The transport of particles through gaseous systems is controlled by three factors: their arrival to the surface; whether or not they bounce upon impact; and when (if ever) they are resuspended from the surface. One of the parameters required in determining whether or not a particle is suspended is the lift force acting on the particle. We demonstrate that the fluid lift forces acting on particles as small as 1 μm in diameter can be modelled by particles of several mm in diameter. However, the forces involved in modelling such small particles are around 10−8 N, which is several orders of magnitude smaller than reported in published measurements of fluid lift forces. A system to determine such lift forces has been developed and is described. Measurements of the mean force acting on particles on both rough and smooth surfaces are presented.

The data recorded here for the mean fluid lift force on a sphere on a smooth surface are in good agreement with the relationship \[ F^{+} = (20.90\pm 1.57)(a^{+})^{2.31\pm 0.02}, \] where F+ is the non-dimensional force and a+ the non-dimensional particle radius scaled on fluid-boundary-layer parameters. It was observed that surface roughness can change the force by up to a factor of six.

A detailed experimental investigation has been made of shock/boundary-layer interactions on curved surfaces at transonic speeds. The shock waves were generated above circular-arc models with different radii mounted on the floor of the wind-tunnel test section. The ratio of the boundary-layer thickness (U/Ue = 0.99) in front of the shock to the radius of the surface curvature ranged from 0 (i.e. a flat surface) to 0.068. The Mach number just in front of the shock varied from 1.00 to 1.82 and the Reynolds number based on the model chord length was about 1.6 million. Interacting-flow studies include flows with shock-induced separation, flows with trailing-edge separation and flows with no separation. From all these studies it was found that separation was most extensive at the critical peak Mach number at which the separation changes from trailing-edge separation to shock-induced separation.

In this paper experimental measurements of the time-dependent velocity and density perturbations upstream of obstacles towed through linearly stratified fluid are presented. Attention is concentrated on two-dimensional obstacles which generate turbulent separated wakes at Froude numbers, based on velocity and body height, of less than 0.5. The form of the upstream columnar modes is shown to be largely that of first-order unattenuating disturbances, which have little resemblance to the perturbations described by small-obstacle-height theories. For two-dimensional obstacles the disturbances are similar to those found by Wei, Kao & Pao (1975) and it is shown that provided a suitable obstacle drag coefficient is specified, the lowest-order modes (at least) are quantitatively consistent with the results of the Oseen inviscid model.

Discussion of some results of similar measurements upstream of three-dimensional obstacles, the importance of towing tank endwalls and the relevance of the Foster & Saffman (1970) theory for the limit of zero Froude number is also included.

The transverse vibrations of a thin, flexible cylinder under nominally constant towing conditions are investigated. The cylinder is neutrally buoyant, of radius aA with a free end and very small bending stiffness. As the cylinder is towed with velocity U, the tangential drag causes the tension in the cylinder to increase from zero at its free end to a maximum at the towing point. Transverse vibrations of the cylinder are opposed by a normal viscous drag force. Both the normal and tangential viscous forces can be described conveniently in terms of drag coefficients CN and CT. The ratio CN/CT has a crucial effect on the motion of the cylinder. The form of the transverse displacement is found to be greatly influenced by the existence of a critical point at which the effect of tension in the cylinder is cancelled by a fluid loading term. Matched asymptotic expansions are used to extend the solution across this critical point to apply the downstream boundary condition. Displacements well upstream of the critical point have a simple form, while nearer to the critical point the solution depends on whether the normal drag coefficient CN is greater or less than one-half CT.

The typical acoustic streamer geometry considered is found to be stable to transverse displacements at all towing speeds. Forced perturbations of frequency ω are investigated. At low frequencies they propagate effectively along the cylinder with speed U. At higher frequencies they are attenuated.

The effect of a rope drogue of length lR, radius aR is investigated. Provided ωlRaR/UaA is very small, the drogue has the same effect as a small increase in the length of the cylinder. However at higher frequencies and for small values of the ratio CN/CT attaching a drogue may be disadvantageous because it reduces the attenuation of high-frequency disturbances as they propagate down the cylinder.

A ship, towing a heavier-than-water cable with a neutrally buoyant slender cylinder attached to the downstream end of the cable, is considered. The neutrally buoyant element contains a sonar array. Linear changes in the ship's velocity cause perturbations of both the cable and cylinder. The form of transverse vibrations of the neutrally buoyant cylinder was determined in Part 1. The propagation of disturbances along the cable is investigated in this paper. In particular, the effectiveness of the cable at isolating the sonar array from forcing due to unsteady ship motion is examined.

The cable and cylinder are found to be stable under constant towing conditions. It is therefore appropriate to investigate their response to forcing. Meanderings in the ship's track produce transverse displacements of both the cable and the cylinder. These transverse oscillations entirely decouple from any in-plane motion. The propagation of disturbances of frequency ω along the cable depends strongly on the value of the non-dimensional frequency ωlC/U, where lC is the cable length and U is the towing speed, and only weakly on the other cable parameters. The cable acts as an effective low-pass filter to transverse oscillations, the amplitude of disturbances with non-dimensional frequency greater than 10 being reduced by at least 90% as they propagate along the cable.

Unsteadiness in the ship's speed can result in in-plane deflections of the cable, and vertical oscillations of the cylinder containing the sonar array. In contrast to the transverse oscillations a significant proportion of the in-plane disturbances at the ship travels to the sonar array at all values of the frequency. Low- and high-frequency analytical forms are derived to explain why this occurs. Perturbations in the ship's position are most effectively transformed into vertical oscillations of the array at a frequency of 2.8U/lC. The effect of cable properties on transmission along the cable is investigated. The transmission again depends on the value of the non-dimensional frequency ωlC/U. Parameter changes, which increase the cable critical angle, increase the proportion of the disturbance at the towing point that is transformed into vertical array motion, for a fixed value of ωlC/U. This is explained by reference to the low- and high-frequency analytical solutions.

Pressure drops occurring in oscillatory viscous flows in wavy-walled tubes have been studied experimentally, for Reynolds numbers up to 1500 and Strouhal numbers in the range 0.005 to 0.02, and by numerical solution of the Navier-Stokes equations, for Reynolds numbers up to 200 and Strouhal numbers between 0.005 and 0.1. Agreement was good for values of the mean modulus of the pressure drop at lower Strouhal numbers and for values of the mean power dissipation at all Strouhal numbers.

Numerical solutions have shown that the pressure drop may vary non-sinusoidally, even though the imposed variation in flow rate is sinusoidal. This cannot be explained by the nonlinearity of the steady pressure drop-flow rate relationship, and arises because the velocity field is not quasi-steady. In particular energy may be stored in strong vortices formed during the acceleration phase of the flow cycle, and partially returned to the main flow later. The peak pressure drops in such flows, which are associated with the formation of these vortices, can be almost twice as large as values predicted by adding the appropriate quasi-steady and unsteady inertial contributions. This finding is important in the wider context of unsteady conduit flow.

The dependences of the mean modulus of the pressure drop and the mean power dissipation on the Strouhal number and frequency parameter were investigated in detail numerically for two geometries. It was not possible to reduce either dependence to a function of a single parameter. The ‘equivalent’ straight-walled tube for power dissipation was found to have a smaller bore than that for pressure drop, leading to smaller ‘phase angles’ than might have been expected at large values of the frequency parameter. This is because as the pressure drop becomes increasingly dominated by unsteady inertia, there remain relatively large recirculations in which energy is dissipated.

If an unpolluted tributary joins a river less than about thirty channel breadths downstream of an effluent outlet, then the additional dilution can reduce the peak pollution level experienced at the shoreline. This paper identifies the optimal sites for steady discharges to take full advantage of the extra dilution.