In this paper we calculate the streaming induced by gravity waves passing over a thin fluid layer, one side of which is rigid while the other is a flexible, inextensible membrane. The problem is relevant to some recent laboratory experiments by Allison (1983) on the pumping action of water waves.

On the assumption that the flow is laminar and that the lateral displacement b of the membrane is small compared with the thickness Δ of the fluid layer, we calculate the velocity profile of the streaming U within the layer. This depends on the ratio Δ/δ, where δ is the thickness of the Stokes layers at the upper and lower boundaries. When 0 < Δ/δ > 6 the boundary layers interact strongly and the velocity profile is unimodal. At large values of Δ/δ the profile of U exhibits thin ‘jets’ near the boundaries.

The calculated drift velocities agree as regards order of magnitude with those observed. However, the pressure gradients observed were larger than those calculated, due possibly to turbulence, but probably also to finite-amplitude and end-effects.

The theory given here can be considered as an extension of the theory of peristaltic pumping to flows at higher Reynolds number.

The effects of imperfect spatial resolution on hot-film and hot-wire measurements of wall-bounded turbulent shear flows were studied. Two hot-film probes of different length were used for measurements of fully developed turbulent channel flow in a water tunnel. In the near-wall region significant effects of spanwise spatial averaging due to finite probe size were found for a probe 32 viscous units long. The maximum turbulence intensity attained a 10% lower value than that for a probe about half as long, and the zero-crossing of the skewness factor was shifted away from the wall. This could be attributed to spatial averaging of narrow low-speed regions. Results for different Reynolds numbers, but with the same sensor length in viscous units, showed that Reynolds-number effects are small, and that much of the reported discrepancies for turbulence measurements in the near-wall region can be ascribed to effects of imperfect spatial resolution. Also the number of events detected with the variable-interval time-averaging (VITA) technique was found to depend strongly on the sensor length, especially for events with short duration.

A three-dimensional linear stability analysis of a baroclinic flow for Richardson number Ri of order unity is presented. The model considered is a thin, horizontal, rotating fluid layer which is subjected to horizontal and vertical temperature gradients. The basic state is a Hadley cell which is a solution of the Navier–Stokes and energy equations and contains both Ekman and thermal boundary layers adjacent to the rigid boundaries; it is given in closed form. The stability analysis is also based on the Navier–Stokes and energy equations; and perturbations possessing zonal, meridional and vertical structures were considered. Numerical methods were developed for the solution of the stability problem, which results in an ordinary differential eigenvalue problem. The objectives of this work were to extend the previous theoretical work on three-dimensional baroclinic instability for small Ri to a more realistic model involving the Prandtl number σ and the Ekman number E, and to finite growth rates and a wider range of the zonal wavenumber. The study covers ranges of 0.135 [les ] Ri [les ] 1.1, 0.2 [les ] σ [les ] 5.0, and 2 × 10−4 [les ] E [les ] 2 σ 10−3. For the cases computed for E = 10−3 and σ ≠ 1, we found that conventional baroclinic instability dominates for Ri > 0.825 and symmetric baroclinic instability dominates for Ri < 0.675. However, for E [ges ] 5 × 10−4 and σ = 1 in the range 0.3 [les ] Ri [les ] 0.8, conventional baroclinic instability always dominates. Further, we found in general that the symmetric modes of maximum growth are not purely symmetric but have weak zonal structure. This means that the wavefronts are inclined at a small angle to the zonal direction. The results also show that as E decreases the zonal structure of the symmetric modes of maximum growth rate also decreases. We found that when zonal structure is permitted the critical Richardson number for marginal stability is increased, but by only a small amount above the value for pure symmetric instability. Because these modes do not substantially alter the results for pure symmetric baroclinic instability and because their zonal structure is weak, it is unlikely that they represent a new type of instability.

A set of measurements using arrays of hot-wire anemometers has been performed in the fully developed turbulent wake of a circular cylinder. The data were digitized, recorded on magnetic tape, and processed using the pattern recognition technique described in Part 1 (Mumford 1982), to yield ensemble averages of the streamwise component of the velocity fields of the large eddies in the flow.

The results indicate that the large-scale structures in the turbulent wake are predominantly the inclined ‘double-roller’ vortices described by Grant (1958). These eddies consist of two contrarotating roller-like vortices with parallel axes displaced in the spanwise direction and approximately aligned with the direction of the strain associated with the mean velocity gradient. It was found that the structures are often confined to either side of the wake centreplane, rather than extending over the entire thickness of the turbulent region. In addition, eddies of similar type tended to occur in pairs or longer groups with their centres separated in the stream direction.