We present an experimental and theoretical investigation of some aspects of the coupling between a premixed laminar quasi-planar flame front and acoustic standing waves in tubes. A multidimensional instability of the front arises from its interaction with the oscillating field of acceleration. This instability can be described by the Clavin–Williams laminar wrinkled flame theory in which the periodic acceleration created by the acoustic field is added to the acceleration due to gravity. As first suggested by Markstein, the resulting equation can be reduced to the Mathieu equation for a parametric oscillator. A cellular instability appears with a finite excitation threshold. This instability is responsible for the spontaneous generation of intense acoustic oscillations observed elsewhere. The value of the acoustic field at the threshold of instability and the wavelength of the cellular structures are measured experimentally for propane flames and are found to be in good agreement with the calculated values. It is also seen, both experimentally and theoretically, that for certain amplitudes of pumping, the parametric mechanism can also stabilize an initially unstable system.

The motion of a rigid disk-shaped particle with rounded edges, which fits closely in the space between two parallel flat plates, and which is suspended in a viscous fluid subject to an imposed pressure gradient, is analysed. This problem is relevant to the squeezing of red blood cells through narrow slot-like channels which are found in certain tissues. Mammalian red cells, although highly flexible, conserve volume and surface area as they deform. Consequently, a red cell cannot pass intact through a channel which is narrower than some minimum width. In channels that are just wide enough to permit cell passage, the cell is deformed into its ‘critical’ shape: a disk with rounded edges. In this paper, the fluid mechanical aspects of such motions are considered, and the particle is assumed to be rigid with the critical shape. The channel cross-section is assumed to be rectangular. The flow of the suspending fluid is described using lubrication theory. Use of lubrication theory is justified by considering the motion of a circular cylinder between parallel plates. For disk-shaped particles, approximate solutions are obtained by applying lubrication equations throughout the flow domain. In the region beyond the particle, this is equivalent to assuming a Hele-Shaw flow. More accurate solutions are obtained by including effects of boundary layers around the particle and at the sides of the channel. Pressure distributions and particle velocities are computed as functions of geometrical parameters, and it is shown that the particle may move faster or slower than the mean velocity of the surrounding fluid, depending on the channel dimensions.

We perform a two-dimensional analytical stability analysis of a viscous, unbounded plane Couette flow perturbed by a finite-amplitude defect and generalize the results obtained in the inviscid limit by Lerner and Knobloch. The dispersion relation is derived and is used to establish the condition of marginal stability, as well as the growth rates at different Reynolds numbers. We confirm that instability occurs at wavenumbers of the order of ε, the non-dimensional amplitude of the defect. For large enough εR (R being the Reynolds number based on the width of the defect), the maximum growth rate is about ½ε, at approximately half the critical wavenumber. We formulate the instability conditions in the case where the flow has a finite extension in the downstream direction. Instability appears when ε is greater than RL1/3, where RL is the Reynolds number based on the downstream scale, and when the ratio of the defect width to the downstream scale lies in the interval [(εRL}−½, ε].

The linear stability of filaments or strips of ‘potential’ vorticity in a background shear flow is investigated for a class of two-dimensional, inviscid, non-divergent models having a linear inversion relation between stream function and potential vorticity. In general, the potential vorticity is not simply the Laplacian of the stream function – the case which has received the greatest attention historically. More general inversion relationships between stream function and potential vorticity are geophysically motivated and give an impression of how certain classic results, such as the stability of strips of vorticity, hold under more general circumstances.

In all models, a strip of potential vorticity is unstable in the absence of a background shear flow. Imposing a shear flow that reverses the total shear across the strip, however, brings about stability, independent of the Green-function inversion operator that links the stream function to the potential vorticity. But, if the Green-function inversion operator has a sufficiently short interaction range, the strip can also be stabilized by shear having the same sense as the shear of the strip. Such stabilization by ‘co-operative’ shear does not occur when the inversion operator is the inverse Laplacian. Nonlinear calculations presented show that there is only slight disruption to the strip for substantially less adverse shear than necessary for linear stability, while for co-operative shear, there is major disruption to the strip. It is significant that the potential vorticity of the imposed flow necessary to create shear of a given value increases dramatically as the interaction range of the inversion operator decreases, making shear stabilization increasingly less likely. This implies an increased propensity for filaments to ‘roll-up’ into small vortices as the interaction range decreases, a finding consistent with many numerical calculations performed using the quasi-geostrophic model.

The performance of a circular electrochemical wall shear rate probe under unsteady flow conditions is analysed through a combined experimental, numerical and analytical approach. The experiments arc performed with a ferri- and ferrocyanide redox couple and compared to finite element analyses of the two-dimensional time-dependent convection—diffusion equation. The results are related to the analytical Lévêque solution for steady flow and for some cases to Pedley's model for heat transfer in reversing shear flow (Pedley 1976).

The steady flow analyses showed that in our experiments axial diffusion is only of minor importance but that for the lower Péclet numbers (< 104) three-dimensional effects, like tangential diffusion, may not be neglected. A similar result is found for the oscillating case. A fair agreement is found between experimental and numerical data during flow acceleration, but during flow reversal remarkable (about 15%) deviations are found. The observed insensitivity of the transducer during flow reversal is quite well predicted by Pedley's model. Finally, the performance of the probe may be improved somewhat by a decrease in cathode length and cathode—anode distance.

The nonlinear effects of longitudinal vorticity elements in boundary layers are studied via a prototype problem: the development of such vorticity elements from initial Görtler vortices in the amplified regime. While a time-dependent, quasi-two-dimensional formulation greatly simplifies the computational framework, full three-dimensionality of the velocity components is obtained. This temporal analogy for spatially developing flows approximates the nonlinear streamwise advection by a constant convection velocity, but the strong cross-sectional, advective nonlinearities are retained. Such an approximation lacks the stretching effect of the streamwise vorticity, since such elements are lifted into regions of higher streamwise velocities. That the temporal analogy is a good theoretical (and experimental) approximation to real developing flows is shown by a posteriori indications that the streamwise vorticity remains weak throughout the nonlinear region (though it has far-reaching nonlinear effects in upwelling in the peak region) and that the region of strong nonlinearities remains in the cross-sectional plane.

The aim of this work is to elucidate the nonlinearities producing sites of secondary instabilities and turbulence generation. The present mushroom-like computed iso-streamwise velocity contours surrounding the peak, as well as the streamwise velocity profiles in the peak and valley regions, agree well with experimental measurements up to the region of expected wavy secondary instabilities. Three local intense vorticity and enstrophy areas are found to be significant and these are thoroughly diagnosed. One such intense vorticity region arises from the upwelling of existing spanwise vorticity and subsequent spanwise stretching in the outer layers, leading to intense local high-shear layers of spanwise vorticity in the vicinity of the peak region, as expected. Primarily through the stretching of the vertical vorticity, intense vertical vorticity (and associated enstrophy) develop (i) in the shoulder regions of the mushroom-like iso-streamwise velocity structures in the outer layers of the boundary layer and (ii) in the inner regions of about thirty viscous lengths from the wall, close to the base of the mushroom-like structures. Of the three regions of intense local ‘free’ shear-layer vorticity, the vertical vorticity in the inner regions near the mushroom stem is dominant. This is entirely consistent with experimental observations of sites of high-frequency secondary and fine-scaled wavy instabilities. This theoretically/computationally obtained ‘parent flow’ essentially sets the stage for continued studies of its wavy instabilities. In order to analyse and control the shear stress at the wall and nonlinear flow development, the effect of initial parameters such as Görtler number, initial amplitudes and wavenumbers is fully explored.

An extension of an axial viewing optical technique (first used by Lee, Adrian & Hanratty) is described which allows the determination of the turbulence characteristics of solid particles being transported by water in a pipe. Measurements are presented of the mean radial velocity, the mean rate of change radial velocity, the mean-square of the radial and circumferential fluctuations, the Eulerian turbulent diffusion coefficient, and the Lagrangian turbulent diffusion coefficient. A particular focus is to explore the influence of slip velocity for particles which have small time constants. It is found that with increasing slip velocity the magnitude of the turbulent velocity fluctuations remains unchanged but that the turbulent diffusivity decreases. The measurements of the average rate of change of particle velocity are consistent with the notion that particles move from regions of high fluid turbulence to regions of low fluid turbulence. Measurements of the root-mean-square of the fluctuations of the rate of change of particle velocity allow an estimation of the average magnitude of the particle slip in a highly turbulent flow, which needs to be known to analyse the motion of particles not experiencing a Stokes drag.