The steady flow of a suspension of closely fitting, neutrally buoyant, incompressible and elastic spheres through a circular cylindrical tube is investigated under the assumption that lubrication theory is valid in the fluid region. A series solution giving the displacement field of an elastic incompressible sphere under axisymmetrically distributed surface tractions is developed. It is found that, for closely fitting particles, flow properties of the suspension are strongly dependent on the shear modulus of the elastic material and the velocity of the particle.

The three-soliton solution of the two-dimensional Korteweg-de Vries equation is analysed to show that the structure of the interaction can be represented in terms of the motion of two-soliton resonant interactions (resonant triads) as described by Miles (1977). The schematic development of the interaction with time is obtained and shown to approximate closely to computer calculations of the analytic solution. Similar results follow for interactions of more solitons and other equations.

It is shown that the Orr-Sommerfeld equation, which governs the stability of any mean shear flow in an unbounded domain which approaches a constant velocity in the far field, has a continuous spectrum. This result applies to both the temporal and the spatial stability problem. Formulae for the location of this continuum in the complex wave-speed plane are given. The temporal continuum eigenfunctions are calculated for two sample problems: the Blasius boundary layer and the two-dimensional laminar jet. The nature of the eigenfunctions, which are very different from the Tollmien-Schlichting waves, is discussed. Three mechanisms are proposed by which these continuum modes could cause transition in a shear flow while bypassing the usual linear Tollmien-Schlichting stage.

The conservation law for the flux of axial momentum in a turbulent jet is examined. The examination discloses that for a plane jet out of a wall the momentum flux is reduced appreciably because the induced flow towards the jet has a component in the direction opposite to the main jet flow and because of the pressure field generated in the ambient fluid. Existing experimental results confirm this conclusion.

The onset of convection in shear flow driven by lateral heating and also uniformly heated from below is investigated numerically by Galerkin's method. Stress-free as well as rigid, perfectly conducting boundaries are considered. The analysis is valid for small and moderate Prandtl numbers. The magnitude of the lateral basic temperature gradient may be expressed by a dimensionless Grashof number G, while the uniform heating from below is represented by a Rayleigh number Ra. Depending on the values of G, Ra and the Prandtl number Pr, a variety of interesting situations arise. In particular it is demonstrated that the form of the most unstable mode, i.e. whether it is a roll with axis aligned along the basic flow (a longitudinal roll) or one with axis normal to the basic flow (a transverse roll), depends on the value of the Prandtl number. For small values of G, the marginally stable disturbances are found to be steady, while for larger values of G, oscillatory instability occurs. For all values of G considered here (G [lsim ] 3000), computations of the energy balance for the marginally stable disturbances show that the main instability mechanism is of thermal origin, while the effect of shear may be important in selecting the preferred mode of disturbance.

A sphere was subjected to a simple harmonic motion in an otherwise undisturbed liquid. Records of the resistance of the liquid to the motion for various amplitudes and frequencies were obtained. The resistance was first represented by an equation consisting of three terms with empirical coefficients: the steady-motion drag, a term due to the ‘added mass’ and a term due to the history of the motion. It was found that the data could be correlated only with a large degree of scatter by this type of equation. Subsequently an attempt was made to represent the resistance by means of a single term, with an empirical coefficient C. It was found that C correlated well with the acceleration number Vd/V2 and the Reynolds number Vd/v, where V, V and d are the acceleration, velocity and diameter of the sphere respectively and v is the kinematic viscosity of the liquid. C increased with Vd/V2 and decreased in the limit to the steady-motion drag coefficient Cd when Vd/V2 became very small. The range of the Reynolds number in the experiments was 102 < Vd/v < 104 and the range of the acceleration number was 0 ≤ Vd/V2 ≤ 10·5.

This paper supplements an earlier study (Singh 1974) of the steady case of ‘Entry flow in a curved pipe’. Here we consider an entrance profile of the form \[ w = Q(t)/(1+\delta r\cos\alpha), \] which is physiologically more relevant for blood being pumped from the left ventricle into the ascending aorta. A boundary-layer analysis is applied to determine the effects of curvature and an adverse pressure gradient (associated with the primary flow) on the wall shear. The study shows how the negative wall shear and backflow near the wall develop during the decelerating phase of the cycle as the boundary layer grows. The analysis shows how the increasing effect of the secondary flow due to curvature draws off slower moving fluid azimuthally from the outer bend to the inner bend; this induces a cross-flow of faster moving fluid from the inner bend to the outer bend which results in a thinning of the boundary layer at the outer bend and a thickening at the inner bend. This implies an increased wall shear at the outer bend compared with that at the inner bend as the flow develops further downstream; this is in contrast with the initial stages of the motion near the entrance where the higher wall shear occurs at the inner bend owing to the external flow and to geometric factors. The analysis shows that the displacement effect of the boundary layer on the core is not significant because the boundary layer remains thin, about one-tenth of the tube diameter.

This paper deals with a two-dimensional turbulent boundary layer disturbed by a circular cylinder. The cylinder was placed inside or outside the boundary layer with its axis parallel to the wall and normal to the flow direction. The mean velocity, wall shear stress, longitudinal turbulent intensity, autocorrelations and turbulent length scale were measured and here the relaxation features of the disturbed boundary layer are discussed. The measurements were made for a ratio of the cylinder diameter d to the undisturbed boundary-layer thickness δ0 equal to 0·30 and for three values of the ratio of the height h of the cylinder axis to δ0 equal to 0·222, 0·556 and 1·24.

The results show that the near-wall region of the disturbed boundary layer recovers much more quickly than the outer region and that in the case h/δ0 = 0·222 the recovery is faster than in other cases, as reported by Clauser (1956). Moreover, it is found that the fluctuating velocity field recovers more slowly than the mean velocity field, and that the characteristics of the turbulence in the outer region are still close to those in the wake of an isolated cylinder at the last measurement station, although the mean velocity profile has almost completely returned to its natural shape.

In the paper we consider harbour oscillations excited by wind-generated gravity waves. The analysis is based on the fact that waves propagate along rays (wave orthogonals). In this way the elliptic boundary-value problem is turned into an initial-value problem along each ray. When a ray strikes the boundary (the harbour walls), reflected rays are produced in accordance with the law of reflexion. When a ray strikes an edge point of the boundary (e.g. the tip of a breakwater) diffracted rays are produced and emitted in all directions into the harbour. Algorithms for the tracing of incident, multiply reflected and singly diffracted rays as well as the computation of the field on each ray are presented. Attenuation mechanisms (e.g. partial reflexion), which limit the number of rays needed to compute the field, are included. Numerical examples for a rectangular and an actual harbour are given. A comparison between the results obtained by ray methods and finite difference methods is included.

A numerical method has been developed for the calculation of the pressure distribution, forces and moments on a two-dimensional aerofoil undergoing an arbitrary unsteady motion in an inviscid incompressible flow. In a discussion of the appropriate Kutta condition(s) it is argued that two Kutta conditions are required to obtain a satisfactory solution. The method is applied to (i) a sudden change in aerofoil incidence, (ii) an aerofoil oscillating at high frequency and (iii) an aerofoil passing through a sharp-edged gust.

The wall of a large tank or reservoir breaks, sending fluid against a secondary containment dyke. The impact of the surging fluid against the safety barrier is studied. The results of theoretical analysis and numerical simulation (for vertical dykes) are in good agreement with experimental data concerning overflow and total spillage as well as the fluid motion after collision, including the development and formation of a strong shock. The dependence of spillage on the inclination of the dyke is also determined by experiment.

The problem of the response of a porous elastic bed to water waves is treated analytically on the basis of the three-dimensional consolidation theory of Biot (1941). Exact solutions for the pore-water pressure and the displacements of the porous medium are obtained in closed form for the case of waves propagating over the poro-elastic bed. The theoretical results indicate that the bed response to waves is strongly dependent on the permeability k and the stiffness ratio G/K’, where G is the shear modulus of the porous medium and K’ is the apparent bulk modulus of elasticity of the pore fluid. The earlier solutions for pore-water pressure by various authors are given as the limiting cases of the present solution. For the limits G/K′ → 0 or k→ ∞, the present solution for pressure approaches the solution of the Laplace equation by Putnam (1949). For the limit G/K′→ ∞, the present solution approaches the solution of the heat conduction equation by Nakamura et al. (1973) and Moshagen & Tørum (1975).

The theoretical results are compared with wave tank experimental data on pore-water pressure in coarse and fine sand beds which contain small amounts of air. Good agreement between theory and experiment is obtained.