This paper describes a comparison of experimental data and theoretical results for the motions in waves of large flat-bottomed barges having zero forward speed. The experimental data are derived from model tests at two scales (1:36 and 1:108). These consist of measurements of motions in surge, sway, heave, roll, pitch and yaw to long-crested seas approaching the barge models at two orientation angles (head and beam seas). The experimental data are compared with results computed from linearized potential-flow theory, which accounts for the diffraction and radiation of gravity waves around the barge. The boundary-integral scheme employed to solve this potential-flow problem is briefly reviewed.

The experimental data at two scales and the theoretical results show that potential-flow theory is in reasonable agreement with experimental data for all motions except roll near resonance. These roll-motion discrepancies, due to vortex shedding from bilge-keel edges, are discussed. Some of the observable effects of scale in the model tests are highlighted.

We calculate the flow induced by a vortex pair in a viscous fluid, which is otherwise at rest, in the presence of a plane boundary. This may be either a no-slip or a stress-free boundary. The phenomenon of rebound of the vortices from the boundary occurs for either type of boundary, and an explanation for this is offered in terms of viscous effects.

The general triple-deck theory of laminar viscous-inviscid interaction is extended to axisymmetric bodies. With body radius/length ratios scaled in terms of Reynolds number as $Re^{\frac{1}{8}\beta} (\beta > 0)$, it is found that for β < 3 the only three-dimensional effect is that on the incoming undisturbed boundary-layer profile as accounted for by the Mangler transformation. When β = 3, however, an explicit axisymmetric effect on the interaction equations also enters: the upper-deck flow is governed by the equation of axisymmetric potential disturbance flow, whereas the middle and lower decks are still governed by equations of two-dimensional form. When β > 3, the body is so slender that transverse curvature effects become important and the lower decks too are explicitly influenced by three-dimensional effects. A detailed example application of this theory is given for weak interactions on a flared cylinder and cone in supersonic flow with β [Lt ] 3. The three-dimensional effects on the interactive pressure and shear-stress distributions are shown to relieve the strength of the interaction and reduce its upstream influence, as expected. Correspondingly, it is found that the smallest flow deflection angle provoking incipient separation increases with increasing axisymmetric body slenderness. These results are shown to be in qualitative agreement with several experimental studies.

It was shown in Part 1 that the amplitude of the spatially growing Tollmien-Schlichting wave generated by a time-harmonic free-stream disturbance is related to the coefficient multiplying the lowest-order Lam & Rott asymptotic eigensolution of the unsteady boundary-layer equation. In this part we use a numerical solution of the unsteady boundary-layer equation to determine that coefficient for the case of a uniformly pulsating stream.

The experimental results of Provis (1975, 1976) for wave amplification at a conical island bear little resemblance to the theoretical predictions of Smith & Sprinks (1975). Here Provis's suggestion is confirmed: that his experiments were dominated by viscous damping and by standing waves between the island and the wavemaker. Estimates are given as to how large an experiment needs to be to avoid these important scale effects.

Nonlinear electrohydrodynamic Rayleigh-Taylor instability is investigated. A charge-free surface separating two semi-infinite dielectric fluids influenced by a normal electric field is subjected to nonlinear deformations. We use the method of multiple-scale perturbations in order to obtain uniformly valid expansions near the cutoff wavenumber separating stable from unstable flows. We obtain two nonlinear Schrödinger equations by means of which we can deduce the cutoff wavenumber and analyse the stability of the system. It is found that if a finite-amplitude wave exists then its small modulation is stable. We also obtain the surface elevation for such waves. The electric field plays a dual role in the stability criterion and the dielectric constant plays a distinctive role in this analysis. If the dielectric constant of the upper fluid is smaller than that of the lower fluid the field has a destabilizing effect for large wavenumbers. For relatively smaller wavenumbers the electric field stabilizes considerable parts of the first and second subharmonic regions in the stability diagrams; a result which is in contrast with the linear theory. If the dielectric constant of the upper fluid is larger than that of the lower fluid, then the field is stabilizing for larger values of the wavenumber K′ when ρ is small (ρ is the density ratio) and destabilizing for smaller values of K′.