A joint experiment to study microscale fluctuations of atmospheric pressure above surface gravity waves was conducted in the Bight of Abaco, Bahamas, during November and December 1974. Field hardware included a three-dimensional array of six wave sensors and seven air-pressure sensors, one of which was mounted on a wave follower. The primary objectives of the study were to resolve differences in previous field measurements by Dobson (1971), Elliott (1972b) and Snyder (1974), and to estimate the vertical profile of wave-induced pressure and the corresponding input of energy and momentum to the wave field.

Analysis of a pre-experiment intercalibration of instruments and of 30 h of field data partially removes the discrepancy between the previous measurements of the wave-induced component of the pressure and gives a consistent picture of the profile of this pressure over a limited range of dimensionless height and wind speed. Over this range the pressure decays approximately exponentially without change of phase; the decay is slightly less steep than predicted by potential theory. The corresponding momentum transfer is positive for wind speeds exceeding the phase speed. Extrapolation of present results to higher frequencies suggests that the total transfer is a significant fraction of the wind stress (0·1 to 1·0, depending on dimensionless fetch).

Analysis of the turbulent component of the atmospheric pressure shows that the ‘intrinsic’ downwind coherence scale is typically an order-of-magnitude greater than the crosswind scale, consistent with a ‘frozen’ turbulence hypothesis. These and earlier data of Priestley (1965) and Elliott (1972c) suggest a horizontally isotropic ‘intrinsic’ turbulent pressure spectrum which decays as k−ν where k is the (horizontal) wave-number and ν is typically −2 to −3; estimates of this spectrum are computed for the present data. The implications of these findings for Phillips’ (1957) theory of wave growth are examined.

Steady solutions in the form of two-dimensional rolls are obtained numerically for convection in a horizontal layer of a low-Prandtl-number fluid heated from below. Prandtl numbers in the range 0·001 [les ] P [les ] 0·71 are investigated for Rayleigh numbers between the critical value, R = 1708, and R = 20,000 in the case of rigid boundaries. The calculations reveal that the convective heat transport is relatively independent of the Prandtl number at Rayleigh numbers greater than a finite critical value R2 of the order of 5 × 103. At R = 10,000 the convective heat transport varies by only about 30% for Prandtl numbers in the range investigated. As the Rayleigh number is increased above the critical value R2, the streamlines of the convection flow become circular, independent of the horizontal wavelength as long as the latter is larger than or about equal to twice the height of the layer.

An approximate solution of two-dimensional convection in the limit of low Prandtl number is presented in which the buoyancy force is balanced by the inertial terms. The results indicate that inertial convection becomes possible when the Rayleigh number exceeds a critical value of about 7 × 103. Beyond this value the velocity and temperature fields become independent of the Prandtl number except in thin boundary layers. The convective heat transport approaches the law Nu = 0·175 R¼ for the Nusselt number Nu. These results are in reasonably close agreement with the numerical results described in the preceding paper by Clever & Busse (1980).

Convection flows have been systematically observed in a layer of fluid between two isothermal horizontal boundaries. The working fluid was a nematic liquid crystal, which exhibits a liquid–liquid phase change at which latent heat is released and the density changed. In addition to ordinary Rayleigh–Bénard convection when either phase is present alone, there exist two distinct types of convective motions initiated by the unstable density difference. When a thin layer of heavy fluid is present near the top boundary, hexagons with downgoing centres exist with no imposed thermal gradient. When a thin layer of light fluid is brought on near the lower boundary, the hexagons have upshooting centres. In both cases, the motions are kept going once they are initiated by the instability due to release of latent heat. Relation of the results to applicable theories is discussed.

The linear stability of the spiral motion induced between concentric cylinders by an axial pressure gradient and independent cylinder rotation is studied numerically and experimentally for a wide-gap geometry. A three-dimensional disturbance is considered. Linear stability limits in the form of Taylor numbers TaL are computed for the rotation ratios μ, = 0, 0·2, and -0·5 and for values of the axial Reynolds number Re up to 100. Depending on the values of μ and Re, the disturbance which corresponds to TaL can have a toroidal vortex structure or a spiral form. Aluminium-flake flow visualization is used to determine conditions for the onset of a secondary motion and its structure at finite amplitude. The experimental results agree with the predicted values of TaL for μ [ges ] 0, and low Reynolds number. For other cases in which agreement is only fair, apparatus length is shown to be a contributing influence. The comparison between experimental and predicted wave forms shows good agreement in overall trends.

The spatial stability of the plane, two-dimensional jet flow to infinitesimal disturbances is investigated by taking into account the effects of transverse velocity component and the streamwise variations of the basic flow and of the disturbance amplitude, wave-number and spatial growth rate. This renders the growth rate dependent on the flow variable as well as on the transverse and streamwise co-ordinates. Growth rates for the energy density of the disturbance and the associated neutral curves are provided as a function of the streamwise co-ordinate. Variation of growth rate of the disturbance stream function and streamwise component of velocity with the transverse co-ordinate is also given for different disturbance frequencies and streamwise locations. Results are compared with those for the parallel-flow stability analysis, and also with those for an analysis that accounts for only some of the non-parallel effects. It is found that the critical Reynolds number based on the growth of energy density of the disturbance depends on the streamwise co-ordinate and lies within the range (around 20) found experimentally, while the parallel-flow theory yields a rather low value of 4·0.

It has been proposed that Langmuir circulations arise as an instability of the equations describing the Eulerian-mean flow in bodies of water supporting surface waves and subject to an applied wind stress. In infinitely deep density-stratified water, the solution of an appropriate initial-value problem is a unidirectional, time-dependent current. The stability of this current to two-dimensional (roll) disturbances is investigated by an energy analysis and by linear theory. It is found that the energy stability estimates and linear stability limits are very close, showing that subcritical instability, if it occurs, is limited to a very narrow region in parameter space. According to the present results, conditions typically occurring in the ocean are highly unstable to the Langmuir circulation instability.

A theory is developed to describe the weakly nonlinear dynamics which applies in the simultaneous presence of several, long, baroclinic waves. The geometry is flat (i.e. β = 0) and dissipation is modelled by Ekman friction in the context of the quasi-geostrophic two-layer model. Three main problems are discussed.

1. For free, unstable waves it is shown that the wave which is realized in finite amplitude is not the linearly most unstable wave. Rather a longer wave, capable of achieving the single largest steady amplitude, is favoured in the competition for the potential energy of the basic state. This result is shown necessary if the end state is steady and numerous numerical calculations indicate the pre-eminence of the same wave if the final state is vacillatory. The notion of conjugate waves, capable of identical final amplitude, is also discussed.

2. If the free waves are subject to time-varying supercriticality so that intervals of stability ensue, the response is asymmetric over the period of the forcing. Sufficiently rapid ‘seasonal’ forcing leads to long-term aperiodic response.

3. If each wave in the spectrum is directly forced a wave hysteresis phenomenon occurs. Sudden jumps in the wave amplitude at critical values of the forcing are intrinsic to the wave response. Again, sufficiently rapid wave forcing produces an aperiodic response.

The forced wave problem exhibits multiple equilibria. Each solution branch corresponds to a different dominant wave. The determination of the realized branch depends on the relative stability criteria developed for the free waves.

Nonlinear thermal convection between two stress-free horizontal boundaries is studied using the modal equations for cellular convection. Assuming a large Rayleigh number R the boundary-layer method is used for different ranges of the Prandtl number σ. The heat flux F is determined for the values of the horizontal wavenumber a which maximizes F. For a large Prandtl number, σ [Gt ] R⅙(log R)−1, inertial terms are insignificant, a is either of order one (for $\sigma \geqslant R^{\frac{2}{3}}$) or proportional to $R^{\frac{1}{3}}\sigma^{-\frac{1}{2}}$ (for $\sigma \ll R^{\frac{2}{3}}$) and F is proportional to $R^{\frac{1}{3}}$. For a moderate Prandtl number, \[ (R^{-1}\log R)^{\frac{1}{9}} \ll \sigma \ll R^{\frac{1}{6}}(\log R)^{-1}, \] inertial terms first become significant in an inertial layer adjacent to the viscous buoyancy-dominated interior, and a and F are proportional to R¼ and \[ R^{\frac{3}{10}}\sigma^{\frac{1}{5}} (\log\sigma R^{\frac{1}{4}})^{\frac{1}{10}}, \] respectively. For a small Prandtl number, $R^{-1} \ll \sigma \ll (R^{-1} \log R)^{\frac{1}{9}}$, inertial terms are significant both in the interior and the boundary layers, and a and F are proportional to ($R \sigma)^{\frac{9}{32}} (\log R\sigma)^{-\frac{1}{32}}$ and ($R \sigma)^{\frac{5}{16}} (\log R \sigma)^{\frac{3}{16}}$, respectively.

In this paper it is shown that layered double-diffusive convection of a fluid within a porous medium is possible. A thin ‘diffusive’ interface was observed in a Hele Shaw cell and in a laboratory porous medium, with salt and sugar or heat and salt as the diffusing components. Heat–salt and salt–sugar fluxes through two-layer convection systems were measured and are compared with predictions of a model. For the thermohaline system the salt and heat buoyancy fluxes are approximately in the ratio r ≃ ετm½, where ε is the porosity and Tm is the appropriate ratio of diffusivities. The behaviour of the heat flux is explained in terms of a coupling between purely thermal convection within each convecting layer and diffusion through the density interface. Salinity gradients are important only within the interface. The presence of a ‘diffusive’ interface in the Wairakei geothermal system is postulated. The ratio of heat and salt fluxes (that can be estimated from existing observations) through this convection system is consistent with the laboratory flux ratio.

Axisymmetric numerical solutions of the Navier–Stokes equations for flow between rotating cylinders are obtained. The stability of these solutions to non-axisymmetric perturbations is considered and the results of these calculations are compared with recent experiments.

We consider a blob of Newtonian fluid sandwiched in the narrow gap between two plane parallel surfaces. At some initial instant, its plan-view occupies a given, simply connected domain, and its growth as further fluid is injected at a number of injection points in its interior is to be determined. It is shown that certain functionals of the domain of a purely geometric character, infinite in number, evolve in a predictable manner, and that these may be exploited in some cases of interest to yield a complete description of the motion.

By invoking images, these results may be used to solve certain problems involving the growth of a blob in a gap containing barriers. Injection at a point in a half-plane bounded by a straight line, with an initially empty gap, is shown to lead to a blob whose outline is part of an elliptic lemniscate of Booth for which there is a simple geometrical construction. Injection into a quarter-plane is also considered in some detail when conditions are such that the image domain involved is simply connected.

Two examples of unsteady, axisymmetric, separated flows are studied: unbounded oscillatory flow around a disk and bounded oscillatory flow through a sharp-edged orifice. Calculations are made assuming that the flow is inviscid and that the shed vortex sheets can be represented by sequences of discrete vortex rings. The solid bodies (i.e. the disk or the orifice and bounding tube) are also represented by a distribution of bound discrete vortex rings whose strengths are chosen to satisfy the Neumann or zero normal velocity boundary condition.

The results of flow visualization experiments and, for the orifice, pressure drop measurements are also reported. In general, the gross properties of the flows are predicted accurately.

A new family of solutions to the steady Euler equations corresponding to spatially periodic states of a free shear layer is reported. This family bifurcates from a parallel shear layer of finite thickness and uniform vorticity, and extends continuously to a shear layer consisting of a row of concentrated pointlike vortices. The energetic properties of the family are considered, and it is concluded that a vortex in a row of uniform vortices produced by periodic roll-up of a vortex sheet must have a major axis of length approximately 50% or more of the distance between vortex centres; it is also concluded that vortex amalgamation events tend to reduce vortex size relative to spacing. The geometric and energetic properties of the solutions confirm the mathematical basis of the tearing mechanism of shear-layer growth first proposed in an approximate theory of Moore & Saffman (1975).

A discrete vortex method was used to analyse the separated non-steady flow about a cambered airfoil. The foil flow modelling is based on the thin lifting-surface approach, where the chordwise location of the separation point is assumed to be known from experiments or flow-visualization data. Calculated results provided good agreement when compared with the post-stall aerodynamic data of two airfoils. Those airfoil sections differed in the extent of travel of the separation point with increasing angle of attack. Furthermore, the periodic wake shedding was analysed and its time-dependent influence on the airfoil was investigated.

A cylinder filled with a viscous, incompressible fluid is in an initial state of rigid-body rotation about its axis of symmetry. If the container is brought to rest impulsively, the resulting unsteady spin-down flow may be subject to sidewall instabilities due to an imbalance between centrifugal and pressure gradient forces. These instabilities are examined numerically using a finite-difference simulation to integrate the axisymmetric Navier–Stokes equations for a variety of aspect ratios and Reynolds numbers. The Taylor–Görtler vortex-wavelength spectrum, the torque and the angular momentum histories are calculated. Criteria for the onset time for instability and the spin-down time are given. The effects of the enhanced mixing due to instability on the spin-down characteristics and torque are discussed. The results are compared with experiment.

In recent comparative measurements using a burst-counter type laser velocimeter and a hot-wire anemometer to assess the capabilities of the velocimeter (e.g. Barnett & Giel 1976; Lau, Morris & Fisher 1979), it was found that the laser velocimeter held good promise as an instrument for turbulence research, especially in high speed, high temperature flows where a hot-wire cannot be used. The axial mean velocities obtained with the LV compared very well with hot-wire measurements. Similarly, the characteristic shapes of the spectra and probability density distributions of the velocity fluctuations were faithfully reproduced. The trends in the distributions of the various turbulence characteristics (e.g. turbulence intensity, velocity covariances, skewness and kurtosis) in a given flow field were identical to those obtained with hotwires. The one significant difference between LV and hot-wire results was the magnitudes of the turbulence level. Since the LV results were obtained with the help of the latest validation and discrimination techniques (Asher 1973), which have now become standard equipment (Durst, Melling & Whitelaw 1976), such a discrepancy was unexpected. The reason for the discrepancy is now fairly clear and a method has been suggested by Whiffen, Lau & Smith (1978) on how to eliminate the error. But the approach is lengthy and time-consuming. This paper describes a method which effectively accomplishes the same end with less effort.

For small-amplitude barotropic wave motion in a shallow fluid, Moore (1970) found that the associated mean mass transport is geostrophic, but otherwise arbitrary in the absence of friction. We show how weak friction, or starting the motion from rest, determines the mass transport by restricting circulation around closed geostrophic (f/h) contours. The resulting transport is quadratic in oscillatory quantities and depends on the friction type, but not on its (weak) magnitude. Comparison is made with earlier results in particular geometries. A tendency for anticyclonic circulation around shallow regions is found, and extends to large-amplitude oscillations where particle excursions exceed the topographic length scale. We suggest that numerical schemes for calculating tidal residuals should conserve mass and vorticity.

This paper employs continuum theory to examine the onset of a particular type of cellular thermal instability in a sample of nematic liquid crystal confined between two infinite, horizontal flat plates when subjected to a vertical temperature gradient. We consider the case in which the anisotropic axis is initially uniformly aligned perpendicular to the plates. Using Chebyshev polynomials, accurate numerical solutions for the critical temperature gradient are obtained and the variation of this quantity with a uniform magnetic field applied vertically across the plates is investigated. In particular we obtain the value of the magnetic field at which the nature of the instability changes from an oscillatory type to a stationary one.

The dynamic effects of an alternating magnetic field on containers of conducting fluid are investigated in two special cases: (i) an infinitely long circular cylinder in a uniform magnetic field normal to the generators; (ii) a truncated circular cylinder in a uniform magnetic field parallel to the axis. Neglecting the motion effects in Maxwell's equations, the problem is conveniently decoupled into electromagnetic and dynamic parts. Using either analytical or numerical solutions of the electromagnetic equations, the electromagnetic forces are calculated and introduced in the motion equations. In the first case, asymptotic solutions of the Navier–Stokes equations valid for high frequencies are calculated and compared with numerical solutions obtained for the same geometry. The second case has been studied numerically, and the solutions are presented and interpreted.