flow as suggested by Bradshaw is shown to be insufficient for two-stream layers, where additional parameters, e.g. the trailing-edge geometry, have to be taken into account. Discrepancies between previously published observations of shear layers, as well as the considerable scatter in reported measurements, may therefore, to a large extent, be attributable to contamination of the experimental facility.

An experiment was performed in a 3·5 by 3·5 m variable-height, closed convection box, with conditions ranging from a Rayleigh number of 4 × 104 up to 7 × 109, using air as the working fluid. Heat-flux measurements made at Rayleigh numbers up to 7 × 109 yielded a Nusselt number Nu = 0·13Ra0·30. Velocities and temperatures were measured up to Ra = 1·7 × 107, and Fourier spectra calculated to find the predominant horizontal scales of the motion midway between the boundaries. The predominant scale at Ra ∼ 105 was approximately four times the distance between plates, changing to six as Ra increased to 106. With side walls introduced so that the transverse aspect ratio was equal to five, Fourier spectra indicated considerable smaller scale motions, approximately equal to the layer depth. These motions decreased in size as Ra was increased. The results are discussed in relation to previous experimental and theoretical work.

Evolving viscoplastic flows upon slopes are an important idealization of many flows in a variety of geophysical situations where yield stress is thought to play a role. For such models, asymptotic expansions suitable for slowly moving shallow fluid layers (lubrication theory) reduce the governing equations to a simpler problem in terms of the fluid thickness. We consider the version of the theory for fluids described by the Herschel–Bulkley constitutive law, and provide a variety of solutions to the reduced equation, both numerical and analytical. For extruded inclined domes, we derive the characteristic temporal behaviour of measures of the dome's dimensions.

An investigation is made into water-wave propagation through an array of vertical cylinders extending to infinity and periodic in both horizontal directions. Methods are presented for the calculation of the frequency ranges for which wave propagation without change of amplitude is possible (‘passing bands’), and for which propagation without change of amplitude is not possible (‘stopping bands’). Some of the techniques may be used to determine the change of wave amplitude for frequencies within the stopping bands. Approximate and numerical techniques are used to show how this infinite-array problem is related to trapped modes, Rayleigh–Bloch waves, and the problem of wave diffraction by a grating made up of a finite number of cylinder rows.

We investigate the dynamics of drop impacts on dry solid surfaces. By synchronising high-speed photography with fast force sensing, we simultaneously measure the temporal evolution of the shape and impact force of impacting drops over a wide range of Reynolds numbers ($\mathit{Re}$). At high $\mathit{Re}$, when inertia dominates the impact processes, we show that the early time evolution of impact force follows a square-root scaling, quantitatively agreeing with a recent self-similar theory. This observation provides direct experimental evidence on the existence of upward propagating self-similar pressure fields during the initial impact of liquid drops at high $\mathit{Re}$. When viscous forces gradually set in with decreasing $\mathit{Re}$, we analyse the early time scaling of the impact force of viscous drops using a perturbation method. The analysis quantitatively matches our experiments and successfully predicts the trends of the maximum impact force and the associated peak time with decreasing $\mathit{Re}$. Furthermore, we discuss the influence of viscoelasticity on the temporal signature of impact forces. Last but not least, we also investigate the spreading of liquid drops at high $\mathit{Re}$ following the initial impact. Particularly, we find an exact parameter-free self-similar solution for the inertia-driven drop spreading, which quantitatively predicts the height of spreading drops at high $\mathit{Re}$. The limit of the self-similar approach for drop spreading is also discussed. As such, our study provides a quantitative understanding of the temporal evolution of impact forces across the inertial, viscous and viscoelastic regimes and sheds new light on the self-similar dynamics of drop-impact processes.

Liquid-infused surfaces present a novel, passive method of turbulent drag reduction. Inspired by the Nepenthes Pitcher Plant, liquid-infused surfaces utilize a lubricating fluid trapped within structured roughness to facilitate a slip at the effective surface. The conceptual idea is similar to that of superhydrophobic surfaces, which rely on a lubricating air layer, whereas liquid-infused surfaces use a preferentially wetting liquid lubricant to create localized fluid–fluid interfaces. Maintaining the presence of these slipping interfaces has been shown to be an effective method of passively reducing skin friction drag in turbulent flows. Given that liquid-infused surfaces have only recently been considered for drag reduction applications, there is no available framework to relate surface and lubricant characteristics to any resulting drag reduction. Here we use results from direct numerical simulations of turbulent channel flow over idealized, liquid-infused grooves to demonstrate that the drag reduction achieved using liquid-infused surfaces can be described using the framework established for superhydrophobic surfaces. These insights can be used to explain drag reduction results observed in experimental studies of lubricant-infused surfaces. We also demonstrate how a liquid-infused surface can reduce drag even when the viscosity of the lubricant exceeds that of the external fluid flow, which at first glance can seem counter-intuitive.

A theoretical study is made of the behaviour of clusters of spheres falling in a viscous fluid under the assumptions that: (a) intertial effects are negligible, (b) the distance between any two spheres is larg compared with their radii. The equations of motion are derived and solved for a number of particular cases and the results compared with the experimental observations of the same motions reported in the preceding paper (Jayaweera, Mason & Slack 1964). For three or four spheres, initially in a horizontal line, the theory is in general agreement with the experiments. Three spheres forming an isosceles triangle are shown to oscillate about the horizontal and about the equlateral shape, so that this theory is unable to explain the observed tendency for three to six spheres to form a regular horizontal polygon. The stability of the steady configuration of n spheres at the vertices of a regular horizontal polygon is examined and it is found that the configuration is only stable for n < 7, which explains why this configuration is not observed for more than six spheres.

The violent collapse of bubble clusters is thought to damage adjacent material in both engineering and biomedical applications. Yet the complexities of the root mechanisms have restricted theoretical descriptions to significantly simplified configurations. Reduced-physics models based upon either homogenization or arrays of idealized spherical bubbles do reproduce important gross cluster-scale features. However, these models neglect detailed local bubble–bubble interactions, which are expected to mediate damage mechanisms. To describe these bubble-scale interactions, we simulate the expansion and subsequent collapse of a hemispherical cluster of 50 bubbles adjacent to a plane rigid wall, explicitly representing both the asymmetric dynamics of each bubble within the cluster and the compressible-fluid mechanics of bubble–bubble interactions. Results show that the collapse propagates inward, as visualized in experiments, and that geometric focusing generates high impulsive pressures. This gross behaviour is nearly independent of the specific arrangement of bubbles within the cluster and matches predictions from the corresponding particle and homogenized models we consider. The peak pressure in the detailed simulations is associated with the centremost bubble, which causes a corresponding peak pressure on the nearby wall. However, the peak pressures in all cases are a small fraction – over a factor of ten times smaller in many cases – of those predicted in the corresponding reduced models. This is due to the enhanced focusing in the homogeneous model and the spherical constraint on each bubble in the particle models assessed. These would be important factors to consider in any subsequent predictions of wall damage based upon reduced models.

In this article, we present a modelling approach for rapid dynamic wetting based on the phase field theory. We show that in order to model this accurately, it is important to allow for a non-equilibrium wetting boundary condition. Using a condition of this type, we obtain a direct match with experimental results reported in the literature for rapid spreading of liquid droplets on dry surfaces. By extracting the dissipation of energy and the rate of change of kinetic energy in the flow simulation, we identify a new wetting regime during the rapid phase of spreading. This is characterized by the main dissipation to be due to a re-organization of molecules at the contact line, in a diffusive or active process. This regime serves as an addition to the other wetting regimes that have previously been reported in the literature.

The buoyant rise of chimney plumes is discussed for relatively large distances from the source, where atmospheric turbulence is the dominant cause of mixing (rather than turbulence due to the plume's own upward motion). A simple theory is developed which shows a number of different shapes plumes can have under different atmospheric conditions (particularly in an unstable environment).

Experimental data are then presented, which were collected in the field near Toronto, with reasonably detailed supporting information on the atmospheric temperature structure. These (and earlier results) often show quite complex plume behaviour at large distances from the source, which can, however, be readily understood in terms of the simple theory presented.

Modelling of turbulent passive-scalar diffusion is studied using the statistical results from a two-scale direct-interaction approximation. In this model, the mean scalar, the scalar variance and the dissipation rate of scalar variance constitute fundamental diffusion quantities. The turbulent scalar flux is written in the form of an anisotropic eddy-diffusivity representation. This representation, paving the way for explaining anisotropic heat transport, is tested against typical experimental data. The present model equation for the dissipation rate of scalar variance also gives a theoretical justification for the existing equations that are adopted in the second-order models.

In applications involving the model-based control of transitional wall-bounded flow systems, it is often desired to estimate the interior flow state based on a history of noisy measurements from an array of flush-mounted skin-friction and pressure sensors on the wall. This paper considers this estimation problem, using a Kalman filter based on the linearized Navier–Stokes equations and appropriate stochastic models for the relevant statistics of the initial conditions, sensor noise and external disturbances acting on the system. We show that a physically relevant parameterization of these statistics is key to obtaining well-resolved feedback kernels with appropriate spatial extent for all three types of flow measurement available on the wall. The effectiveness of the resulting Kalman and extended Kalman filters that implement this feedback is verified for both infinitesimal and finite-amplitude disturbances in direct numerical simulations of a perturbed laminar channel flow. The consideration of time-varying feedback kernels is shown to be particularly advantageous in accelerating the convergence of the estimator from unknown initial conditions. A companion paper (Part 2) considers the extension of such estimators to the case of fully developed turbulence.