A solution has been found for the transient behaviour of resonant growing standing waves by using a perturbation expansion. Comparison with laboratory experiments as well as a numerical nonlinear solution of the same problem leads to the conclusion that: (i) the transient behaviour and the nonlinear tendency of the standing waves are described well by the analytic expression; (ii) the numerical results describe the solution very well until the wave starts to break; (iii) from the laboratory experiments and the numerical results, the standing internal gravity waves break owing to local gravitational instability at a critical amplitude which is similar to the one predicted by the expansion theory; (iv) the critical amplitude seems to be the maximum amplitude that a wave can reach; (v) when the generation of turbulence is violent, the small eddies begin forcing a secondary flow characterized by layers of strong jets separated by patches of turbulence.

Convective motions in rectangular boxes with one side horizontal have been studied. The critical Rayleigh numbers were determined. In most cases cell patterns with rolls parallel to the shorter side wall of the rectangular box were observed. The results have been compared with the known theoretical results of Davis (1967). In general, good agreement has been found.

Data for the fluctuating mass-transfer coefficient to point electrodes on the surface of a rotating disk are presented for transition and turbulent flow, along with analysis of the energy spectrum. The results corroborate previous evidence of standing vortices on the surface in the transition region. It is shown that the electrochemical method gives a more sensitive probe of flow instabilities than has been possible previously; the transition region is found to be wider than has been previously thought to be and lies between roughly Re = 1·7 × 105 and 3·5 × 105, where Re = r2ω/v is the Reynolds number, ω being the angular velocity of the disk (in rad/s) and v the kinematic viscosity. As the Reynolds number is increased, the stationary vortices in the transition region propagate primarily with a frequency matching that of the disk speed. After a peak energy has been reached at Re = 2·6 × 105, the vortices break down into a fully developed turbulent flow.

Salt fingering across a density interface produced by sugar and salt is investigated experimentally for varying values of initial concentrations and for times sufficiently long to observe the régimes of growth, equilibrium and final decay. Simultaneous measurements of sugar and salt concentrations and interface geometry are made. Calculations based on Stern's collective instability model allow explicit evaluation of the coefficients of the $\frac{4}{3}$-law for the sugar flux in the form suggested by Stern & Turner (1969) for the equilibrium régime. The results are verified by the experimental data. Predictions of the finger wavelengths from this model are in general agreement with the results of previous authors, while the flux-law coefficient is an order of magnitude smaller. It is concluded that the collective instability mechanism is an adequate physical description of the salt-finger mechanism.

The stability of a helical vortex filament of finite core and infinite extent to small sinusoidal displacements of its centre-line is considered. The influence of the entire perturbed filament on the self-induced motion of each element is taken into account. The effect of the details of the vorticity distribution within the finite vortex core on the self-induced motion due to the bending of its axis is calculated using the results obtained previously by Widnall, Bliss & Zalay (1970). In this previous work, an application of the method of matched asymptotic expansions resulted in a general solution for the self-induced motion resulting from the bending of a slender vortex filament with an arbitrary distribution of vorticity and axial velocity within the core.

The results of the stability calculations presented in this paper show that the helical vortex filament has three modes of instability: a very short-wave instability which probably exists on all curved filaments, a long-wave mode which is also found to be unstable by the local-induction model and a mutual-inductance mode which appears as the pitch of the helix decreases and the neighbouring turns of the filament begin to interact strongly. Increasing the vortex core size is found to reduce the amplification rate of the long-wave instability, to increase the amplification rate of the mutual-inductance instability and to decrease the wavenumber of the short-wave instability.

A detailed study has been made of the solutions to cone boundary-layer equations in the symmetry plane in order to increase understanding of the mathematical nature and physical meaning of these solutions. A typical set of symmetry-plane solutions is presented. Included in this set are various solution branches not previously published. A double-valued solution curve is found which has not been studied prior to this time except at one trivial point. The extension of an existing solution branch through a removable singular point has also been accomplished. The solutions presented are categorized according to whether they are dependent on or independent of the boundary layer outside the symmetry plane. The region in which no solutions to the usual symmetry-plane equations exist is examined. Solutions in which the usual boundary-layer model predicts that conservation of mass is not satisfied at the symmetry plane are discussed. Non-analytical behaviour at the symmetry plane is also investigated. In both of these cases a boundary region exists at the symmetry plane.

Semi-infinite double rows of vortices are used to study the periodic wake of both oscillating and stationary two-dimensional bodies immersed in a uniform incompressible stream. Analytical expressions for the induced Velocities on the body, for trails with constant spacing, which are valid for small values of the oscillation amplitude are presented while, for the general case of vortex shedding, an iterative procedure for the representation of trails of variable spacing is developed and used. Vortex streets due to oscillating bodies are obtained as a function of three non-dimensional parameters: the Strouhal number (initial spacing ratio), a non-dimensional vortex strength and the downstream spacing ratio. Criteria establishing when such trails are expected to widen, become narrow or stay of constant width are presented, as well as expressions for the induced velocities.

The trails and their induced velocities enable the calculation of the vortex strength from measurable quantities. Thus they can serve as a method for estimating the hydrodynamic forces on the airfoil due to large amplitude oscillations, such as those observed in the propulsive movements of fish and cetaceans, as well as the small amplitude oscillations due to hydroelastic interactions.

Experiments have been conducted to determine the effect of density stratification upon certain characteristic features of so-called Taylor columns. The interior structure of the homogeneous Taylor column is first of all described and compared with flow patterns obtained when the fluid is stratified. Qualitative features of the horizontal and vertical motion (in particular, the attenuation with height of the distortion created by the obstacle) are then described for values of the stratification parameter S (defined as S = N/2 Ω, whereN and Ω are the Brunt-Väisälä and rotation frequencies respectively) in the range 0 [les ] S [les ] 0·24. The effect of density stratification upon, specifically, the length of the column is then described. A working definition for the existence of a Taylor column in a given experimental situation is formulated, enabling the strength of the column to be quantified at a particular height above the obstacle. Using this method the column length is measured as a function of S in the range 0 [les ] S [les ] 0·24. It is shown that even very slight stratification is sufficient to produce noticeable modification of all aspects of the flow. In particular, the column length is considerably reduced by weak stratification.

The steady, two-dimensional motion which can occur when a body moves horizontally at large Richardson number is examined. Theoretical evidence is presented for two propositions: (i) The nature of the motion depends on whether the vertical thickness of the body is large compared with an intrinsic length scale of the motion. (ii) If the body is sufficiently thick, then diffusion or heat conduction are important, even if the Schmidt or Prandtl number is large. The notion of ‘near-similar’ solutions (§4) is used to obtain a description of the motion past a thick body which is likely to approximate the real motion everywhere except fairly close to the body surface (§5). It predicts a very long wake, at the core of which is a blocking column, both fore and aft of the body (§5). The same prediction is implied for the two-dimensional Taylor column in a rotating system (§6).

Two-dimensional upstream and downstream wakes are produced by extremely slowly moving cylinders in a tank containing a linearly stratified salt solution. The upstream and downstream wakes appear to be of comparable strength, consistent with the symmetry predicted by theories that take account of density diffusion as well as viscosity. This contrasts with the quasi-non-diffusive régime recently studied experimentally by Browand & Winant (1972). The present velocity profiles are essentially similar to those predicted by diffusion theories, althought the magnitudes of the velocities appear to be greatly attenuated by the proximity of the upstream and downstream walls.

Some properties of trapped oscillations in an inviscid rotating fluid were studied by Stewartson (1971, 1972). In this paper the modifications necessary to allow for a small viscosity in the fluid are discussed. It is found that concentrated disturbances of the kind used in ray theory are only possible if the rays are thought of as emanating from two sources outside the fluid and at opposite ends of the ray. Otherwise the ray must have a lateral tail, which vitiates the notion of a ray. The double-source character of rays is preserved at reflexions except when at glancing incidence. In this case a substantial part of the ray strength is lost and may give rise to a lateral tail if uncompensated. The focusing of the rays at the limit cycle is also discussed and shown to lead to a catastropic loss of energy, so that a free oscillation if set up rapidly decays. A simple forced oscillation is considered and shown to lead to weak resonances in the bands of trapped oscillations.