The work presented in this paper represents an experimental investigation into secondary flows, turbulent boundary layers and the interaction of the two as they develop in a zero-pressure-gradient rotating flow field. A duct of intermediate aspect ratio was used to examine secondary flows and determine when they begin to govern the boundary layer development. The aspect ratio (A) was defined as duct height/width at the upstream end of the working section. Measurements were taken at three aspect ratios: A=1, 2 and 4.

A qualitative indication of secondary flow strength was established with mean-cross-stream-plane velocity measurements. A first-order analysis of the secondary flow is presented which provides a reasonable estimation of their strength. Mid-span mean-flow, turbulence and spectra profiles were measured on the duct walls parallel to the axis of rotation. Results are generally presented for A=2 and 1. For A=4 and 2 there were minor effects of secondary flows observed on the mid-span mean flow parameters. The turbulent shear measurements showed some secondary flow effect for A=2. All turbulence and mean-flow quantities were strongly affected by secondary flows for A=1. Spectra results presented for A=2 showed most variation at the low-to-mid wavenumber end. Spectra results for A=1 showed a bodily shift of the whole spectrum towards low wavenumber on the pressure side and high wavenumber on the suction side.

Measurements of the mean velocity profile and pressure drop were performed in a fully developed, smooth pipe flow for Reynolds numbers from 31×103 to 35×106. Analysis of the mean velocity profiles indicates two overlap regions: a power law for 60<y+<500 or y+<0.15R+, the outer limit depending on whether the Kármán number R+ is greater or less than 9×103; and a log law for 600<y+<0.07R+. The log law is only evident if the Reynolds number is greater than approximately 400×103 (R+>9×103). Von Kármán's constant was shown to be 0.436 which is consistent with the friction factor data and the mean velocity profiles for 600<y+<0.07R+, and the additive constant was shown to be 6.15 when the log law is expressed in inner scaling variables.

A new theory is developed to explain the scaling in both overlap regions. This theory requires a velocity scale for the outer region such that the ratio of the outer velocity scale to the inner velocity scale (the friction velocity) is a function of Reynolds number at low Reynolds numbers, and approaches a constant value at high Reynolds numbers. A reasonable candidate for the outer velocity scale is the velocity deficit in the pipe, UCL−Ū, which is a true outer velocity scale, in contrast to the friction velocity which is a velocity scale associated with the near-wall region which is ‘impressed’ on the outer region. The proposed velocity scale was used to normalize the velocity profiles in the outer region and was found to give significantly better agreement between different Reynolds numbers than the friction velocity.

The friction factor data at high Reynolds numbers were found to be significantly larger (>5%) than those predicted by Prandtl's relation. A new friction factor relation is proposed which is within ±1.2% of the data for Reynolds numbers between 10×103 and 35×106, and includes a term to account for the near-wall velocity profile.

Using photographic imaging and dye tracking experiments, we scrutinize the dynamics of a contact line when a finite volume of partially wetting fluid is driven by gravity to spread over a slightly inclined dry plane. Unlike spreading mechanisms driven by molecular forces, gravity-driven spreading over a dry plane is shown to possess a characteristic interfacial ‘nose’ that overhangs the contact line when the film thickness is in excess of the capillary length. A unique recirculating vortex exists within the nose front which spreads at speeds corresponding to capillary numbers in excess of 10−2. Our experiments show that fingering from a gravity-driven straight front occurs when the above nose configuration cannot be sustained across the entire front as the film thins and the apparent contact angle θ reaches π/2. The fingers retain the nose configuration while the remaining segments of the front evolve into a wedge configuration and stop abruptly due to their large resistance to fluid flow. This fingering mechanism is insensitive to fluid wettability, noise or surface heterogeneity. Via matched asymptotics, we obtain accurate estimates of fingering position and speed at θ=π/2 that are in good agreement with measured values. This new mechanism is distinct from other instability and sensitivity fingering mechanisms and can be in play whenever θ of the straight front approaches π/2 from above as the film thins.

The simplest receptivity problem of linear disturbances artificially excited in a three-dimensional boundary layer adjacent to a solid surface is studied in the framework of the generalized triple-deck theory. In order to provide a mathematical model to be compared with experimental data from wind-tunnel tests we consider the base flow over a swept flat plate. Then crossflow in the near-wall region originates owing to an almost constant pressure gradient induced from outside with a displacement body on top. A pulsed or vibrating ribbon installed on the solid surface serves as an external agency provoking initially weak pulsations. A periodic dependence of the ribbon shape on a coordinate normal to the streamwise direction makes the receptivity problem effectively two-dimensional, thereby allowing a rigorous analysis to be carried out without additional assumptions.

The most striking result from the asymptotic theory is the discovery of streamwise absolute instability intrinsic to a three-dimensional boundary layer at high Reynolds numbers. However, due to limitations imposed on the receptivity problem no definite conclusions can be made with regard to possible continued convection of disturbances in the crossflow direction. An investigation of the dispersion-relation roots points to the fact that wave packets of different kinds can be generated by an external source operating in the pulse mode. Rapidly growing wave packets sweep downstream, weaker wave packets move against the oncoming stream. Insofar as the amplitude of all of the modulated signals increases exponentially in time and space, the excitation process gives rise to absolutely unstable disturbances in the streamwise direction. The computation confirms the theoretical prediction about the existence of upstream-advancing wave packets. They can be prevented from being persistently amplified only in a region ahead of the ribbon where nearly critical values of the Reynolds number are attained.

The results achieved are shown to be broadly consistent with wind-tunnel measurements. Hence a conjecture is made that the onset of transition is probably associated, under some environmental conditions, with the mechanism of streamwise absolute instability in the supercritical range of the Reynolds numbers.

The unsteady interaction between a vortex and a wall-bounded vorticity layer is studied as a model for transport and mixing between rotational and irrotational flows. The problem is formulated in terms of contour integrals and a kinematic condition along the interface which demarcates the vortical and potential regions. Asymptotic solutions are derived for linear, weakly nonlinear and nonlinear long-wave approximations. The solutions show that the initial process of ejection of vorticity into the irrotational flow occurs at a stationary point along the interface. A nonlinear model is derived and shows that such a stationary point is more likely to exist when the circulation of the vortex is counter to the vorticity in the layer. A Lagrangian numerical method based on contour dynamics is then developed for the general nonlinear problem. Two sets of results are presented where for every initial height of the vortex its magnitude and sign are varied. In both sets, it is observed that when the magnitude of the vortex is held constant a much stronger interaction occurs when the sign of the vortex circulation is opposite to that of the vorticity in the layer. Moreover, when the horizontal velocity of the vortex is close to the velocity of the interfacial waves a strong nonlinear interaction between the vortex and the layer ensues and results in the ejection of thin filaments of vorticity into the irrotational flow. In order to study the dynamical consequences of strong unsteady interaction, the wall pressure distribution is computed. The results indicate that a significant rise in the magnitude of the wall pressure is associated with ejection of vorticity from the wall. The present analysis confirms that coherent vortical structures in the outer layer of a turbulent boundary layer can cause ejection of concentrated wall-layer vorticity and explains how and when this process occurs.

We simulate the behaviour of suspensions of large-particle, non-Brownian, neutrally-buoyant spheres in a Newtonian liquid with a Galerkin, finite element, Navier–Stokes solver into which is incorporated a continuum constitutive relationship described by Phillips et al. (1992). This constitutive description couples a Newtonian stress/shear-rate relationship (where the local viscosity of the suspension is dependent on the local volume fraction of solids) with a shear-induced migration model of the suspended particles. The two-dimensional and three-dimensional (axisymmetric) model is benchmarked with a variety of single-phase and two-phase analytic solutions and experimental results. We describe new experimental results using nuclear magnetic resonance imaging to determine non-invasively the evolution of the solids-concentration profiles of initially well-mixed suspensions as they separate when subjected to slow flow between counter-rotating eccentric cylinders and to piston-driven flow in a pipe. We show good qualitative and quantitative agreement of the numerical predictions and the experimental measurements. These flows result in complex final distributions of the solids, causing rheological behaviour that cannot be accurately described with typical single-phase constitutive equations.

Experiments indicate that turbulent free convection over a horizontal surface (e.g. Rayleigh–Bénard convection) consists of essentially line plumes near the walls, at least for moderately high Rayleigh numbers. Based on this evidence, we propose here a two-dimensional model for near-wall dynamics in Rayleigh–Bénard convection and in general for convection over heated horizontal surfaces. The model proposes a periodic array of steady laminar two-dimensional plumes. A plume is fed on either side by boundary layers on the wall. The results from the model are obtained in two ways. One of the methods uses the similarity solution of Rotem & Classen (1969) for the boundary layer and the similarity solution of Fuji (1963) for the plume. We have derived expressions for mean temperature and temperature and velocity fluctuations near the wall. In the second approach, we compute the two-dimensional flow field in a two-dimensional rectangular open cavity. The number of plumes in the cavity depends on the length of the cavity. The plume spacing is determined from the critical length at which the number of plumes increases by one. The results for average plume spacing and the distribution of r.m.s. temperature and velocity fluctuations are shown to be in acceptable agreement with experimental results.

The statistical properties of the strong coherent vortices observed in numerical simulations of isotropic turbulence are studied. When compiled at axial vorticity levels ω/ω′∼Re1/2λ, where ω′ is the r.m.s. vorticity magnitude for the flow as a whole, they have radii of the order of the Kolmogorov scale and internal velocity differences of the order of the r.m.s. velocity of the flow u′. Theoretical arguments are given to explain these scalings. It is shown that the filaments are inhomogeneous Burgers' vortices driven by an axial stretching which behaves like the strain fluctuations of the background flow. It is suggested that they are the strongest members in a class of coherent objects, the weakest of which have radii of the order of the Taylor microscale, and indirect evidence is presented that they are unstable. A model is proposed in which this instability leads to a cascade of coherent filaments whose radii are below the dissipative scale of the flow as a whole. A family of such cascades separates the self-similar inertial range from the dissipative limit. At the vorticity level given above, the filaments occupy a volume fraction which scales as Re−2λ, and their total length increases as O(Reλ). The length of individual filaments scales as the integral length of the flow, but there is a shorter internal length of the order of the Taylor microscale.

An efficient and robust computational method, based on the lattice-Boltzmann method, is presented for analysis of impermeable solid particle(s) suspended in fluid with inertia. In contrast to previous lattice-Boltzmann approaches, the present method can be used for any solid-to-fluid density ratio. The details of the numerical technique and implementation of the boundary conditions are presented. The accuracy and robustness of the method is demonstrated by simulating the flow over a circular cylinder in a two-dimensional channel, a circular cylinder in simple shear flow, sedimentation of a circular cylinder in a two-dimensional channel, and sedimentation of a sphere in a three-dimensional channel. With a solid-to-fluid density ratio close to one, new results from two-dimensional and three-dimensional computational analysis of dynamics of an ellipse and an ellipsoid in a simple shear flow, as well as two-dimensional and three-dimensional results for sedimenting ellipses and prolate spheroids, are presented.

This work concerns the combined oscillatory flow and current in a circular, smooth pipe. The study comprises wall shear stress measurements, and laser-Doppler-anemometer velocity and turbulence measurements. Three kinds of pipes were used, with diameters D=19 cm, 9 cm, and 1.1 cm, enabling the influence of the parameter R/δ to be studied in the investigation (R/δ ranging from about 3 to 53), where R is the radius of the pipe, and δ is the Stokes layer thickness. The ranges of the two other parameters of the combined flow processes, namely the current Reynolds number, Rec, and the oscillatory-flow boundary-layer (i.e. the wave–boundary layer) Reynolds number, Rew, are: Rec=0−1.6×105, and Rew=0−7×106. The transition to turbulence in the combined flow case occurs at a current Reynolds number larger than the conventional value, ca. 2×103, depending on Rew, and R/δ. A turbulent current can be laminarized by superimposing an oscillatory flow. The overall average value of the wall shear stress (the mean wall shear stress) may retain its steady-current value, it may decrease, or it may increase, depending on the flow regime. The increase (which can be as much as a factor of 4) occurs when the combined flow is in the wave-dominated regime, while the oscillatory-flow component of the flow is in the turbulent regime. The component of the wall shear stress oscillating around the mean wall shear stress can also increase with respect to its oscillatory-flow-alone value. For this to occur, the originally laminar oscillatory boundary layer needs to become a fully developed turbulent boundary layer, when a turbulent current is superimposed. This increase can be as much as O(3–4). The velocity profiles across the cross-section of the pipe change near the wall when an oscillatory flow is superimposed on a current, in agreement with the results of the wall shear stress measurements. The period-averaged turbulence profiles across the cross-section of the pipe behave differently for different flow regimes. When the two components of the flow are equally significant, the turbulence profile appears to be different from those corresponding to the fundamental cases; the level of turbulence increases (only slightly) with respect to those experienced in the fundamental cases.

The design of fluids management processes in the low-gravity environment of space requires an accurate description of capillarity-controlled flow in containers. Here we consider the spontaneous redistribution of fluid along an interior corner of a container due to capillary forces. The analytical portion of the work presents an asymptotic formulation in the limit of a slender fluid column, slight surface curvature along the flow direction z, small inertia, and low gravity. The scaling introduced explicitly accounts for much of the variation of flow resistance due to geometry and so the effects of corner geometry can be distinguished from those of surface curvature. For the special cases of a constant height boundary condition and a constant flow condition, the similarity solutions yield that the length of the fluid column increases as t1/2 and t3/5, respectively. In the experimental portion of the work, measurements from a 2.2 s drop tower are reported. An extensive data set, collected over a previously unexplored range of flow parameters, includes estimates of repeatability and accuracy, the role of inertia and column slenderness, and the effects of corner angle, container geometry, and fluid properties. At short times, the fluid is governed by inertia (t[lsim ]tLc). Afterwards, an intermediate regime (tLc[lsim ]t[lsim ] tH) can be shown to be modelled by a constant-flow-like similarity solution. For t[ges ]tH it is found that there exists a location zH at which the interface height remains constant at a value h(zH, t)=H which can be shown to be well predicted. Comprehensive comparison is made between the analysis and measurements using the constant height boundary condition. As time increases, it is found that the constant height similarity solution describes the flow over a lengthening interval which extends from the origin to the invariant tip solution. For t[Gt ]tH, the constant height solution describes the entire flow domain. A formulation applicable throughout the container (not just in corners) is presented in the limit of long times.

Journal of Fluid Mechanics, vol. 360 (1998), pp. 213–228

As pointed out to us by Mr T. Heath, the following printing errors can be quite misleading when using the formulas in the paper to obtain eigenfrequencies and damping rates to compare with experiments:

in (A 13) 1 should read −1 on the right-hand side;

in (A 22) and (A 26) Ω20 should read Ω−20;

in (A 25) the factor Ω40 must be omitted on the right-hand side.

When revising again the printed version of the paper, we discovered several additional misprints:

A factor C was omitted in the first two integrals in the expression for J2, immediately following equation (2.9).

The sign of the second expression for I1 in (2.23) should be changed.

The expression (W0Wz +3WW0z)z=0 should read 2(W0Wz +WW0z)z=0 in equation (2.24).

The expression W0(1, z)W0z(1, z) in (2.26) should read W0(r, 0)W0z(r, 0).

None of the misprints above affect the results of the paper, which were obtained with the correct expressions.