Wind tunnel experiments are performed on a body of revolution with aft-section designed to be an axisymmetric Stratford ramp (i.e. the flow over the ‘ramp’ experiences an adverse pressure gradient that causes it to be continuously on the verge of separation). Digital particle image velocimetry (DPIV) measurements over the ramp reveal a thick boundary layer that is characterized by self-similar velocity profiles with a large wake component and organized vorticity structures. The mean skin friction quickly drops to a value near zero.

The sensitivity of the boundary layer to the degree of severity of the adverse pressure gradient is investigated by testing two additional ramps; one is slightly more conservative (i.e. less steep) than the Stratford ramp while the other is slightly more radical (i.e. steeper). In comparison to the Stratford ramp, the conservative ramp is characterized by a thinner boundary layer, with velocity profiles that start attached and gradually develop a large wake component, a much more gradual drop in the skin friction, and vorticity that is concentrated very close to the wall. On the other hand, the boundary layer over the radical ramp is unsteady and separates intermittently. Measurements of the drag force on each of the three bodies confirm that the Stratford ramp experiences the least amount of drag.

Finally, additional data are gathered on the windward and leeward sides of the Stratford ramp when subjected to a small angle of attack. This case exhibits a more complex flow structure: the flow remains attached over the windward side of the ramp while separating over the leeward side.

In previous experiments, the vortex-shedding frequency in the flow around rectangular prisms has been found to follow a stepwise variation with chord-to-thickness ratio for two different situations: the natural shedding at low Reynolds number and the excitation of a resonant transverse acoustic mode of a duct for flows at moderate Reynolds numbers. This stepwise variation disappears for natural shedding at Reynolds number higher than approximately 2000; however, it is present at the higher Reynolds numbers for the acoustically perturbed case. The present experimental study shows that if the flow is forced by small transverse oscillations, similar in form to the resonant transverse acoustic mode, the leading-edge and trailing-edge vortex shedding are locked over a wide range of forcing frequencies. However, a stepwise variation in the frequency at which peak base drag occurs is found even at these higher Reynolds numbers. The stepwise frequency variation of vortex shedding in the natural shedding case and the acoustic resonance case are then explained in terms of preference of the flow to shed trailing-edge vortices at peak base drag.

We demonstrate that an unusually small pipe flow apparatus using both liquid helium and room temperature gases can span an enormous range of Reynolds numbers. This paper describes the construction and operation of the apparatus in some detail. A wide range of Reynolds numbers is an advantage in any experiment seeking to establish scaling laws. This experiment also adds to evidence already in hand that the normal phase of liquid helium is a Navier–Stokes fluid. Finally, we explore recent questions concerning the influence of molecular motions on the transition to turbulence (Muriel 1998) and are unable to observe any influence.

A new approach to the classic closure problem for turbulent boundary layers is presented. This involves, first, using the well-known mean-flow scaling laws such as the log law of the wall and the law of the wake of Coles (1956) together with the mean continuity and the mean momentum differential and integral equations. The important parameters governing the flow in the general non-equilibrium case are identified and are used for establishing a framework for closure. Initially closure is achieved here empirically and the potential for achieving closure in the future using the wall-wake attached eddy model of Perry & Marusic (1995) is outlined. Comparisons are made with experiments covering adverse-pressure-gradient flows in relaxing and developing states and flows approaching equilibrium sink flow. Mean velocity profiles, total shear stress and Reynolds stress profiles can be computed for different streamwise stations, given an initial upstream mean velocity profile and the streamwise variation of free-stream velocity. The attached eddy model of Perry & Marusic (1995) can then be utilized, with some refinement, to compute the remaining unknown quantities such as Reynolds normal stresses and associated spectra and cross-power spectra in the fully turbulent part of the flow.

The linear receptivity of a swept-wing three-dimensional boundary layer is studied experimentally and theoretically. Cross-flow instability normal modes are excited by means of surface vibration or roughness perturbations. The resulting disturbances are investigated, and the normal modes are linked to the source perturbations. Experiments are performed under controlled disturbance conditions with a time-harmonic source that is localized in the spanwise direction. A localized surface vibration is used to excite wave trains consisting of cross-flow instability waves. Normal oblique modes (harmonic in time and space) are obtained by Fourier decomposition of the wave trains. This provides the spatial variation of the normal modes and, in particular, the initial amplitudes and phases of the modes at the source location. The shape of the surface vibrator is measured and used to determine the complex receptivity coefficients for the normal modes (i.e. for various spanwise wavenumbers, wave propagation angles, and disturbance frequencies – including zero frequency). The experimental receptivity coefficients are independent of the specific shape of the surface non-uniformities and can be directly compared with calculations. The theoretical work is based on a linear approximation to the disturbance source – valid for small forcing amplitudes. Like earlier studies on roughness-induced receptivity, the basic flow is locally assumed to satisfy the parallel-flow approximation. The modal response for the cross-flow instability is determined from the residue associated with the least-stable eigenmode.

A detailed quantitative comparison between the experimental and theoretical receptivity characteristics is carried out. Good agreement is found for the roughness–vibrational receptivity coefficients of the swept-wing boundary layer (especially for the most-unstable cross-flow modes) over a range of disturbance frequencies and spanwise wavenumbers. The theory correctly predicts the initial spectra for the travelling and stationary cross-flow instabilities excited by the surface vibrations and surface roughness, respectively. The good agreement between theory and experiment suggests that the linear receptivity theory can be used effectively in engineering methods for transition prediction. The experimental data can also be used for validation of other theoretical approaches to the problem.

The random motion of nearly spherical bubbles in the turbulent flow behind a grid is studied experimentally. In quiescent water these bubbles rise at high Reynolds number. The turbulence is generated by an active grid of the design of Makita (1991), and can have turbulence Reynolds number Rλ of up to 200. Minor changes in the geometry of the grid and in its mode of operation improves the isotropy of the turbulence, compared with that reported by Makita (1991) and Mydlarski & Warhaft (1996). The trajectory of each bubble is measured with high spatial and temporal resolution with a specially developed technique that makes use of a position-sensitive detector. Bubble statistics such as the mean rise velocity and the root-mean-square velocity fluctuations are obtained by ensemble averaging over many identical bubbles. The resulting bubble mean rise velocity is significantly reduced (up to 35%) compared with the quiescent conditions. The vertical bubble velocity fluctuations are found to be non-Gaussian, whereas the horizontal displacements are Gaussian for all times. The diffusivity of bubbles is considerably less than that of fluid particles. These findings are qualitatively consistent with results obtained through theoretical analysis and numerical simulations by Spelt & Biesheuvel (1997).

This study is an experimental investigation of the probability density function (p.d.f.) and the fine structure of temperature fluctuations in uniformly sheared turbulence with a passively introduced uniform mean temperature gradient. The shear parameter was relatively large, resulting in vigorous turbulence production and a total mean strain up to 23. The turbulence Reynolds number was up to 253. The scalar fluctuations grew in a self-similar fashion and at the same exponential rate as the turbulence stresses, in conformity with predictions based on an analytical solution of the scalar variance equation. Analytical considerations as well as measurements demonstrate that the scalar p.d.f. is essentially Gaussian and that the scalar–velocity joint p.d.f. is essentially jointly Gaussian, with the conditional expectations of the velocity fluctuations linearly dependent on the scalar value. Joint statistics of the scalar and its dissipation rate indicate a statistical independence of the two parameters. The fine structure of the scalar was invoked from statistics of derivatives and differences of the scalar, in both the streamwise and transverse directions. Probability density functions of scalar derivatives and differences in the dissipative and the inertial ranges were strongly non-Gaussian and skewed, displaying flared, asymmetric tails. All measurements point to a highly intermittent scalar fine structure, even more intermittent than the fine structure of the turbulent velocity.

This work examines the sudden erosional flow initiated by the release of a dam-break wave over a loose sediment bed. Extended shallow-water equations are formulated to describe the development of the surge. Accounting for bed material inertia, a transport layer of finite thickness is introduced, and a sharp interface view of the morphodynamic boundary is adopted. Approximations are sought for an intermediate range of wave evolution, in which equilibration of the sediment load can be assumed instantaneous but momentum loss due to bed friction has not yet been felt. The resulting homogeneous hyperbolic equations are mathematically tractable using the Riemann techniques of gas dynamics. Dam-break initial conditions give rise to self-similar flow profiles. The wave structure features piecewise constant states, two smoothly varied simple waves, and a special type of shock: an erosional bore forming at the forefront of the wave. Profiles are constructed through a semi-analytical procedure, yielding a geomorphic generalization of the Stoker solution for dam-break waves over rigid bed. For most flow properties, the predictions of the theoretical treatment compare favourably with experimental tests visualized using particle imaging techniques.

When an electric field is applied across a conducting and ion-selective porous granule in an electrolyte solution, a polarized surface layer with excess counter-ions is created. The depth of this layer and the overpotential V across this layer are functions of the normal electric field j on the granule surface. By transforming the ionic flux equations and the Poisson equation into the Painlevé equation of the second type and by analysing the latter's asymptotic solutions, we derive a linear universal j–V correlation at large flux with an electrokinetic slip length β. The flux-induced surface polarization produces a nonlinear Smoluchowski slip velocity that can couple with the granule curvature to produce micro-vortices in micro-devices. Such vortices are impossible in irrotational electrokinetic flow with a constant zeta-potential and a linear slip velocity.

We show how the variational formulation introduced by Doering & Constantin to rigorously bound the long-time-averaged total dissipation rate [ ] in turbulent shear flows can be extended to treat other long-time-averaged functionals lim supT→∞(1/T)×∫0Tf(D, Dm, Dv)dt of the total dissipation D, dissipation in the mean field Dm and dissipation in the fluctuation field Dv. Attention is focused upon the suite of functionals f = D(Dv/Dm)n and f = Dm(Dv/Dm)n (n [ges ] 0) which include the ‘efficiency’ functional f = D(Dv/Dm) (Malkus & Smith 1989; Smith 1991) and the dissipation in the mean flow f = Dm (Malkus 1996) as special cases. Complementary lower estimates of the rigorous bounds are produced by generalizing Busse's multiple-boundary-layer trial function technique to the appropriate Howard–Busse variational problems built upon the usual assumption of statistical stationarity and constraints of total power balance, mean momentum balance, incompressibility and boundary conditions. The velocity field that optimizes the ‘efficiency’ functional is found not to capture the asymptotic structure of the observed mean flow in either plane Couette flow or plane Poiseuille flow. However, there is evidence to suppose that it is ‘close’ to a neighbouring functional that may.

The two components of the force acting on a clean almost spherical bubble rising near a plane vertical wall in a quiescent liquid are determined experimentally. This is achieved by using an apparatus in which a CCD camera and a microscope follow the rising bubble. This apparatus allows us to measure accurately the bubble radius, rise speed and distance between the bubble and the wall. Thereby the drag and lift components of the hydrodynamic force are determined for Reynolds numbers Re (based on bubble diameter, rise velocity U, and kinematic viscosity ν) less than 40. The results show the existence of two different regimes, according to the value of the dimensionless separation L* defined as the ratio between the distance from the bubble centre to the wall and the viscous length scale ν/U. When L* is O(1) or more, experimental results corresponding to Reynolds numbers up to unity are found to be in good agreement with an analytical solution obtained in the Oseen approximation by adapting the calculation of Vasseur & Cox (1977) to the case of an inviscid bubble. When L* is o(1), higher-order effects not taken into account in previous analytical investigations become important and measurements show that the deformation of the bubble is significant when the viscosity of the surrounding liquid is large enough. In this regime, experimental results for the drag force and shape of the bubble are found to agree well with recent theoretical predictions obtained by Magnaudet, Takagi & Legendre (2002) but the measured lift force tends to exceed the prediction as the separation decreases.

The effect of compressibility on the critical swirl level for breakdown of subsonic vortex flows in a straight circular pipe of finite length is studied. This work extends the critical-state concept of Benjamin (1962) to include the influence of Mach number on the flow behaviour. The analysis is based on a linearized version of the equations for the motion of a steady, axisymmetric, inviscid and compressible swirling flow of a perfect gas. The relationship between the velocity, density, temperature and pressure perturbations to a base columnar flow state are derived. An eigenvalue problem is formulated to determine the first critical level of swirl at which a special mode of a non-columnar small disturbance may appear on the base flow. It is found that when the characteristic Mach number of the base flow tends to zero the eigenvalue problem and the critical swirl are the same as defined by Wang & Rusak (1996a, 1997a) in their study of incompressible swirling flows in pipes. As the characteristic Mach number is increased, the critical swirl level increases and the flow perturbation expands in the radial direction. As the Mach number is increased toward a certain limit value related to the core size of the vortex, the critical swirl reaches very large values and becomes singular. The present results indicate that the axisymmetric breakdown of high-Reynolds-number compressible vortex flows may be delayed with the increase of the flow Mach number.

We apply the J-integral to free-boundary flows in a channel geometry such as viscous fingering or blob injection in Hele-Shaw cells, void propagation in electromigration, and injection of air bubbles into inviscid liquids. The theory of that and related conservation integrals, developed in elasticity, is outlined in a way that is applicable to fluid mechanics problems. Depending on the boundary conditions, for infinite bubbles in Laplacian fields we are able to use the J-integral to predict finger width if such solutions exist or to predict that there are no solutions. For finite sized bubbles, bounds can sometimes be derived. In the case of Hele-Shaw flows, in which solutions appear as a continuum, finger width cannot be constrained, but we do obtain a new derivation and generalization of Richardson moment conservation. Applications to vortex motion are also outlined briefly.

We consider problems based on linear water wave theory concerning the interaction of oblique waves with horizontal cylinders in a fluid consisting of a layer of finite depth bounded above by a free surface and below by an infinite layer of fluid of greater density. For such a situation time-harmonic waves can propagate with two different wavenumbers K and k. The particular problems of wave scattering by a horizontal circular cylinder in either the upper or lower layer are solved using multipole expansions.

Numerical simulations are conducted for laminar flow past a sphere rotating in the streamwise direction, in order to investigate the effect of the rotation on the characteristics of flow over the sphere. The Reynolds numbers considered are Re = 100, 250 and 300 based on the free-stream velocity and sphere diameter, and the rotational speeds are in the range of 0 [les ] ω* [les ] 1, where ω* is the maximum azimuthal velocity on the sphere surface normalized by the free-stream velocity. At ω* = 0 (without rotation), the flow past the sphere is steady axisymmetric, steady planar-symmetric, and unsteady planar-symmetric, respectively, at Re = 100, 250 and 300. Thus, the time-averaged lift forces exerted on the stationary sphere are not zero at Re = 250 and 300. When the rotational speed increases, the time-averaged drag force increases for the Reynolds numbers investigated, whereas the time-averaged lift force is zero for all ω* > 0. On the other hand, the lift force fluctuations show a non-monotonic behaviour with respect to the rotational speed. At Re = 100, the flow past the sphere is steady axisymmetric for all the rotational speeds considered and thus the lift force fluctuation is zero. At Re = 250 and 300, however, the flows are unsteady with rotation and the lift force fluctuations first decrease and then increase with increasing rotational speed, showing a local minimum at a specific rotational speed. The vortical structures behind the sphere are also significantly modified by the rotation. For example, at Re = 300, the flows become ‘frozen’ at ω* = 0.5 and 0.6, i.e. the vortical structures in the wake simply rotate without temporal variation of their strength and the magnitude of the instantaneous lift force is constant in time. It is shown that the flow becomes frozen at higher rotational speed with increasing Reynolds number. The rotation speed of the vortical structures is shown to be slower than that of the sphere.

The free-surface flow past a semi-infinite horizontal plate in a finite-depth fluid is considered. It is assumed that the fluid is incompressible and inviscid and that the flow approaches a uniform shear flow downstream. Exact relations are derived using conservation of mass and momentum for the case where the downstream free surface is flat. The complete nonlinear problem is solved numerically using a boundary-integral method and these waveless solutions are shown to exist only when the height of the plate above the bottom is greater than the height of the uniform shear flow. Interesting results are found for various values of the constant vorticity. Solutions with downstream surface waves are also considered, and nonlinear results of this type are compared with linear results found previously. These solutions can be used to model the flow near the stern of a (two-dimensional) ship.

Journal of Fluid Mechanics, vol. 436 (2001), pp. 1–39