The present study deals with the influence of a magnetic-fluid coating, held onto a circular cylinder surface by a magnetic field, on the viscous fluid flow structure round the cylinder in the Reynolds number range of 1–100. The influence of the coating thickness, magnetic fluid viscosity, and Reynolds number on flow separation and drag reduction is determined. The interface shape of the magnetic fluid coating and its behaviour, depending on the flow parameters, are also established.

Richtmyer–Meshkov instability causes spatially periodic perturbations initially imposed on a shock-accelerated, thin gas layer to develop into one of three distinct flow patterns. Planar laser-induced fluorescence imaging of the evolving layer, produced by a perturbed SF6 planar jet in air, shows an apparent flow bifurcation that is observed as mushroom-shaped or sinuous-shaped interfacial patterns. Analysis of this nonlinear instability growth, accomplished by modelling the flow field as a row of line vortices, predicts that the layer thickness grows logarithmically at later times and compares well with our measurements. Because the row of vortices is unstable, the model also provides an explanation for the appearance of the three observed interfacial patterns.

Our flow-visualization and spectral studies of spherical Couette flow between two concentric spheres with only the inner sphere rotating for the clearance ratio (or gap ratio) 0.14 where the Taylor instability occurs have been pursued to systematically explore how and why a variety of wavenumbers and rotation frequencies of the non-axisymmetric periodic disturbances occurs at the same supercritical Reynolds number. The observed periodic disturbances constitute six kinds of disturbances: spiral TG (Taylor–Görtler) vortices, twists developing within toroidal TG vortices, both unmodulated and modulated waves travelling on the TG vortices, and both Stuart vortices and shear waves developing within the Ekman-type secondary flow. Development of these disturbances depends strongly on the flow mode at the initial Reynolds number (initial flow mode) and on the Reynolds-number evolution process approaching the final Reynolds number (acceleration rate and history of the Reynolds number). In our previous studies (Nakabayashi 1983; Nakabayashi & Tsuchida 1988 a, b), we clarified the structures, wavenumbers and rotation frequencies of the periodic disturbances caused by a quasi-static increasing of the Reynolds number. In the present study, we consider how the characteristics of periodic disturbances depend on the following three factors: (i) the rate of increase of the Reynolds number; (ii) the number of toroidal vortices in an initial flow mode; and (iii) the quasi-static Reynolds-number history. The flow modes observed in the present study are all stable to small perturbations, and the transitions among the flow modes are reproducible.

A series solution approach to the forced and damped quasi-geostrophic barotropic vorticity equation is considered in order to examine the strongly forced and inertial limits of ocean gyre dynamics. The strongly forced limit is the limit investigated numerically by Veronis (1966b). It is shown that this limit, although superficially having the same symmetry properties as the inertial limit, is distinguishably different from the latter. After isolating the inertial limit in an appropriate way it is shown that our series solution method is able to find the ‘free mode’ and its ‘almost free correction’, that the ‘free mode’ obeys the integral criteria of Niiler (1966) and Pierrehumbert & Malguzzi (1984) and that the relationship between the streamfunction and the absolute vorticity is in general a nonlinear one.

In this paper we present a general method for calculating the hydrodynamic loads (forces and moments) acting on a deformable body moving with six degrees of freedom in a non-uniform ambient potential flow field. The corresponding expressions for the force and moment are given in a moving (body-fixed) coordinate system. The newly derived system of nonlinear differential equations of motion is shown to possess an important antisymmetry property. As a consequence of this special property, it is demonstrated that the motion of a rigid body embedded into a stationary flow field always renders a first integral. In a similar manner, we show that the motion of a deformable body in the presence of an arbitrary ambient flow field is Hamiltonian. A few practical applications of the proposed formulation for quadratic shapes and for weakly non-uniform external fields are presented. Also discussed is the self-propulsion mechanism of a deformable body moving in a non-uniform stationary flow field. It leads to a new parametric resonance phenomenon.

Steady waves at the interface between two immiscible and inviscid fluids of differing density are studied. The governing equations are reformulated as a spatial Hamiltonian system leading to new variational principles for uniform states and travelling waves. Analytical methods based on the properties of the Hamiltonian structure and numerical methods are used to find new branches of steady nonlinear interfacial waves in the neighbourhood of the singularity c = cg. While the water-wave problem (upper fluid density negligible) near this singularity has received considerable attention the results for interfacial waves present some new features. The branches of travelling waves when plotted in ($\tilde{F}, \bar{S}$)-space, where $\tilde{F}$ and $\bar{S}$ are related to the energy flux and flow force respectively, show new bifurcations in the context of hydrodynamic waves even at very low amplitudes. The secondary bifurcations are explained by a spatial analogue of the superharmonic instability. An interesting analogy is also found between the spatial bifurcations of travelling waves and the Kelvin–Helmholtz instability. The new branches of waves occur at physically realizable values of the parameters and therefore could have implications for interfacial waves in applications.

An asymptotic analysis of the compressible turbulent boundary-layer equations is carried out for large Reynolds numbers and mainstream Mach numbers of O(1). A self-consistent two-layer asymptotic structure is described wherein the time-mean velocity and total enthalpy are logarithmic within the overlap zone but in terms of the Howarth–Dorodnitsyn variable; the proposed structure leads to a compressible law of the wall for high-speed turbulent flows with surface heat transfer. Simple outer-region algebraic turbulence models are formulated to reflect the effects of compressibility. To test the proposed asymptotic structure and turbulence models, a set of self-similar outer-region profiles for velocity and total enthalpy is obtained for constant-pressure flow and for constant wall temperature; these are combined with wall-layer profiles to form a set of composite profiles valid across the entire boundary layer. A direct comparison with experimental data shows good agreement over a wide range of conditions for flows with and without surface heat transfer.

Direct numerical simulation is used to examine the interaction of turbulence with a wall in the absence of mean shear. The influence of a solid wall on turbulence is analysed by first considering two ‘simpler’ types of boundaries. The first boundary is an idealized permeable wall. This boundary isolates and elucidates the viscous effects created by the wall. The second boundary is an idealized free surface. This boundary complements the first by allowing one to isolate and investigate the kinematic effects that occur near boundaries. The knowledge gained from these two simpler flows is then used to understand how turbulence is influenced by solid walls where both viscous and kinematic effects occur in combination.

Examination of the instantaneous flow fields confirms the presence of previously hypothesized structures (splats), and reveals an additional class of structures (antisplats). Statistical analysis of the Reynolds stresses and Reynolds stress transport equations indicates the relative importance of dissipation, intercomponent energy transfer, and energy transport. It is found that it is not the structures themselves, but the imbalance between structures which leads to intercomponent energy transfer. Remarkably, this imbalance (and hence near-wall intercomponent energy transfer) is controlled by viscous processes such as dissipation and diffusion. The analysis presented herein is a departure from past notions of how boundaries influence turbulence. The efficacy of these qualitative physical concepts is demonstrated in Part 2 where improved near-wall turbulence models are derived based on these ideas.

Models for the dissipation tensor and (slow) pressure–strain terms of the Reynolds stress transport equations are presented which are applicable near boundaries. These models take into account the large inhomogeneity and anisotropy that can be present near walls and surfaces, and are inspired by the physical insights developed in Part 1 of this paper. The dissipation tensor model represents a fundamentally new approach to dealing with turbulence inhomogeneities. The pressure–strain model shows how the classic return-to-isotropy model of Lumley (1978) can be adapted to the near-wall region. The closure hypotheses underlying these two models are tested in an a priori fashion using direct numerical simulation (DNS) data.

Macroscopic phase separation and the evolution of the drop size distribution for non-homogeneous dispersions, in which buoyancy-driven settling and coalescence of drops cause spatial as well as temporal variations of the drop size distribution, was analysed by numerical solution of the population dynamics equations. Collision efficiencies based on detailed hydrodynamic interactions of spherical drops with clean interfaces were incorporated in the description of the pairwise drop coalescence rates. A dimensionless parameter that characterizes the relative importance of settling and coalescence was identified. For finite values of this parameter, the phase separation rates and average drop size initially increase owing to coalescence, and then decrease owing to the larger drops settling out of the dispersion.

To determine a suitable boundary-condition model for the contact line in oscillatory flow, an upright plate, oscillated vertically with sinusoidal motion in dye-laden water with an air interface, is considered experimentally. Constrained by the desirability of a two-dimensional flow field, eight frequencies in the 1–20 Hz range, each with seven different stroke amplitudes (0.5–6 mm) are chosen. The Reynolds number varies from 1.6 to 1878.3 in the experiments, large relative to the Reynolds number in the conventional uni-directional contact-line experiments (e.g. Dussan V.'s 1974 experiments). To facilitate prediction, a high-speed video system is used to record the plate displacement, the contact-line displacement, and the dynamic behaviour of the contact angle. Several interesting contact-line phenomena are shown in the present results. An expression for λ, the dimensionless capillary coefficient, is formulated such that the dynamic behaviour at the contact line is predicted reasonably well. A particle-tracking-velocimetry (PTV) technique is used to detect particle trajectories near the plate such that the boundary condition along the entire plate can be modelled. Two sets of PTV experiments are conducted. One set is for stick contact-line motion, the other set is for stick–slip contact-line motion. The results from the PTV experiments show that a vortex is formed near the meniscus in the stick-slip contact-line experiments; however, in the stick contact-line experiments, no such vortex is present. Using the present experimental results, a model is developed for the boundary condition along the vertically oscillating vertical plate. In this model, slip occurs within a specific distance from the contact line while the flow obeys the no-slip condition outside this slip region. Also, the mean slip length is determined for each experimental stroke amplitude.

Larraza & Putterman (1984) and Miles (1984b) derived a nonlinear Schrödinger (NLS) equation for the envelope r(X,τ) of a spatially and temporally modulated cross-wave for which the spatial mean square $\overline{|r|^2} $ vanishes (e.g. a solitary wave). Sasaki (1993) found that the accommodation of non-vanishing $\overline{|r|^2} $ (e.g. a cnoidal wave) introduces a non-local term proportional to $\overline{|r|^2} $ in the coefficient of r in the NLS equation. Sasaki's result is confirmed through an average-Lagrangian formulation, in which the functional $\overline{|r|^2} $ appears (after appropriate normalization) as the Lagrange multiplier associated with the constraint of conservation of mass for the envelope. This functional is a constant, and implies a quadratic (in amplitude) shift of the resonant frequency, for a periodic ($(\partial r/\partial\tau = 0) $) wave; but if the X and τ dependencies of r are not separable it implies the replacement of the NLS equation by a nonlinear integral-partial-differential equation.

This paper presents laser-Doppler measurements of the mean velocity and statistical moments of turbulent velocity fluctuations in the near-wall region of a fully developed pipe flow at low Reynolds numbers. A refractive-index-matched fluid was used in a Duran-glass test section to permit access to the near-wall region without distortion of the laser beams. All measurements were corrected for the influence of the finite size of measuring control volume. Measurements of long-time statistical averages of all three fluctuating velocity components in the near-wall region are presented. It is shown that the turbulence intensities in the wall region do not scale with inner variables. However, the limiting behaviour of the intensity components very close to the wall show only small variations with the Reynolds number. Measurements of higher-order statistical moments, the skewness and flatness factors, of axial and tangential velocity components confirm the limiting behaviour of these quantities obtained from direct numerical simulations of turbulent channel flow. The comparison of measured data with those obtained from direct numerical simulations reveals that noticeable discrepancies exist between them only with regard to the flatness factor of the radial velocity component near the wall. The measured v’ flatness factor does not show the steep rise close to the wall indicated by numerical simulations. Analysis of the measured data in the near-wall region reveals significant discrepancies between the present LDA measurements and experimental results obtained using the hot-wire anemometry.

The exact problem of steady periodic waves (Stokes waves) on the surface of an ideal liquid above a horizontal bottom is reconsidered in order to confirm a general property conjectured by Benjamin & Lighthill (1954). Specifically, in terms of parameters r and s proportional respectively to the total-head and flow-force constants for steady flows, such waves are proved to realize points (r, s) inside the region of the (r, s)-plane that is bounded by the cusped curve representing all possible uniform streams. A corresponding attribute of steady periodic waves on the surface of an infinitely deep ideal liquid will also be demonstrated. The concluding discussion refers to steady water waves that are not periodic Stokes waves, and comments with reference to Appendix B on the significance of the flow-force invariant s in Hamiltonian representations of the steady-wave problem.

The shadowgraph technique is used for visualizing the early stages of the flow in a water-filled square cavity which is suddenly heated and cooled on the opposing sidewalls. These sidewalls are perfect heat conductors, while the top and bottom boundaries of the cavity are thermally insulating. For the first time, a clear visualization is given of the first group of waves travelling up the hot boundary layer immediately after start-up, of the initial horizontal intrusions and of the second group of waves resulting from the interaction of the incoming intrusion with the boundary layer. The properties of the waves are examined and shown to be in agreement with previous numerical predictions. Special attention is paid to the initial horizontal intrusions, and their connection to gravity currents is discussed. One feature in particular which makes these intrusions unique is the interaction with the first group of waves coming from the vertical boundary layers. This interaction together with what appears to be a thermal instability of the intrusion nose are discussed in detail.

Two-dimensional weakly nonlinear surface gravity–capillary waves in an ideal fluid of finite water depth are considered and nonlinear evolution equations which are correct up to the third order of wave steepness are derived including the applied pressure on the free surface. Since no assumptions are made on the length scales, the equations can be applied to a fluid of arbitrary depth and to disturbances with arbitrary wavelength. For one-dimensional gravity waves, these evolution equations are reduced to those derived by Matsuno (1992). Most of the known equations for surface waves are recovered from the new set of equations as special cases. It is shown that one set of equations has a Hamiltonian formulation and conserves mass, momentum and energy. The analysis for irrotational flow is extended to two-dimensional uniform shear flow.

This theoretical work, on the spot in an otherwise laminar boundary layer, concerns the initial-value problem for three-dimensional inviscid disturbances covering a wide range of scales. The study asks whether or not comparatively short scales can have a substantial impact on the spot spreading rate, as well as on other important features including the spot structure. It is found that such scales act to reduce the spread angle to approximately 11°, close to the experimental observations for transitional/turbulent spots, as opposed to the angle of 19.47° for waves near or behind the spot trailing edge. The scales emerge from coupling uniform shear flow directly with the local uniform stream and then analysing large-time features. The leading edge and trailing edge of the spot are also examined in detail, along with other structural properties. It is concluded that nonlinearity and short-scale effects probably combine to restrict the global spread angle as above, while viscous sublayer bursting among other things completes the spot structure. Related work on nonlinear, trailing-edge and leading-edge behaviours and comparisons with experiments are also discussed.