The force on a charged solid particle (of general shape) suspended in a flowing polar fluid (e.g. an aqueous electrolyte solution) in the presence of a solid bounding wall (of general shape) is obtained for the situation in which the electrical double-layer thickness is very much smaller than the particle size (and the distance between particle and wall). The very general results so obtained are applied to the sedimentation of a charged spherical particle in an unbounded polar fluid (with no walls present) for which the drag force is found to be in complete agreement with Ohshima et al. (1984). However, there is disagreement between the present results and those obtained in a number of published papers owing to incorrect assumptions being made in the latter as to what physical mechanism gives rise to the dominant contribution to the electroviscous force on the particle.

We introduce a new technique to model spherical geophysical fluid dynamics in the terrestrial laboratory. The local vertical projection of planetary vorticity, f, varies with latitude on a rotating spherical planet and allows an important class of waves in large-scale atmospheric and oceanic flows. These Rossby waves have been extensively studied in the laboratory for middle and polar latitudes. At the equator f changes sign where gravity is perpendicular to the planetary rotation. This geometry has made laboratory studies of geophysical fluid dynamics near the equator very limited. We use ferrofluid and static magnetic fields to generate nearly spherical geopotentials in a rotating laboratory experiment. This system is the laboratory analogue of those large-scale atmospheric and oceanic flows whose horizontal motions are governed by the Laplace tidal equations. As the rotation rate in such a system increases, waves are trapped to latitudes near the equator and the dynamics can be formulated on the equatorial β-plane. This transition from planetary modes to equatorially trapped modes as the rotation rate increases is observed in the experiments. The equatorial β-plane solutions of non-dispersive Kelvin waves propagating eastward and non-dispersive Rossby waves propagating westward at low frequency are observed in the limit of rotation fast compared to gravity wave speed.

Previous research has established that surfaces with tiny ribs (riblets) aligned in the streamwise direction can reduce the turbulent wall-shear stress below that of a smooth surface. Typical skin-friction reductions have been found to be about 5%. The results of the present investigation, however, demonstrate a considerable improvement over this value. This improvement is achieved by a systematic experimental optimization which has been guided by theoretical concepts.

A key feature of our experiments is the utilization of an oil channel. Previous experiments in wind tunnels had to contend with very small riblet dimensions which typically had a lateral rib spacing of about 0.5 mm or less. By contrast, in our oil channel, the ribs can have a lateral spacing of between about 2 and 10 mm. This increased size of the surface structures enables test surfaces to be manufactured with conventional mechanical methods, and it also enables us to build test surfaces with adjustable geometry. In addition, the Berlin oil channel has a novel shear stress balance with an unprecedented accuracy of ±0.3%. This latter feature is a prerequisite for a systematic experimental optimization.

In the present investigation, surfaces with longitudinal ribs and additional slits are studied. The experiments cover a fairly large range of parameters so that the drag reduction potential of a surface with ribs and/or slits is worked out conclusively. A large parameter range is made possible because of the adjustability of the surfaces as well as the automatic operation of the oil channel. In particular, the following tests were run:

(i) Shear stress measurements with conventional riblet configurations, i.e. with triangular and semi-circular grooves, have been carried out. These measurements were necessary in order to establish the connection between our oil channel data and previous data from wind tunnels. As was previously established, we found a drag reduction of about 5%.

(ii) An adjustable surface with longitudinal blade ribs and with slits was built and tested. Both groove depth and slit width could be varied separately and continuously during the experiment. It turned out, that slits in the surface did not contribute to the drag reduction. Nevertheless, these investigations show how perforated surfaces (e.g. for boundary-layer control) can be designed for minimal parasitic drag. On the other hand, with closed slits, an optimal groove depth for the rib surface could be determined, i.e. half of the lateral rib spacing. For this configuration, we found an 8.7% skin-friction reduction. By carefully eliminating deleterious effects (caused by little gaps, etc.), the skin-friction reduction could be improved to a record value of 9.9%.

(iii) A quantitative comparison between theory and experiment was carried out. The theory is based on the assumption that riblets impede the fluctuating turbulent crossflow near the wall. In this way, momentum transfer and shear stress are reduced. The simplified theoretical model proposed by Luchini (1992) is supported by the present experiments.

(iv) For technological applications of riblets, e.g. on long-range commercial aircraft, the above thin-blade ribs are not practical. Therefore, we have devised a surface that combines a significantly improved performance (8.2 %) with a geometry which exhibits better durability and enables previously developed manufacturing methods for plastic riblet film production to be used. Our riblet geometry exhibits trapezoidal grooves with wedge-like ribs. The flat floor of the trapezoidal grooves permits an undistorted visibility through the transparent riblet film which is essential for crack inspection on aircraft.

Results from an earlier experimental assessment of fractal scale similarity in one-dimensional spatial and temporal intersections in turbulent flows are here extended to two- and three-dimensional spatial intersections. Over 25000 two-dimensional (2562) intersections and nearly 40 three-dimensional (2563) intersections, collectively representing more than 2.3 billion data points, were analysed using objective statistical methods to determine which intersections were as fractal as stochastically scale-similar fractal gauge sets having the same record length. Results for the geometry of Sc [Gt ]1 scalar isosurfaces and the scalar dissipation support span the range of lengthscales between the scalar and viscous diffusion scales λD and λν. The present study finds clear evidence for stochastic fractal scale similarity in the dissipation support. With increasing intersection dimension n, the data show a decrease in the fraction of intersections satisfying the criteria for fractal scale similarity, consistent with the presence of localized non-fractal inclusions. Local scale similarity analyses on three-dimensional (643) intersections directly show such intermittent non-fractal inclusions with characteristic lengthscale comparable to λν. These inclusions lead to failure of the relation among codimensions Dn≡D−(3−n) when applied to simple average dimensions, which has formed the basis for most previous assessments of fractal scale-similarity. Unlike the dissipation support geometry, scalar isosurface geometries from the same data were found not to be as fractal as fractional Brownian motion gauge sets over the range of scales examined.

Earlier experimental assessments of fractal scale similarity in geometric properties of turbulent flows are extended to assess the applicability of multifractal scale-similarity in the conserved scalar field ζ(x, t) and in the true scalar energy dissipation rate field ∇ζ·∇ζ(x, t). Fully resolved four-dimensional spatio-temporal measurements from a turbulent flow at Reλ≈41 and Reδ≈3000 are analysed. The utility of various classical constructs for identifying multifractal scale similarity in data records of finite length is examined. An objective statistical criterion based on the maximum allowable scale-to-scale variation L1(ε) in multiplier distributions 〈P(Mε)〉 obtained from multifractal gauge fields is developed to allow accurate discrimination between multifractal and non-multifractal scaling in finite-length experimental data records. Results from analyses of temporal intersections show that for scales greater than 0.03 λν/u, corresponding to 1.4 λD/u, the scalar dissipation field clearly demonstrates a scale-invariant similarity consistent with a multiplicative cascade process that can be modelled with a bilinear multiplier distribution. However, the conserved scalar field from precisely the same data does not follow any scale similarity consistent with a multiplicative cascade at scales below 0.5 λν/u. At larger scales, there are indications of a possible scale-invariant similarity in the scalar field, but with a fundamentally different multiplier distribution.

In shallow turbulent wake flows (typically an island wake), the flow patterns have been found experimentally to depend mainly on a shallow wake parameter, S=cfD/h in which cf is a quadratic-law friction coefficient, D is the island diameter and h is water depth. In order to understand the dependence of flow patterns on S, the shallow-water stability equation (a modified Orr–Sommerfeld equation) has been derived from the depth-averaged equations of motion with terms which describe bottom friction. Absolute and convective instabilities have been investigated on the basis of wake velocity profiles with a velocity deficit parameter R. Numerical computations have been carried out for a range of R-values and a stability diagram with two dividing lines was obtained, one defining the boundary between absolute and convective instabilities Sca, and another defining the transition between convectively unstable and stable wake flow Scc. The experimental measurements (Chen & Jirka 1995) of return velocities in shallow wakes were used to compute R-values and two critical values, SA=0.79 and SC=0.85, were obtained at the intersections with lines Sca and Scc. Through comparison with transition values observed experimentally for wakes with unsteady bubble (recirculation zone) and vortex shedding, SU and SV respectively, the sequence SC>SA> SU>SV shows vortex shedding to be the end product of absolute instability. This is analogous to the sequence of critical Reynolds numbers for an unbounded wake of large spanwise extent. Experimental frequency characteristics compare well with theoretical results. The observed values of SU and SV for different flow patterns correspond to the velocity profile with R=−0.945, which is located at the end of the wake bubble, and it provides the dominant mode.

Drops fall off a viscous pendent rivulet on the underside of a plane when the inclination angle θ, measured with respect to the horizontal, is below a critical value θc. We estimate this θc by studying the existence of finite-amplitude drop solutions to a long-wave lubrication equation. Through a partial matched asymptotic analysis, we establish that fall-off occurs by two distinct mechanisms. For θ>ϕ, where ϕ is the static contact angle, a jet mechanism results when a mean-flow steepening effect cannot provide sufficient axial curvature to counter gravity. This fall-off mechanism occurs if the rivulet width B, which is normalized with respect to the capillary length H=(σ/ρg cosθ)1/2, exceeds a critical value defined by β=−cosB>1/4. For θ<ϕ, the normal azimuthal curvature is the dominant force against fall-off and the azimuthal capillary force. The corresponding critical condition is found to be 1.5β1/6>tanθ/tanϕ. Both criteria are in good agreement with our experimental data.

The physical reasons for the diffculty in predicting accurately strong swept-shock-wave/turbulent-boundary-layer interactions are investigated. A well-documented sharp-fin/plate flow has been selected as the main test case for analysis. The selected flow is calculated by applying a version of the Baldwin–Lomax turbulence model, which is known to provide reliable results in flows characterized by the appearance of crossflow vortices. After the validation of the results, by comparison with appropriate experimental data, the test case flow is studied by means of stream surfaces which start at the inflow plane, within the undisturbed boundary layer, and which are initially parallel to the plate. Each of these surfaces has been represented by a number of streamlines. Calculation of the spatial evolution of some selected stream surfaces revealed that the inner layers of the undisturbed boundary layer, which are composed of turbulent air, wind around the core of the vortex. However, the outer layers, which are composed of low-turbulence air, fold over the vortex and at the reattachment region penetrate into the separation bubble forming a low-turbulence tongue, which lies along the plate, underneath the vortex. The conical vortex at its initial stage of development is completely composed of turbulent air, but gradually, as it grows linearly in the flow direction, the low-turbulence tongue is formed. Also the tongue grows in the flow direction and penetrates further into the separation region. When it reaches the expansion region inboard of the primary vortex, the secondary vortex starts to be formed at its tip. Examination of additional test cases indicated that the turbulence level of the elongated tongue decreases if the interaction strength increases. The existence of the low-turbulence tongue in strong swept-shock-wave/turbulent-boundary-layer interactions creates a mixed-type separation bubble: turbulent in the region of the separation line and almost laminar between the secondary vortex and the reattachment line. This type of separation cannot be simulated accurately with the currently used algebraic turbulence models, because the basic relations of these models are based on the physics of two-dimensional flows, whereas in a separation bubble the whole recirculation region is turbulent. For improving the accuracy of the existing algebraic turbulence models in predicting swept-shock-wave/turbulent-boundary-layer interactions, it is necessary to develop new equations for the calculation of the eddy viscosity in the separation region, which will consider the mixed-flow character of the conical vortex.

A methodology for vectoring the near-wake flow behind a bluff body without any mechanical movement of the physical boundaries of the generating body is described. The sole control input is suction applied at the fixed base of the forebody. Once the suction volume flux exceeds a critical value needed to suppress the global dynamics associated with vortex shedding, local directional control of the near wake can be achieved. The distribution of suction velocities across the base can be varied to obtain proportional directional control. The role of symmetries in stimulating aerodynamic vectoring of a streaming flow is emphasized and illustrated.

Random flows in rotating fluid layers are studied in two spatial dimensions. The Eulerian and Lagrangian correlation functions for such flows are analysed by approximating the actual two-dimensional flow by an autonomous system consisting of many overlapping and mutually convecting vortices. Analytical expressions for the full space–time-varying Eulerian velocity correlation are derived solely in terms of flow parameters. An extension of the arguments giving these results also allows the derivation of analytical expressions for the Lagrangian velocity correlation function. The analytical results are supported by a numerical simulation.

We study the displacement of miscible fluids between two parallel plates, for different values of the Péclet number Pe and of the viscosity ratio M. The full Navier–Stokes problem is addressed. As an alternative to the conventional finite difference methods, we use the BGK lattice gas method, which is well suited to miscible fluids and allows us to incorporate molecular diffusion at the microscopic scale of the lattice. This numerical experiment leads to a symmetric concentration profile about the middle of the gap between the plates; its shape is determined as a function of the Péclet number and the viscosity ratio. At Pe of the order of 1, mixing involves diffusion and advection in the flow direction. At large Pe, the fluids do not mix and an interface between them can be defined. Moreover, above M∼10, the interface becomes a well-defined finger, the reduced width of which tends to λ∞=0.56 at large values of M. Assuming that miscible fluids at high Pe are similar to immiscible fluids at high capillary numbers, we find the analytical shape of that finger, using an extrapolation of the Reinelt–Saffman calculations for a Stokes immiscible flow. Surprisingly, the result is that our finger can be deduced from the famous Saffman–Taylor one, obtained in a potential flow, by a stretching in the flow direction by a factor of 2.12.

A boundary integral formulation is used to investigate the interaction between a pair of deformable drops in a simple shear flow. The interactions do not promote appreciably the breakup of the drops. For certain ratios of the viscosities of the drops and the suspending fluid, the lubrication gap that separates the two drops can diminish rapidly in the extensional quadrant of the flow. Slight deformation endows the drops with an apparent short-range repulsive interaction: drop coalescence requires van der Waals attraction which was not included in this study. From the trajectories of different collisions, the self-diffusion coefficients that describe the cross-flow migration of the non-Brownian drops in a dilute sheared emulsion are obtained. The self-diffusivities are very anisotropic, depend strongly on the viscosity ratio, and depend modestly on the shear rate.

New scaling laws are presented for the spatial variation of the mean velocity and lateral extent of a two-dimensional turbulent wall jet, flowing over a fixed rough boundary. These scalings are analogous to those derived by Wygnanski et al. (1992) for the flow of a wall jet over a smooth boundary. They reveal that the characteristics of the jet depend weakly upon the roughness length associated with the boundary, as confirmed by experimental studies (Rajaratnam 1967).

These laws are used in the development of an analytical framework to model the progressive erosion of an initially flat bed of grains by a turbulent jet. The grains are eroded if the shear stress, exerted on the grains at the surface of the bed, exceeds a critical value which is a function of the physical characteristics of the grains. After the wall jet has been flowing for a sufficiently long period, the boundary attains a steady state, in which the mobilizing forces associated with the jet are insufficient to further erode the boundary. The steady-state profile is calculated separately by applying critical conditions along the bed surface for the incipient motion of particles. These conditions invoke a relationship between the mobilizing force exerted by the jet, the weight of the particles and the local gradient of the bed. Use of the new scaling laws for the downstream variation of the boundary shear stress then permits the calculation of the shape of the steady-state scour pit. The predicted profiles are in good agreement with the experimental studies on the erosive action of submerged water and air jets on beds of sand and polystyrene particles (Rajaratnam 1981).

The shape of the eroded boundary at intermediate times, before the steady state is attained, is elucidated by the application of a sediment-volume conservation equation. This relationship balances the rate of change of the bed elevation with the divergence of the flux of particles in motion. The flux of particles in motion is given by a semi-empirical function of the amount by which the boundary shear stress exceeds that required for incipient motion. Hence the conservation equation may be integrated to reveal the transient profiles of the eroded bed. There is good agreement between these calculated profiles and experimental observations (Rajaratnam 1981).

We study the paths of fluid particles in velocity fields modelling rigidly rotating velocity fields that occur in the concentric Taylor problem. We set up velocity fields using the model of Davey, DiPrima & Stuart (1968) based on small-gap asymptotics. This allows a numerical study of the Lagrangian properties of steady flow patterns in a rotating frame. The spiral and Taylor vortex modes are integrable, implying that in these cases almost all particle paths are confined to two-dimensional surfaces in the fluid. For the case of Taylor vortices the motion on these surfaces is quasi-periodic, whereas for spirals the particles propagate up or down the cylinder on these surfaces.

The non-axisymmetric modes we consider are wavy vortices, spirals, ribbons and twisted Taylor vortices. All of these flows have the property that they are steady flows when examined in a rotating frame of reference. For all non-axisymmetric modes with the exception of spirals, we observe the existence of regions of chaotic mixing within the fluid. We discuss mixing of the fluid by these flows with reference to the pattern of stagnation points and some of the periodic trajectories within the fluid and on the boundary.

The mean shear has a major influence on near-wall turbulence but there are also other important physical processes at work in the turbulence/wall interaction. In order to isolate these, a shear-free boundary layer was studied experimentally. The desired flow conditions were realized by generating decaying grid turbulence with a uniform mean velocity and passing it over a wall moving with the stream speed. It is shown that the initial response of the turbulence field can be well described by the theory of Hunt & Graham (1978). Later, where this theory ceases to give an accurate description, terms of the Reynolds stress transport (RST) equations were measured or estimated by balancing the equations. An important finding is that two different length scales are associated with the near-wall damping of the Reynolds stresses. The wall-normal velocity component is damped over a region extending roughly one macroscale out from the wall. The pressure–strain redistribution that normally would result from the Reynolds stress anisotropy in this region was found to be completely inhibited by the near-wall influence. In a thin region close to the wall the pressure–reflection effects were found to give a pressure–strain that has an effect opposite to the normally expected isotropization. This behaviour is not captured by current models.

The unsteady behaviour of an infinitely long fluid-loaded elastic plate which is driven by a single-frequency point-force excitation in the presence of mean flow is known to exhibit a number of unexpected features, including absolute instability when the normalized flow speed, U, lies above some critical speed U0, and certain unusual propagation effects for U<U0. In the latter respect Crighton & Oswell (1991) have demonstrated most significantly that for a particular frequency range there exists an anomalous neutral (negative energy) mode which has group velocity pointing towards the driver, in violation of the usual radiation condition of outgoing waves at infinity. They show that the rate of working of the driver can be negative, due to the presence of other negative-energy waves, and can also become infinite at a critical frequency corresponding to a real modal coalescence. In this paper we attempt to extend these results by including, as is usually the case in a practical situation, plate curvature in the transverse direction, by considering a fluid-loaded cylinder with axial mean flow. In the limit of infinite normalized cylinder radius, a, Crighton & Oswell's results are regained, but for finite a very significant modifications are found. In particular, we demonstrate that the additional stiffness introduced by the curvature typically moves the absolute-instability boundary to a much higher flow speed than for the flat-plate case. Below this boundary we show that Crighton & Oswell's anomalous neutral mode can only occur for a>a1(U), but in practical situations it turns out that a1(U) is exceedingly large, and indeed seems much larger than radii of curvature achievable in engineering practice. Other negative-energy waves are seen to exist down to a smaller, but still very large, critical radius a2(U), while the existence of a real modal coalescence point, leading to a divergence in the driver admittance, occurs down to a slightly smaller critical radius a3(U). The transition through these various flow regimes as U and a vary is fully described by numerical investigation of the dispersion relation and by asymptotic analysis in the (realistic) limit of small U. The inclusion of plate dissipation is also considered, and, in common with Abrahams & Wickham (1994) for the flat plate, we show how the flow then becomes absolutely unstable at all flow speeds provided that a>a2(U).