A unified linear viscous stability theory is developed for a certain class of stratified parallel channel and boundary-layer flows with Prandtl number equal to unity. Results are presented for plane Poiseuille flow and the asymptotic suction boundary-layer profile, which show that the asymptotic behaviour of both branches of the curve of neutral stability has a universal character. For velocity profiles without inflexion points it is found that a mode of instability disappears as η, the local Richardson number evaluated at the critical point, approaches 0.0554 from below. Calculations for Grohne's inflexion-point profile show both major and minor curves of neutral stability for 0 < η [les ] 0.0554; for \[ 0.0554 < \eta < 0.0773 \] there is only a single curve of neutral stability; and, for η > 0.0773, the curves of neutral stability become closed, with complete stabilization being achieved for a value of η of about 0·107.

The results of an experimental investigation of separation in oscillating laminar boundary layers is reported. Instantaneous velocity profiles obtained with multiple hot-wire anemometer arrays reveal that the onset of wake formation is preceded by the initial vanishing of shear at the wall, or reverse flow, throughout the entire cycle of oscillation. Correlation of the experimental data indicates that the frequency, Reynolds number and dynamic history of the boundary layer are the dominant parameters and oscillation amplitude has a negligible effect on separation-point displacement.

The buoyant rise of chimney plumes is discussed for relatively large distances from the source, where atmospheric turbulence is the dominant cause of mixing (rather than turbulence due to the plume's own upward motion). A simple theory is developed which shows a number of different shapes plumes can have under different atmospheric conditions (particularly in an unstable environment).

Experimental data are then presented, which were collected in the field near Toronto, with reasonably detailed supporting information on the atmospheric temperature structure. These (and earlier results) often show quite complex plume behaviour at large distances from the source, which can, however, be readily understood in terms of the simple theory presented.

A thermally conducting body floating in a fluid that is stably stratified by heat may develop unstable oscillations provided the body temperature shows a large enough time-lag relative to the fluid temperature. A gravitationally stable, non-Boussinesq fluid may itself become unstable in an oscillatory way through a similar diffusive time-lag. One case, that is investigated in the present work, occurs when the basic vertical temperature gradient β = dT/dz and the thermal expansion coefficient α vary in an opposite sense: β is large when α is small and vice versa. The variation in β is here assumed to be caused by internal heat sources and sinks.

If vertical oscillations are started in such a fluid temperature variations will be produced in the regions of large β but the buoyancy forces do not develop until these perturbations have diffused to regions of large α. With an appropriate lag, the buoyancy forces may give a positive work and the oscillations can grow.

Two models are investigated. The first one is a non-viscous two-layer model with β = 0, α = α0 in one layer and β = β0, α = 0 in the other layer. For this model analytical results are derived. The second model is more realistic, having continuous profiles β(z) and α(z), viscosity and horizontal boundaries. The case is studied by a numerical technique, solving the equations directly in time.

A discussion of the numerical method is given in an appendix by K. Holmaker.

The hydrodynamic stability of an ideal mixture of two viscous, dissimilar liquids contained between two concentric rotating cylinders is analyzed. The basic flow of the mixture is determined by coupling the mass and momentum equations with an equation for the equilibrium concentration distribution. Infinitesimal, axisymmetric disturbances are assumed, and the disturbance equations are written for the limiting case of large Schmidt numbers (no diffusion).

The presence of density and viscosity variations leads to a twelfth-order eigenvalue problem with two-point boundary conditions that has the appearance of a combined Taylor and density-stratified shear flow problem. A numerical technique is devised to determine the stability boundary and to calculate Taylor numbers and oscillation frequencies for different growth rates.

It is found that very small mean density gradients alter the critical Taylor number and that oscillations occurring in both the growing and neutral solutions are the dominant mode.

We consider the propagation of sound in a two-dimensional shear layer in a duct. Initially plane sound waves propagate in a subsonic flow whose steady velocity U(y) is in the axial direction and is a function of the normal co-ordinate alone. The initial-value problem in time and space is solved within the framework of a perturbation scheme. Far from the wave front and for large time the refractive effects are considerable. However, the present results indicate that standing wave type patterns lead to a strong dependence on axial location in the duct. The paper also points out the Weakness inherent in theories which attempt to treat the refraction problem without considering the source conditions.

Various theoretical aspects of peristaltic motion have attracted considerable attention in the recent literature. There also exists a difference of opinion concerning the definition of peristaltic reflux. Thus far, there has been no completely satisfactory experimental verification of any of the theoretical analyses. The present article describes some details of an experimental work which was carried out to verify the theoretical analysis of peristaltic transport in a two-dimensional channel with one fixed wall and one flexible wall on which a travelling sine wave is imposed. An approximate correction for finite width was introduced. Comparison of the theoretical and experimental results shows a good agreement and gives verification to the theoretical analysis. In the light of the experimental results, a discussion of the different definitions of peristaltic reflux is presented.

The influence of large variations of viscosity on convection in a layer of fluid heated from below has been investigated. Solutions for the flow and temperature fields were obtained numerically assuming infinite Prandtl number, free-surface boundary conditions, and two-dimensional motion of fixed horizontal wavelength. The effects of a temperature-dependent and a depth-dependent viscosity were each studied; calculations were also carried out using a temperature- and depth-dependent viscosity model appropriate to the earth's mantle.

A quasi-one-dimensional non-linear model is developed for the axisymmetric dynamics. Streaming is coaxial with a cylindrical ‘wall’ supporting a potential having a linear axial dependence. In addition to a tangential field due to an axial current, the stream surface supports charges in proportion to the stream-wall potential difference; hence it is driven by normal and shear electric stresses. Free charge and polarization waves compete with the destabilizing effect of capillarity. With supercritical steady flow (the local jet velocity exceeds the wave velocity), it is found that the stream accelerates or decelerates in accordance with whether an equivalent longitudinal force density is respectively positive or negative. With subcritical flow, the effect of the force is reversed. Experiments demonstrate accelerating and decelerating flow régimes. Model and experiment are in agreement with regard to choking at a critical radius, and the dependence of radius and potential on position. Hysteretic switching between flow régimes is obtained by adjustment of stream and wall potentials, and is explained in terms of the model.

A schematic picture of the structure of a mature hurricane is hypothesized. The heat and moisture transfer, the boundary-layer dynamics and the overall dynamic and thermodynamic balances are analysed crudely, but sufficiently accurately to provide support for the hypothesis.

We consider the two-dimensional flow produced by the slow horizontal motion of a vertical plate of height 2b through a vertically stratified (ρ = ρ0(1 - βz)) non-diffusive viscous fluid. Our results are valid when U2 [Lt ] Ub/ν [Lt ] 1, where U is the speed of the plate and ν the kinematic viscosity of the fluid. Upstream of the body we find a blocking column of length 10−2b4/(Uν/βg. This column is composed of cells of closed streamlines. The convergence of these cells near the tips of the plate leads to alternate jets. The plate itself is embedded in a vertical shear layer of thickness (Uν/βg)1/3. In the upstream portion of this layer the vertical velocities are of order U and in the downstream portion of order Ub/(Uν/βg)1/3 ([Gt ] U). The flow is uniform and undisturbed downstream of this layer.

This paper presents a laboratory study of the dynamic properties of air flow over small wind-generated water waves. On the basis of measurements of mean velocity profiles, turbulent intensity profiles and energy spectra, the detailed structure of turbulent wind immediately above and between the crests of progressive water waves has been examined.

The velocity sensor (a hot-wire anemometer) was fastened to a self-adjusting positioner to measure instantaneous air velocities at a fixed distance from a moving water surface. The waves had a dominant frequency, 2·4 Hz, and a ratio of wave celerity and air friction velocity close to one. With the aid of a digital computer, the desired parameters of air flow were obtained by a statistical technique which was developed to sample and average simultaneous recordings of water surface displacements and instantaneous air velocities.

The results of the wind field measurements over representative waves indicate that, on the average, the air flow separates from the wavy water surface just behind crests, and reattaches somewhere on the windward face of the next wave. The measured turbulent quantities consistently show the characteristics of separated air flow. The separation phenomenon suggests that, without some modification, the Benjamin-Miles shearing flow mechanism is inapplicable to the growth of fully-developed small water waves, at least when the ratio of the phase speed to air friction velocity is of order unity. The observed flow configuration tends to support the separation mechanism of energy transfer originally outlined by Jeffreys and later explored further by Stewart and Deardorff.

Mean properties of the turbulent air flow referred to the mean water level were obtained by continuous sampling of the air flow over many waves with a sensing probe, either at a fixed distance from the mean water level (fixed probe measurement) or at a constant distance from the moving water surface (moving probe measurement). It was found that for continuously averaged measurements, the fixed probe yielded results which deviate less from the local mean than the moving probe results. This holds for the mean velocity distributions and especially for the turbulent quantities.