Wind-tunnel experiments were conducted to investigate the cause of large pressure fluctuations near leading edges of sharp-edged bluff bodies. Measurements obtained with a blunt flat plate showed that very low pressures occur in a narrow region located approximately 0.25XR from the leading edge, where XR defines the distance from the leading edge to the mean reattachment location. This phenomenon occurs in the undisturbed flow as well as turbulent flow, although the magnitude of peak pressure fluctuations increases with both turbulence intensity, σu/u, and turbulence scale, LX.

Flow visualization experiments conducted with a high-speed cine-camera reveal the process that causes large pressure fluctuations in separation bubbles. This process is initiated when a perturbation in the approaching flow causes a roll-up of the separated shear layer, producing a strong vortex near the surface. Conditional sampling of pressure data was used to determine the spanwise length of the vortex. A significant increase in the spanwise correlation of pressure fluctuations occurs when the shear layer rolls up. Coherence measurements indicate that the spanwise length of vortices in the separation bubble is not directly related to longitudinal velocity fluctuations in the free-stream.

The gravitational settling of a homogeneous suspension of Brownian particles on an inclined plate is considered. The hindered settling towards the wall and the viscous, buoyancy-driven bulk motion of the sediment are considered assuming steady conditions and accounting for the effects of Brownian diffusion, shear-induced diffusion and migration of particles due to a gradient in shear stress. Generally, the results show the development of a sediment boundary layer where the settling towards the wall is balanced by Brownian diffusion at the beginning of the plate and by shear-induced diffusion further downstream. Compared to previous results in the literature, the present theory allows steady-state solutions for extended values of the plate inclination and particle volume fraction above the sediment; upon reconsidering the case with non-Brownian particles, a new similarity solution, with a stable shock in particle density, is developed.

The dynamics of a spreading liquid body are dictated by the interface shape and flow field very near the moving contact line. The interface shape and flow field have been described by asymptotic models in the limit of small capillary number, Ca. Previous work established the validity and limitations of these models of the interface shape (Chen et al. 1995). Here, we study the flow field near the moving contact line. Using videomicroscopy, particle image velocimetry, and digital image analysis, we simultaneously make quantitative measurements of both the interface shape and flow field from 30 μm to a few hundred microns from the contact line. We compare our data to the modulated-wedge solution for the velocity field near a moving contact line (Cox 1986). The measured flow fields demonstrate quantitative agreement with predictions for Ca[les ]0.1, but deviations of ∼5% of the spreading velocity at Ca≈0.4. We observe that the interface shapes and flow fields become geometry independent near the contact line. Our experimental technique provides a way of measuring the interface shape and velocity field to be used as boundary conditions for numerical calculations of the macroscopic spreading dynamics.

FENE-P bead–spring chains unravel in the presence of large enough velocity gradients. In a turbulent flow, this can result in intermittent added stresses and exchanges of energy between the chains and the fluid, whose magnitudes depend on the degree of unravelling and on the orientations of the bead–spring chains. These effects are studied by calculating the average behaviour at different times of an ensemble of chains, contained in a fluid particle that is moving around in a random velocity field obtained from direct numerical simulation of turbulent flow of a Newtonian fluid in a channel. The results are used to evaluate theoretical explanations of drag reduction observed in very dilute solutions of polymers.

In regions of the flow in which the energy exchange with the fluid is positive, the possibility arises that turbulence can be produced by mechanisms other than the interaction of Reynolds stresses and the mean velocity gradient field. Of particular interest, from the viewpoint of understanding polymer drag reduction, is the finding that the exchange is negative in velocity fields representative of the wall vortices that are large producers of turbulence. One can, therefore, postulate that polymers cause drag reduction by selectively changing the structures of eddies that produce Reynolds stresses. The intermittent appearance of large added shear stresses is consistent with the experimental finding of a stress deficit, whereby the total local shear stress is greater than the sum of the Reynolds stress and the time-averaged shear stress calculated from the time-averaged velocity gradient and the viscosity of the solvent.

The problem for a thin near-wall region is reduced, within the triple-deck approach, to unsteady three-dimensional nonlinear boundary-layer equations subject to an interaction law. A linear version of the boundary-value problem describes eigenmodes of different nature (including crossflow vortices) coupled together. The frequency ω of the eigenmodes is connected with the components k and m of the wavenumber vector through a dispersion relation. This relation exhibits two singular properties. One of them is of basic importance since it makes the imaginary part Im(ω) of the frequency increase without bound as k and m tend to infnity along some curves in the real (k, m)-plane. The singularity turns out to be strong, rendering the Cauchy problem ill posed for linear equations.

Accounting for the second-order approximation in asymptotic expansions for the upper and main decks brings about significant alterations in the interaction law. A new mathematical model leans upon a set of composite equations without rescaling the original independent variables and desired functions. As a result, the right-hand side of a modified dispersion relation involves an additional term multiplied by a small parameter ε=R−1/8, R being the reference Reynolds number. The aforementioned strong singularity is missing from solutions of the modified dispersion relation. Thus, the range of validity of a linear approximation becomes far more extended in ω, k and m, but the incorporation of the higher-order term into the interaction law means in essence that the Reynolds number is retained in the formulation of a key problem for the lower deck.

In this paper we study the interaction of a shock with an axisymmetric longitudinal vortex. A linearized analysis for small vortex strength is performed, and compared with results from a high-order axisymmetric shock-fitted Euler solution. It is confirmed that for weak vortices, predictions from linear theory agree well with results from nonlinear numerical simulations at the shock location. To handle very strong longitudinal vortices, which may ultimately break the shock, we use an axisymmetric high-order essentially non-oscillatory (ENO) shock-capturing scheme. Comparisons of shock-captured and shock-fitted results are performed in their regions of common validity. We also study the vortex breakdown as a function of Mach number ranging from 1.3 to 10, thus extending the range of existing results. For vortex strengths above a critical value, a triple point forms on the shock, leading to a Mach disk. This leads to a strong recirculating region downstream of the shock and a secondary shock forms to provide the necessary deceleration so that the fluid velocity can adjust to downstream subsonic conditions.

The structure, transport properties and regimes of flow exhibited in a rotating fluid annulus, subject to internal heating and sidewall cooling, are studied both in the laboratory and in numerical simulations. The performance of the numerical model is verified quantitatively to within a few per cent in several cases by direct comparison with measurements in the laboratory of temperature and horizontal velocity fields in the axisymmetric and regular wave regimes. The basic azimuthal mean flow produced by this distribution of heat sources and sinks leads to strips of potential vorticity in which the radial gradient of potential vorticity changes sign in both the vertical and horizontal directions. From diagnosis of the energy budget of numerical simulations, the principal instability of the flow is shown to be predominantly baroclinic in nature, though with a non-negligible contribution towards the maintenance of the non-axisymmetric flow components from the barotropic wave–zonal flow interaction. The structure of the regime diagram for the internally heated baroclinic waves is shown to have some aspects in common with conventional wall-heated annulus waves, but the former shows no evidence for time-dependence in the form of ‘amplitude vacillation’. Internally heated flows instead evidently prefer to make transitions between wavenumbers in the regular regime via a form of vortex merging and/or splitting, indicating a mixed vortex/wave character to the non-axisymmetric flows in this system. The transition towards irregular flow occurs via a form of wavenumber vacillation, also involving vortex splitting and merging events. Baroclinic eddies are shown to develop from an initial axisymmetric flow via a mixed sinuous/varicose instability, leading to the formation of detached vortices of the same sign as the ambient axisymmetric potential vorticity at that level, in a manner which resembles recent simulations of atmospheric baroclinic frontal instability and varicose barotropic instabilities. Dye tracer experiments confirm the mixed wave/vortex character of the equilibrated instabilities, and exhibit chaotic advection in time-dependent flows.

In order to study the roles of stress anisotropy and of elasticity in the mechanism of drag reduction by polymer additives we investigate a turbulent pipe flow of a dilute polymer solution. The investigation is carried out by means of direct numerical simulation (DNS) and laser Doppler velocimetry (LDV). In our DNS two different models are used to describe the effects of polymers on the flow. The first is a constitutive equation based on Batchelor's theory of elongated particles suspended in a Newtonian solvent which models the viscous anisotropic effects caused by the polymer orientation. The second is an extension of the first model with an elastic component, and can be interpreted as an anisotropic Maxwell model. The LDV experiments have been carried out in a recirculating pipe flow facility in which we have used a solution of water and 20 w.p.p.m. Superfloc A110. Turbulence statistics up to the fourth moment, as well as power spectra of various velocity components, have been measured. The results of the drag-reduced flow are first compared with those of a standard turbulent pipe flow of water at the same friction velocity at a Reynolds number of Reτ≈1035. Next the results of the numerical simulation and of the measurements are compared in order to elucidate the role of polymers in the phenomenon of drag reduction. For the case of the viscous anisotropic polymer model, almost all turbulence statistics and power spectra calculated agree in a qualitative sense with the measurements. The addition of elastic effects, on the other hand, has an adverse effect on the drag reduction, i.e. the viscoelastic polymer model shows less drag reduction than the anisotropic model without elasticity. Moreover, for the case of the viscoelastic model not all turbulence statistics show the right behaviour. On the basis of these results, we propose that the viscous anisotropic stresses introduced by extended polymers play a key role in the mechanism of drag reduction by polymer additives.

An experimental analysis of the turbulence in an axisymmetrical jet within a closed tube is presented. At some distance from the nozzle, a turbulent region develops, where the kinetic energy of the mean flow almost vanishes. In this region, the turbulence is transported by turbulent diffusion and its energy decreases with the distance from the inlet. A complete description of the flow field has been achieved using laser Doppler anemometry. Some unusual features are highlighted: the statistical moments of the velocity decay exponentially, the integral length scales remain constant, the radial profiles are self-similar and the Reynolds stress tensor is isotropic and homogeneous in the radial direction. These results highlight the roles of pressure fluctuations and any mean residual motion in the return to isotropy.

A model is presented for viscous flow in a cylindrical cavity (a half-filled annulus lying between horizontal, infinitely long concentric cylinders of radii Ri, Ro rotating with peripheral speeds Ui, Uo). Stokes' approximation is used to formulate a boundary value problem which is solved for the streamfunction, ω, as a function of radius ratio R¯= Ri/Ro and speed ratio S=Ui/Uo.

Results show that for S>0 (S<0) the flow domain consists of two (one) large eddies (eddy), each having a stagnation point on the centreline and a potentially rich substructure with separatrices and sub-eddies. The behaviour of the streamfunction solution in the neighbourhood of stagnation points on the centreline is investigated by means of a truncated Taylor expansion. As R¯ and S are varied it is shown that a bifurcation in the flow structure arises in which a centre becomes a saddle stagnation point and vice versa. As R¯→1, a sequence of ‘flow bifurcations’ leads to a flow structure consisting of a set of nested separatrices, and provides the means by which the two-dimensional cavity flow approaches quasi-unidirectional flow in the small gap limit. Control-space diagrams reveal that speed ratio has little effect on the flow structure when S<0 and also when S>0 and aspect ratios are small (except near S=1). For S>0 and moderate to large aspect ratios the bifurcation characteristics of the two large eddies are quite different and depend on both R¯ and S.

Coherent vortex structures are formed in the late wakes of towed spheres for all values of the internal Froude number, F≡2U/ND∈ [10, 240] (U is the body speed, D its diameter, and N is the buoyancy frequency). The eventual emergence of the long-lived and stable pattern of alternating-signed patches of vertical vorticity is characteristic of all towed-sphere wakes, from those dominated by internal lee waves at F=1, to initially fully turbulent early wakes at F[ges ]4. At late times, the local Froude number is always low, and a characteristic stratified wake structure and dynamics result. These wakes have high mean wake defect velocities compared with non-stratified wakes, but the decay rates of energy and enstrophy are similar. Experimental evidence is presented for the existence of an intermediate non-equilibrium (NEQ) regime with very low decay rates of kinetic energy, that precedes the late wake. The NEQ regime is the period when the initial turbulence reorganizes under the increasingly (relative to the decaying turbulent kinetic energy) powerful influence of the background density gradient, accompanied by conversion of potential to kinetic energy as the wake turbulence collapses. The stable long-lived late-wake structure that eventually emerges has a high degree of order and coherence that reflects the initial wake instability. A universal curve for the energy decay of all stratified drag wakes at high Froude and Reynolds numbers is proposed.

The influence of rotation on the spectral energy transfer of homogeneous turbulence is investigated in this paper. Given the fact that linear dynamics, e.g. the inertial waves regime found in an RDT (rapid distortion theory) analysis, cannot affect a homogeneous isotropic turbulent flow, the study of nonlinear dynamics is of prime importance in the case of rotating flows. Previous theoretical (including both weakly nonlinear and EDQNM theories), experimental and DNS (direct numerical simulation) results are collected here and compared in order to give a self-consistent picture of the nonlinear effects of rotation on turbulence.

The inhibition of the energy cascade, which is linked to a reduction of the dissipation rate, is shown to be related to a damping of the energy transfer due to rotation. A model for this effect is quantified by a model equation for the derivative-skewness factor, which only involves a micro-Rossby number Roω=ω′/(2Ω) – ratio of r.m.s. vorticity and background vorticity – as the relevant rotation parameter, in accordance with DNS and EDQNM results.

In addition, anisotropy is shown also to develop through nonlinear interactions modified by rotation, in an intermediate range of Rossby numbers (RoL<1 and Roω>1), which is characterized by a macro-Rossby number RoL based on an integral lengthscale L and the micro-Rossby number previously defined. This anisotropy is mainly an angular drain of spectral energy which tends to concentrate energy in the wave-plane normal to the rotation axis, which is exactly both the slow and the two-dimensional manifold. In addition, a polarization of the energy distribution in this slow two-dimensional manifold enhances horizontal (normal to the rotation axis) velocity components, and underlies the anisotropic structure of the integral length-scales. Finally a generalized EDQNM (eddy damped quasi-normal Markovian) model is used to predict the underlying spectral transfer structure and all the subsequent developments of classic anisotropy indicators in physical space. The results from the model are compared to recent LES results and are shown to agree well. While the EDQNM2 model was developed to simulate ‘strong’ turbulence, it is shown that it has a strong formal analogy with recent weakly nonlinear approaches to wave turbulence.

The rate of growth of the nonlinear terms in the vorticity equation are analysed for a turbulent flow with r.m.s. velocity u0 and integral length scale L subjected to a strong uniform irrotational plane strain S, where (u0/L)/S=ε[Lt ]1. The rapid distortion theory (RDT) solution is the zeroth-order term of the perturbation series solution in terms of ε. We use the asymptotic form of the convolution integrals for the leading-order nonlinear terms when β= exp(−St)[Lt ]1 to determine at what time t and beyond what wavenumber k (normalized on L) the perturbation series in ε fails, and hence derive the following conditions for the validity of RDT in these flows. (a) The magnitude of the nonlinear terms of order ε depends sensitively on the amplitude of eddies with large length scales in the direction x2 of negative strain. (b) If the integral of the velocity component u2 is zero the leading-order nonlinear terms increase and decrease in the same way as the linear terms, even those that decrease exponentially. In this case RDT calculations of vorticity spectra become invalid at a time tNL∼L/u0k−3 independent of ε and the power law of the initial energy spectrum, but the calculation of the r.m.s. velocity components by RDT remains accurate until t= TNL∼L/u0, when the maximum amplification of r.m.s. vorticity is ω/S∼εexp(ε−1)[Gt ]1. (c) If this special condition does not apply, the leading-order nonlinear terms increase faster than the linear terms by a factor O(β−1). RDT calculations of the vorticity spectrum then fail at a shorter time tNL∼(1/S) ln(ε−1k−3); in this case TNL∼(1/S) ln(ε−1) and the maximum amplification of r.m.s. vorticity is ω/S∼1. (d) Viscous effects dominate when t[Gt ](1/S) ln(k−1(Re/ε)1/2). In the first case RDT fails immediately in this range, while in the second case RDT usually fails before viscosity becomes important. The general analytical result (a) is confirmed by numerical evaluation of the integrals for a particular form of eddy, while (a), (b), (c) are explained physically by considering the deformation of differently oriented vortex rings. The results are compared with small-scale turbulence approaching bluff bodies where ε[Lt ]1 and β[Lt ] 1.

These results also explain dynamically why the intermediate eigenvector of the strain S aligns with the vorticity vector, why the greatest increase in enstrophy production occurs in regions where S has a positive intermediate eigenvalue; and why large-scale strain S of a small-scale vorticity can amplify the small-scale strain rates to a level greater than S – one of the essential characteristics of high-Reynolds-number turbulence.

A thin rigid plate is submerged beneath the free surface of deep water. The plate performs small-amplitude oscillations. The problem of calculating the radiated waves can be reduced to solving a hypersingular boundary integral equation. In the special case of a horizontal circular plate, this equation can be reduced further to one-dimensional Fredholm integral equations of the second kind. If the plate is heaving, the problem becomes axisymmetric, and the resulting integral equation has a very simple structure; it is a generalization of Love's integral equation for the electrostatic field of a parallel-plate capacitor. Numerical solutions of the new integral equation are presented. It is found that the added-mass coefficient becomes negative for a range of frequencies when the disc is sufficiently close to the free surface.

The effects of an insoluble surfactant on the motion of a drop or bubble as it is driven by a pressure gradient through a capillary tube is investigated numerically. We find that a drop in a straight capillary tube can either approach a steady-state shape or develop a re-entrant cavity at its rear. For a gas bubble moving through a constricted capillary tube, we find that snap-off can occur and surfactants enhance the snap-off process. The effects of the parameters on the dynamics of bubble snap-off are illustrated and discussed.