Experiments were conducted in a long channel in which a mixed region was allowed to collapse in the thermocline region of a stratified fluid. Two solitary wave-like disturbances were generated travelling to the right and left of the mixed region. The mixed region fluid was partly entrained in these waves. The waves were allowed to reflect from the end walls and to collide after the reflexions. The velocity structure of the wave was studied before, during and after a collision by means of hot-film anemometry and streak pictures. Wave speeds were accurately determined by two hot-film probes. Permanence of form and amplitude decay of the waves were observed over long distances and through successive collisions and reflexions. An analytical result for the structure of the solitary wave in an ambient stratification of the hyperbolic tangent type, but of finite total water depth, was obtained using Benney's method. Excellent agreement between the experimental and theoretical results was obtained. The results showed that the generated waves were indeed solitary waves.

A transonic-flow theory of thin, oblique wing of high aspect ratio is presented, which permits a delineation of the influence of wing sweep, the centre-line curvature, and other three-dimensional (3D) effects on the nonlinear mixed flow in the framework of small-disturbance theory. In the (parameter) domain of interest, the flow field far from the wing section pertains to a high subsonic, or linear sonic, outer flow, representable by a Prandtl–Glauert solution involving a swept, as well as curved, lifting line in the leading approximation.

Among the 3D effects is one arising from the compressibility correction to the velocity divergence, absent in classical works; this effect also leads to a correction in the outer flow in the form of an oblique line source. More important is the upwash corrections which includes the influence of both the near and far wakes, as well as the local curvature of the centre-line. For straight oblique wings, local similarities exist in the 3D flow structure, permitting the reduced equations to be solved once for all span stations. An analogy also exists between the oblique-wing problem and that of a 2D transonic flow which is weakly time-dependent; this provides an alternative method of solving numerically the inner airfoil problem.

Solutions to the reduced problem are demonstrated and compared with full-potential solutions for elliptic oblique wings involving high subcritical as well as slightly supercritical component flows.

A theoretical investigation is made of turbulent thermal convection in a horizontally infinite layer of fluid confined between a rigid isothermal upper plate and a rigid adiabatic lower plate, driven by a temperature difference between the plates that is totally induced by volumetric heating of the layer. The dependence of upper surface Nusselt number, Nu, on both Prandtl number, Pr, and internal Rayleigh number, RaI, is obtained from considerations of the Boussinesq equations of motion. Also obtained is the dependence of various turbulence quantities upon distance from the upper plate. At a sufficiently high Rayleigh number, the present theory gives $Nu \sim Ra^{\frac{1}{4}}_I$ for large Pr and Nu ∼ Pr¼Ra¼I for small Pr. At lower Rayleigh numbers, however, the Nusselt number is found to vary according to $Nu \sim (a-b\,Ra^{-\frac{1}{12}}_I)^{-1} Ra^{\frac{1}{4}}_I$, where a and b are coefficients dependent upon Pr. The asymptotic $Ra^{\frac{1}{4}}_I$ law tends to support the boundary layer instability model of Howard (1966), although significant deviation from the model is predicted by the present theory over the range of Rayleigh numbers explored experimentally (Kulacki & Nagle 1975; Kulacki & Emara 1977). Based upon the results of this study the empirical power-law representation of Nu is critically examined and found to be adequate within finite ranges of RaI. Comparison of the present flow situation is made with the corresponding case of turbulent Bénard convection.

This paper is concerned with understanding the development of a free surface and the velocity of a thick creeping film emerging from a slit onto a plate. There is a difference between free surface flows with film thickness of 10 to 20 mm and thin film flows of less than 1 to 2 mm due to surface tension influence.

A laser–Doppler velocimeter of high spatial and temporal resolution has been used to measure the decreasing thickness of slowly flowing liquid and the velocity profiles at the exit of the slit and in the transition region of the plate. The hydrodynamic entrance length can be calculated from an empirical dimensionless relation that includes only the plate inclination angle β as a parameter.

Numerical solutions are presented for the unsteady irrotational flow generated by the movement of the stern of a two-dimensional semi-infinite body at the free surface of an incompressible fluid. When separation occurs other than at a sharp trailing edge, the location of the separation point is computed as part of the solution. Linear and nonlinear results are compared. It is shown that for draught-based Froude numbers greater than 3 the nonlinear effects are negligible for most practical purposes while for Froude numbers less than three these effects can be significant.

A possible model of the flow in the neighbourhood of a point of reattachment of a supersonic laminar boundary layer consists of a three-tiered ‘triple-deck’ structure in which the basic problem reduces to that of solving the incompressible boundary-layer equations in the lower deck, a region of lateral and streamwise extent $O(R^{-\frac{5}{8}})$ and $O(R^{-\frac{3}{8}})$, where R is a representative Reynolds number of the flow (Daniels 1979). The present paper describes a scheme for the numerical solution of this problem which provides evidence in support of the proposed model and quantitative values for the O(R−¼) correction to the base pressure in the flow upstream and the O(R−⅝) correction to the position of reattachment relative to the point of intersection of the incoming shear layer and the wall. An important feature of the scheme is that it copes successfully with a flow which contains substantial reverse velocities.

In an ocean of uniform depth the propagation of small-amplitude plane waves is impeded by two vertical semi-infinite perfectly reflecting barriers extending from the bottom of the sea to above the free surface. The two screens do not lie in general in the same plane, and they are separated by a gap through which wave energy is transmitted from the open sea into the sheltered region. A transmission coefficient is established for small gap widths relative to the wavelength and the agreement with existing theoretical results for special cases is found to be very good.

This paper describes an analysis of the forces induced by separation and vortex shedding from sharp-edged bodies in oscillatory flow at high Reynolds number. The analysis which is valid for the case of small oscillations of the fluid is compared with experimental data obtained at fairly low Keulegan–Carpenter numbers.The main conclusions of this paper were presented at the International Symposium on Wave Induced Forces on Structures at Bristol, 1978.

Eulerian direct interaction is used to close Liouville's equation central to the transport of particles in a turbulent fluid where the dominant drag force is derived from the particle and local fluid velocities. The reliability of the equation is then tested by comparison of solutions with those of a computer simulation of particle motion with Stokes drag in a random velocity field. Using an empirical drag law accurate for particle Reynolds numbers up to 500, formulae are derived for the statistical moments central to particle dispersion for a weak drag force operating in a Gaussian isotropic stationary velocity field. These show for instance that the long time particle diffusion coefficient is in general greater than the equivalent value based on Stokes drag.

The design of most aerodynamic surfaces, as for example the helicopter rotor, is based essentially on quasi-steady theories. However, the dynamics of a rotating blade introduce unexpected fluctuations and overshoots of properties like lift, drag, etc. The phenomenon of unsteady stall is intimately connected with the development of an oscillating boundary layer and separation. Experimental investigation of such flows was undertaken by a method of visualization developed especially for the study of laminar or turbulent boundary layers and separation. The method captures the instantaneous two-dimensional flow field, including regions of separated flow, and provides accurate quantitative information. Laser-doppler anemometer measurements complement the optically obtained data. Results reveal that separation responds with time-lag to external disturbances, in agreement with unsteady stall data. Oscillating outer flows result in displacement of the point of separation and, under certain conditions, the Despard & Miller (1971) criterion was found to hold. Earlier theoretical models of separation are confirmed qualitatively and for the early stages of the transient phenomena. The findings provide physical insight and quantitative data that may help explain the phenomenon of unsteady stall and unsteady separation.

To account for our previous experimental results, the flow past a flat plate set parallel to a uniform stream is investigated on the basis of Oseen's equations of motion. We are mainly concerned with the wake region and calculate the velocity field in detail for the range of Reynolds numbers 20–3000, corresponding to the experiments. The calculation shows that there is a velocity overshoot in the velocity distribution near the trailing edge, with the same magnitude as in the experiments. Furthermore, we confirm the experimental fact that the velocity on the centre-line of wake recovers in proportion to the square root of the distance from the trailing edge in the near wake. The pressure field is also examined to see the streamwise pressure gradient in the near wake.

The lateral extent of the large-scale features of a high-Reynolds-number, turbulent mixing layer are studied by means of an array of twelve hot wires placed across the span of the wind tunnel. Correlation measurements show that the large-scale structure rapidly approaches an asymptotic state, in which the lateral correlation length becomes proportional to the local mixing-layer thickness. Visualizations of the instantaneous hot-wire outputs show the large structure to extend across the wind tunnel, but to contain spanwise irregularities. It is argued that these spanwise irregularities are produced by the pairing interactions between adjacent vortices.

Periodic wave trains propagating over water which varies in depth in the direction of wave propagation are studied by using accurate solutions for wave trains in constant depth of water. The accurate solutions are (i) Cokelet's (1977) extension of Stokes’ approximation and, for the longer waves, (ii) a solution for trains of solitary waves using the solitary-wave solution of Longuet-Higgins & Fenton (1974).

A representative selection of results is shown in diagrams. A feature which arises from the use of these accurate solutions is that near the highest wave two solutions are possible for a given incoming wave. Although the solutions cannot describe waves that break, it is shown that as depth is decreased a point is reached beyond which no solution can be found. This is taken to indicate the region in which waves break.

The limitations of the theory are discussed and analysed. Comparisons with experimental measurements of Hansen & Svendsen (1979) are included.

This paper presents an approximate method for solving Oseen's linearized equations for a two-dimensional steady flow of incompressible viscous fluid past arbitrary cylindrical bodies at low Reynolds numbers. The formulation is based on a discrete singularity method with a least squares criterion for satisfying the no-slip boundary condition. That is, sets of Oseenlets, sinks, sources and vortices are discretely distributed in the interior of the body, and then the least squares criterion attempts to minimize the integrated squares of velocities along the body contour, thus leading to a system of simultaneous algebraic equations. Complex-variable arithmetic, usually available on modern computers, makes the computation algorithm very simple. Furthermore, the method is applicable to cases that cannot be solved by classical analytical approaches. As examples of application, we computed the forces acting on a single circular cylinder, two circular cylinders of equal radius separated by a distance, an inclined elliptic cylinder and an inclined square cylinder all of which are immersed in uniform flow fields. The computed results agree very well with those of classical analytical methods.

An examination of the isotropic vorticity theory was made in an adverse pressure gradient flow based on experimental data obtained in a conical diffuser having a total divergence angle of 8° and an area ratio of 4:1 with fully-developed pipe flow at entry. The results showed that the rates and the ratio of production and dissipation of the turbulent vorticity were constant in the core region of the diffuser but increase significantly in the wall layer. The overall vorticity balance was essentially the same at all axial stations. The analysis of Batchelor & Townsend (1947) for isotropic vorticity was found to be valid in the core region of the diffuser for an order-of-magnitude higher Rλ (200 [les ] Rλ 600) than in grid turbulence. The magnitude of the skewness of ∂u1/∂t was constant in the core region and comparable to that for grid turbulence. Also, this region of constant skewness extended over a larger portion of the flow cross-section compared to pipe flow. On the basis of these results, it was concluded that assumptions of isotropy in the fine structure are valid in the core region of the diffuser.

The fluid mechanics of self-propelling, slender uniflagellar micro-organisms is examined theoretically. The mathematical analysis of these motions is based upon the Stokes equations, and the body is represented by a continuous distribution of stokeslets and doublets of undetermined strength. Since the body is self-propelling, additional constraints on the total force and moment upon it are applied. A system of singular integral and auxiliary equations, in which the propulsive velocity and viscous force per unit length are the unknowns, is derived. The vector integral equation is decomposed into near- and far-field contributions, and the solution is determined by a straightforward iterative procedure. The flagella considered are of constant radius and are restricted to planar undulations. The analysis is applied to a small amplitude wave form of infinite length, and a third-order analytic solution is obtained. By means of numerical computation, the method is extended to large amplitude wave forms of both infinite and finite length. The validity and accuracy of the solution method, the effect of local curvature, and an approximate model for an attached cell body-proper are evaluated in light of alternative theories.

The solution method is systematically applied to a variety of wave-form shapes representative of actual flagella. For a sinusoidal wave form, the variations in propulsive velocity, power output and propulsive efficiency are examined as functions of the number of wavelengths on the flagellum, the amplitude and the flagellar radius. Wave forms of variable amplitude and variable wavelength are also considered. Among the significant results are the effect of the cell body on pitching, the significant differences between constant frequency and constant phase-speed undulations for variable wavelength wave forms, and comparisons with other pertinent theories.

The vorticity dynamics of a convective swirling boundary layer are studied from the viewpoint of steady, inviscid fluid-dynamics theory. Attention is confined to the region of flow lying directly below and within a circularly shaped updraft. Fluid enters the updraft region without vorticity save for that in the boundary layer upstream of the updraft radius. Solutions of the equation \[ r\eta = r^2\frac{dH}{d\psi}-\frac{d}{d\psi}\bigg(\frac{\Gamma^2}{2}\bigg) \] (e.g. Batchelor 1967, p. 545) are presented. By the nature of this approach it allows one to compute the ‘outer’ flow together with the outer boundary-layer structure and hence side-step the interaction problem. A drawback is that the inner viscous structure is not captured. These solutions are compared to some numerical solutions of the time-dependent, viscous axisymmetric Navier-Stokes equations which are reported elsewhere (Rotunno 1979). Although the agreement is not perfect, model results are close enough whereby a number of useful deductions concerning the effects of viscous diffusion and time-dependence may be made.

In a recent paper, Tatsumi, Kida & Mizushima (1978) have made a numerical study of the quasi-normal Markovian (QNM) equation for homogeneous isotropic incompressible turbulence at Reynolds numbers R up to 800.

Analytical investigations of the QNM equation support the contention of Tatsumi et al. that, at R = ∞, the decay of an initial energy spectrum of the form ka exp (− k2) leads to an initial energy-conserving regularity phase followed by a self-similar decay phase. During the former we give explicit expressions for the enstrophy and skewness. During the latter we show that for 1 < a < 4 the energy follows, for t → ∞, a t−b law with the usual value b = 2(a + 1)/(a + 3); when a [ges ] 4 deviations from Kolmogorov's (1941) $t^{\frac{10}{7}}$ law originate from non-local ‘beating’ interactions between eddies with sizes of the order of the integral scale.

We also show, analytically, that the QNM equation has a k−2, not a $k^{-\frac{5}{3}}$, inertial range and that its dissipation range is of the form k3e−k/kD, rather than e−σk1.5.

Our results are illustrated by numerical integration of the QNM equation for R up to 106 and by comparison with results from the eddy-damped quasi-normal Markovian equation which is known to produce a k−5/3 spectrum.

In view of the importance of concentration fluctuations in practical and theoretical problems of turbulent diffusion, there are presented here some invariant properties of the distribution of fluctuations associated with a cloud of contaminant containing a finite quantity Q of material. These properties are invariant provided only that Q is conserved, no assumption whatsoever being made about the random turbulent velocity field. Consequences of the results for (i) steady plumes, (ii) the representation of the distribution of concentration by series of (generalized) Hermite polynomials, and (iii) the relationship of the ensemble mean concentration with the distance–neighbour function, are discussed using experimental evidence.

Axisymmetric steady motion of an inhomogeneous rotating fluid is considered. A system of equations, with appropriate boundary conditions, controlling the smooth interior fields is derived under the assumption of small dissipation and small side-boundary conductance. It is argued that this system, being derived without linearization of the equations, might form the basis of valuable numerical analysis. Assuming sufficiently weak forcing, i.e. high insulation of the non-horizontal boundaries, a linear system is derived. An explicit solution is presented and discussed for a particularly simple and important case.