Flows in thin-walled, collapsible tubes are of fundamental importance to various physiologic phenomena and clinical devices.

A one-dimensional, unsteady theory is developed for flows generated either by externally applied pressures or by body forces. Part 1 deals with small-amplitude, linearized flows, part 2 with large amplitude, nonlinear flows. Experimental results for a tube collapsing under external pressure are given in part 3, together with theoretical interpretations and comparative results of numerical simulations.

Several new and unanticipated phenomena are revealed. These are in part associated with the highly nonlinear ‘equation of state’ (transmural pressure versus area) for a partially collapsed tube, and in part with whether the flow speed is sub- or supercritical relative to the speed of area waves. For instance, a flow produced by a spatially uniform external pressure applied to a limited region becomes choked at a flow-limiting throat at which point the fluid speed reaches the local wave speed. This throat forms at the edge of the pressurized region. The critical velocity can be exceeded with the application of certain types of spatially graded external pressures.

Previous experimental work on the diffraction of a detonation wave at a large and abrupt area change in a tube, has shown that every system is characterized by a critical tube diameter at which quenching of the detonation occurs. Zeldovich, Kogarko & Simonov (1956) established that the critical tube diameter, for the oxy-acetylene system with varying dilution of nitrogen, lies between 500 and 700 times the one-dimensional induction zone length. Later, Mitrovanov & Soloukhin (1964) discovered that, for the same system, the critical diameter is 10 or 13 times the transverse wave spacing for a flat channel and cylindrical tube respectively. The two results are shown to be equivalent and are confirmed by further experiments in a 75 × 6 mm channel in which the flow is two-dimensional.

Smoked foil and schlieren records show that, for supercritical waves, re-ignition occurs at sites along the wedge formed by the head of the expansion from the diffracting aperture and criticality is attained when the site is located at the apex of the wedge. A universal feature of re-initiation, which is also observed in liquid and solid explosives, is the sudden appearance of a transverse detonation which sweeps through the compressed, but unreacted, gas of the dissociated shock-reaction zone regime; this is signalled by the appearance of fine triple-point writing on smoked-foil records.

A criterion for re-initiation is formulated by equating the critical velocity gradient which characterizes the decay of the wavefront in a cell, to that obtaining in the diffracted shock front at the head of the expansion fan; an expression for the latter is derived from Whitham's (1957) theory for non-reactive shocks. The prediction of the criterion is in good agreement with observation.

The effects of thermally insulating boundaries on rapidly and almost rigidly rotating gas flows are examined. It is shown that, on a thermally insulating boundary, all boundary layers disappear to zeroth order and that the geostrophic flow alone satisfies the kinematical boundary condition on such a boundary. The temperature gradient of the geostrophic flow is on a horizontal thermally insulating boundary corrected by a weak Ekman layer of strength E½ where E is the Ekman number. On a vertical thermally insulating boundary, the temperature gradient of the geostrophic flow is in the general case corrected by E¼ and $E^{\frac{1}{3}}$ Stewartson layers of strengths E¼ and $E^{\frac{1}{3}}$ respectively.

A numerical method is presented for the computation of two-dimensional periodic progressive surface waves propagating under the combined influence of gravity and surface tension. The dynamic boundary equation is used in its exact nonlinear form. The procedure involves a boundary-integral formulation coupled with a Newtonian iteration. Solutions of high accuracy can be achieved over much of the range of wavelengths and heights including limiting waves. A number of different continuous families of solutions have been produced, all of which ultimately exhibit closed bubbles at their troughs. The so-called critical wavelengths are less important than have been previously assumed; the number of possible wave forms does increase with increasing wavelength, however.

The linearized problem of water-wave reflexion by a thin barrier of arbitrary permeability is considered with the restriction that the flow be two-dimensional. The formulation includes the special case of transmission through one or more gaps in an otherwise impermeable barrier. The general problem is reduced to a set of integral equations using standard techniques. These equations are then solved using a special decomposition of the finite depth source potential which allows accurate solutions to be obtained economically. A representative range of solutions is obtained numerically for both finite and infinite depth problems.

A parabolic approximation to the reduced wave equation is investigated for the propagation of periodic surface waves in shoaling water. The approximation is derived from splitting the wave field into transmitted and reflected components.

In the case of an area with straight and parallel bottom contour lines, the asymptotic form of the solution for high frequencies is compared with the geometrical optics approximation.

Two numerical solution techniques are applied to the propagation of an incident plane wave over a circular shoal.

An experimental study of the flow past a thin finite length plate in a supersonic low density stream is reported. The paper discusses the corrections that are necessary for surface pressures measured under rarefied conditions. It is shown that the recent method of ‘orifice’ corrections due to Harbour & Bienkowski is versatile and reliable to use for both cold wall and insulated wall measurements. For the conditions of the experiment, the flow over the plate was found to be dominated by both leading-edge and trailing-edge interactions.

The velocity induced by a transversely waving infinite flexible sheet in a viscoelastic liquid is investigated by a method of successive approximation up to second order in the amplitude of oscillation of the sheet. The incompressible second-order fluid model has been used and it is found that the elastic property of the fluid augments self-propulsion (increases the induced velocity) in some range of Reynolds number (based on the phase velocity) and hampers it (reduces the induced velocity) in some other range with higher values of Reynolds number.

Monochromatic waves obliquely incident on a plane beach, and strongly reflected there, are unstable to perturbations by edge waves. Theory suggests the possible width of the resonant edge wave frequency band. Experiments on beaches with absorbers at both ends show that the excited waves have frequencies at the centre of the band, as predicted by Guza & Bowen (1975). Advection by mean longshore currents must be taken into account. If reflectors are placed at the beach ends, the additional boundary conditions apparently lead to resonances scattered across the resonant band.