It is shown that two-dimensional MHD turbulence is in certain respects closer to three-dimensional than to two-dimensional hydrodynamic turbulence. A second-order closure indicates that:

1. at zero viscosity and magnetic diffusivity, a singularity appears at a finite time;

2. there is an energy cascade to small scales and an inverse cascade of squared magnetic potential, in agreement with a conjecture of Fyfe & Montgomery (1976);

3. small-scale magnetic energy acts like a negative eddy viscosity on large-scale magnetic fields;a

4. (iv) upon injection of magnetic energy, a stationary state is obtained which has zero magnetic energy for a positive magnetic diffusivity λ (anti-dynamo theorem); however, this stationary state is preceded by a very long non-zero magnetic energy plateau which probably extends to infinite times as λ → 0.

It is suggested that direct numerical simulation of the two-dimensional MHD equations with high resolution (a 5122 or 10242 grid) could lead to a better understanding of the small-scale structure of fully developed turbulence, especially questions of intermittency and geometry.

The authors present the matched asymptotic expansion type of solution for the unsteady viscous incompressible flow past a sphere. Most of the analysis is developed under the assumption that a constant rectilinear velocity is suddenly imparted to a sphere in an otherwise quiescent infinite body of fluid. The Reynolds number based on that velocity is taken to be small, and the analysis is then extended to other transient flows that satisfy this requirement. Evidently in the unsteady cases under discussion one can recognize inner and outer regimes. The leading terms in the expansions representing the flow in these are governed by the unsteady Stokes and the hitherto unreported unsteady Oseen equations. The streamline patterns calculated show the ‘birth’ of a ring vortex close to the equator and its gradual migration downstream and outwards. This result is also verified qualitatively by a crude experiment.

A new interpretation of a nonlinear wind-wave system is proposed. It is proposed that, for steady wind blowing in one direction, a nonlinear wind-wave system can be completely characterized, to a good first approximation, by a single nonlinear wave train having a carrier frequency equal to that of the dominant frequency in the wind-wave spectrum. In this model, the spectral components of the wind-wave system are not considered a random collection of free waves, each obeying the usual dispersion relation, but are effectively non-dispersive bound-wave components of a single dominant wave, travelling at the speed of the dominant wave. To first order, the nonlinear wind-wave system is considered to be a coherent bound-wave system which propagates energy only at the group velocity of the dominant wave and is governed by nonlinear self-interactions of the type found in amplitude-modulated wave trains. The role of short free waves in the system is discussed. Results of laboratory experiments performed by the authors and by Ramamonjiarisoa & Coantic (1976) are found to provide evidence supporting the applicability of such a model to wind waves under virtually all laboratory conditions. Preliminary consideration is given to possible application of the model to oceanic wind waves and conditions are identified for which the model would be most likely to apply.

Previous measurements in the moderate to small Reynolds number range of isotropic turbulence have all shown the skewness factor $S\equiv -{\overline{(\partial u/\partial x)^3}}/[\overline{(\partial u/\partial x)^2}]^{\frac{3}{2}}$ of the streamwise velocity derivative to increase with decreasing Reynolds number. This ‘paradoxical’ trend was found for 150 ≥ Rλ ≥ 4. New data covering the range 4 ≥ Rλ ≥ 1 show a maximum S for Rλ between 4 and 3 and a rapid decrease for Rλ < 2.

The growth of small disturbances in the incompressible axisymmetric wake of a slender body of revolution has been studied experimentally. The experiments were performed in a running water channel at a Reynolds number of 3600 based on the body diameter and free-stream velocity, without any artificial stimulation of the wake. Digital techniques have been used to analyse the output signals of a multichannel hot-film anemometer system.

Analysis of the mean velocity profiles and the velocity fluctuations shows that the wake can be divided into three regimes: the near wake or adjustment region, a region of locally parallel flow, and the far wake. The near wake is characterized by the adjustment of the mean velocity profile from that in the boundary layer of the body to the wake profile. At the same time, the structure of the disturbances in the boundary layer seems to adjust to a different structure in the wake. Large velocity gradients in both the streamwise and the radial direction are present in this region. In the region of locally parallel flow, a helical mode disturbance is superseded by a mode which appears to be mostly a planar oscillation of higher frequency and amplification rate. Higher-order harmonics of dominant frequency components have been identified in these experiments. The far wake is the region in which nonlinear interactions appear to predominate. The experimental measurements and hydrogen bubble photographs indicate the presence of large scale transverse disturbances in this region, associated with roll-up of the fluid.

In discussing turbulent shear layers, experimentalists have divided the flow into a turbulent region, which is vortical, and a non-turbulent region, which is irrotational but unsteady. This paper introduces a theoretical method of decomposing the velocity field into potential and vortical components that is compatible with the experimentalists’ viewpoint. Specifically, only potential motions will exist in the non-turbulent region, while the decomposition shows that the turbulent region consists of both potential and vortical motions. The kinematic decomposition used is called a potential/complex-lamellar decomposition. Compared with the standard Helmholtz decomposition, the complex-lamellar decomposition is not widely known, and this article includes a discussion of its properties and characteristics. The vector components in this decomposition may be represented by three scalar potentials: ϕ, ψ and χ. One of the important physical interpretations of the potentials concerns vortex lines. Vortex lines are defined by the intersection of a surface ψ = constant with a surface χ = constant. Since these surfaces are a function of time, this establishes a sound kinematic theory for following the history of vortex lines in a turbulent or viscous flow.

We consider the problem of mass injection from a flat plate into uniform supersonic flow when the boundary layer is blown off at the leading edge to form a thin free shear layer separating the inviscid injectant layer from the external flow. The injection is moderate, i.e. of the same order of magnitude as the velocity of entrainment into the base of the shear layer. For simplicity, we consider similarity blowing, proportional to x*−½, where x* is measured along the plate from the leading edge. We find that the solution in the injectant region, based on initial conditions at the leading edge, is non-unique unless fixed by downstream conditions. When injection is cut off at a finite distance along the plate, this enables us to find a solution to the problem in which the shear layer eventually reattaches to the plate and for which the pressure and the height of the injectant layer are continuous at cut-off. The study provides a partial connexion between the earlier studies of weak blowing in which the boundary layer is not blown off and of strong blowing for which the boundary layer is blown off and the entrainment into the shear layer is negligible.

The temperature and velocity fields in a round heated jet were investigated in detail. Both conventional measurements and conditional measurements (zone averages and point averages) were performed. The probability density functions of the lengths of turbulent and non-turbulent durations were also measured. Filtered correlation measurements show that large-scale turbulent motions were responsible for the bulk of momentum and heat transport, and also that small scales were more efficient in transporting heat than in transporting momentum. In no case was heat transported further or more than momentum, however. These results are discussed in detail, particularly with regard to the entrainment. Conservation equations for turbulent-zone variables and the intermittency factor are derived and a model for some of the resulting higher-order correlations is suggested. An exact equation for the intermittency function is presented.

A nonlinear study of harbour resonance is carried out for a rectangular bay indented from a straight coast. Boussinesq equations with nonlinearity and dispersion are used. Simplifying approximations are made for a narrow bay to decouple the nonlinear problem in the bay from the approximately linear problem in the ocean. Harmonic generation in the bay is studied numerically. Experiments for three different bay lengths and three amplitudes are compared with the numerical theory. The relative importance of entrance loss and boundary-layer dissipation to nonlinearity is estimated.

Small amplitude, axially symmetric waves in a thin-walled viscoelastic tube containing a viscous compressible fluid are considered. Previous authors have found two modes of propagation for such waves but have studied them only in the low frequency, long wavelength limit. We show that there are infinitely many modes and study them at all frequencies. The appropriate dispersion equation was derived previously (Rubinow & Keller 1971) and analysed for an inviscid fluid. Now it is analysed for a viscous fluid. Asymptotic formulae for the propagation constant k are obtained for both low and high frequencies and for various ranges of the parameters characterizing the tube and the fluid. Special attention is paid to the case of a rigid tube and to parameter values that characterize the flow of blood in mammalian arteries. In addition, numerical results are obtained which complement the asymptotic formulae. Graphs of the velocity c vs. the frequency ω are presented for various modes and for various ranges of the parameters. Transmission-line equations and formulae for the impedance and compliance of the fluid-tube system are obtained, together with asymptotic and numerical results.