When a ferromagnetic fluid with a horizontal free surface is subjected to a uniform vertical applied magnetic field B0, it is known (Cowley & Rosensweig 1967) that the surface may be unstable when the field strength exceeds a certain critical value Bc. In this paper we consider, by means of an energy minimization principle, the possible forms that the surface may then take. Under the assumption that |μ − 1| [Lt ] 1 (where μ is the magnetic permeability of the fluid), it is shown that when B0 is near to Bc there are three equilibrium configurations for the surface: (i) flat surface, (ii) stationary hexagonal pattern, (iii) stationary square pattern. Configuration (i) is stable for B0 < Bc, (ii) is stable for B0 > Bc and B0−Bc sufficiently small, and (iii) is stable for some higher values of B0. In each configuration the fluid is static, and the surface is in equilibrium under the joint action of gravity, surface tension, and magnetic forces. The amplitude of the surface perturbation in cases (ii) and (iii) is calculated, and hysteresis effects associated with increase and decrease of B0 are discussed.

The flow in a partially filled cylinder rotating at right angles to the earth's gravity is found under the assumptions of rapid rotation and small viscosity. Effects of viscosity, nonlinear interaction and finite container length are included.

The one-dimensional unsteady flow equations for flow in an elastic tube have been solved by employing the method of characteristics and used to predict the development of the flow and pressure wave forms in the left coronary artery system of the horse. Input data to this model include in vivo measurements of wave speed and aortic-root pressure, both of which were carried out in horse experiments. In addition, estimates of vessel taper and fluid losses due to branching were established from plastic casts of the horse coronary arteries and from in vivo flowmeter data. The calculated results have confirmed earlier experiments in revealing a relatively large systolic component of flow in the major epicardial vessels. However, the calculations indicate that, once within the myocardium, the systolic flow component quickly diminishes and the diastolic flow component becomes increasingly important. The pressure pulse does not peak as observed in the aorta, but rather rounds out with systolic pressures decreasing slowly and diastolic pressures decreasing more rapidly with distance from the coronary ostium. The presence of relatively large amplitude, low frequency waves (of the order of 5–10 Hz), which were observed mainly during diastole in horse experiments, has also been confirmed by the computer calculations. Similar calculations carried out for conditions simulating the dog and human coronary systems indicate that such oscillations become higher in frequency and lower in amplitude with decreasing animal size.

The growth of an unbounded, density-stratified, turbulent shearing layer in the presence of a gravity field is studied using the postulate of marginal instability. It is found, for a similarity mean velocity and density distribution, that after a rapid initial growth rate the growth slows asymptotically to zero as the Richardson number approaches a value of 1/4. Furthermore, the theory predicts a constant dominant turbulent eddy scale in all but the initial stages of growth of the turbulent shearing layer.

Both the general growth characteristics and the constant dominant turbulent eddy scale predicted by the theory are confirmed by experimental data.

A strict distinction is made between the two fundamental assumptions in the Stuart-Watson theory of nonlinear stability, one of which is that the amplitude of disturbance is sufficiently small, while the other is that the damping or amplification rate for an infinitesimal disturbance is small. This distinction leads to classification of the nonlinear stability theory into two asymptotic theories: the theory based on the first assumption can be applied to subcritical flows with Reynolds numbers away from the neutral curve, even to flows with no neutral curve, such as plane Couette flow or pipe Poiseuille flow, while the theory based on the second assumption is available only for Reynolds numbers and wavenumbers in the neighbourhood of the neutral curve. In the theory based on the first assumption the concept of trajectories in phase space, together with the method of eigenfunction expansion, is introduced in order to display nonlinear behaviour of the disturbance amplitude and to provide the most rational definition of the Landau constant available for classification of the behaviour patterns.

A theoretical study is presented of the spatial stability of flow in a circular pipe to small but finite axisymmetric disturbances. The disturbance is represented by a Fourier series with respect to time, and the truncated system of equations for the components up to the second-harmonic wave is derived under a rational assumption concerning the magnitudes of the Fourier components. The solution provides a relation between the damping rate and the amplitude of disturbance. Numerical calculations are carried out for Reynolds numbers R between 500 and 4000 and βR [les ] 5000, β being the non-dimensional frequency. The results indicate that the flow is stable to finite disturbances as well as to infinitesimal disturbances for all values of R and βR concerned.

Decaying grid turbulence was passed over a wall moving at the stream speed. For the high Reynolds number of the experiment, the field due to the wall constraint on the normal component of the velocity fluctuations is found to extend further into the flow than the influence of the viscous boundary condition on the tangential-component fluctuations. Measurements of the variances, length scales and spectra of the three velocity components of the turbulence are compared with the results of a previous experiment and with the theoretical predictions for an idealization of the flow. A simple model for some departures from the theory is proposed.

The stability of time-periodic flows in a circular pipe is investigated. The disturbance is assumed to be axially symmetric and to have a small amplitude, so that the governing differential equation is linear. Calculations are carried out for the first ten modes for a range of values of the frequency of the primary motion, of the wavenumber of the disturbance, and of the Reynolds number of the primary flow. In the ranges of the parameters for which the calculations have been carried out, the flows are found to be stable and, as for Stokes flows (von Kerczek & Davis 1974), it is conjectured that the flows under study here are stable for all frequencies and all Reynolds numbers.

The behaviour of a fully rough turbulent boundary layer subjected to favourable pressure gradients both with and without blowing was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Measurements of profiles of mean velocity and the components of the Reynolds-stress tensor are reported for both unblown and blown layers. Skin-friction coefficients were determined from measurements of the Reynolds shear stress and mean velocity.

An appropriate acceleration parameter Kr for fully rough layers is defined which is dependent on a characteristic roughness dimension but independent of molecular viscosity. For a constant blowing fraction F greater than or equal to zero, the fully rough turbulent boundary layer reaches an equilibrium state when Kr is held constant. Profiles of the mean velocity and the components of the Reynolds-stress tensor are then similar in the flow direction and the skin-friction coefficient, momentum thickness, boundary-layer shape factor and the Clauser shape factor and pressure-gradient parameter all become constant.

Acceleration of a fully rough layer decreases the normalized turbulent kinetic energy and makes the turbulence field much less isotropic in the inner region (for F equal to zero) compared with zero-pressure-gradient fully rough layers. The values of the Reynolds-shear-stress correlation coefficients, however, are unaffected by acceleration or blowing and are identical with values previously reported for smooth-wall and zero-pressure-gradient rough-wall flows. Increasing values of the roughness Reynolds number with acceleration indicate that the fully rough layer does not tend towards the transitionally rough or smooth-wall state when accelerated.

The purpose of the present paper is to reach some general conclusions on the motion of rigid particles in a homogeneous shear flow of a viscoelastic fluid. Under the basic assumption of nearly Newtonian slow flow, the creeping-motion equations for a second-order fluid with characteristic time constants κ0(2) and κ0(11) can be employed. It is shown that the κ0(2) contributions to the hydrodynamic force F and couple G depend upon the hydrodynamic force, couple and stresslet which act upon the particle in a Newtonian fluid (termed F(1), G(1) and S(1), respectively). Since this relation involves time derivatives of F(1) and G(1), a little reflexion is needed to realize that the modification of the classical Stokes law for steady translation in a quiescent fluid can have no κ0(2) term. Since no results of such generality are possible for the κ0(11) contributions we focus attention on transversely isotropic particles. Employing the concept of material tensors, the symmetry of such particles dictates the form these tensors adopt. This alone is sufficient to show that sedimentation in a quiescent fluid is accompanied by a change in orientation until a stable terminal orientation is attained. Depending upon the type of particle only one of the two orientations, axis of symmetry parallel or perpendicular to the external force, is stable. Another result concerns two-dimensional shear flow, for which we show that the symmetry axis has to drift through various Jeffery orbits until an equilibrium orientation is reached. While the orbits C = 0 and C = ∞ are equilibrium orbits for every transversely isotropic particle there may be a third such preferred orbit, which we denote by C*. In order for these orbits to be stable certain restrictions have to hold, showing that the orbits C = 0 and C* cannot both be stable. For the special case of a rigid tridumbbell of axis ratio s the orbit C* does not exist. If s > 1 the drift for this particle is into the orbit C = 0 while for s < 1 it is into the orbit C = ∞. This agrees qualitatively quite well with experimental results obtained for rods and disks. No quantitative comparison is possible; the particle shape influences the result quantitatively owing to its effect on the combination of the fluid parameters κ0(2) and κ0(11).

The migration of a rigid sphere in a two-dimensional unidirectional shear flow of a second-order fluid was considered by Ho & Leal (1976). It was found that the sphere would migrate in the direction of decreasing absolute shear rate. The present paper extends the previous results to a general quadratic flow, and also considers the case of a spherical drop.

A recent theoretical description of interactions between surface waves and currents in the ocean is extended to allow density stratification. The interaction leads to a convective instability even when the density stratification is statically stable. An unspecified random surface wave field is permitted provided that it is statistically stationary.

The instability can be traced to torques produced by variations of a ‘vortex force’. Non-diffusive instabilities produced by this mechanism in water of infinite depth are explored in detail for arbitrary distributions of the destabilizing force. Stability is determined by an eigenvalue problem formally identical to that determining normal modes of infinitesimal internal waves in fluid with a density profile that is not monotone and thereby has a statically unstable region. Some tentative remarks are offered about the problem when dissipation is allowed.

Application of the present theory to Langmuir circulations is discussed. Also, according to the present theory, internal wave propagation should be modified by the vortex force arising from the interaction between the surface waves and the current.

In Weinbaum et al. (1976) a simple new pressure hypothesis is derived which enables one to take account of the displacement interaction, the geometrical change in streamline radius of curvature and centrifugal effects in the thick viscous layers surrounding two-dimensional bluff bodies in the intermediate Reynolds number range O(1) < Re < O(102) using conventional Prandtl boundary-layer equations. The new pressure hypothesis states that the streamwise pressure gradient as a function of distance from the forward stagnation point on the displacement body is equal to the wall pressure gradient as a function of distance along the original body. This hypothesis is shown to be equivalent to stretching the streamwise body co-ordinate in conventional first-order boundary-layer theory. The present investigation shows that the same pressure hypothesis applies for the intermediate Reynolds number flow past axisymmetric bluff bodies except that the viscous term in the conventional axisymmetric boundary-layer equation must also be modified for transverse curvature effects O(δ) in the divergence of the stress tensor. The approximate solutions presented for the location of separation and the detailed surface pressure and vorticity distribution for the flow past spheres, spheroids and paraboloids of revolution at various Reynolds numbers in the range O(1) < Re < O(102) are in good agreement with available numerical Navier–Stokes solutions.