The coupling between imposed disturbances and capillary instabilities on a liquid jet is examined. It is shown that in most physical situations the forcing produces neutral waves which can then turn into growing waves as the profile relaxes or may be amplified nonlinearly by a mechanism of the type considered by Akylas & Benney (1980). The effectiveness of the coupling is expressed quantitatively by numerically computed values of the ‘coupling coefficient’.

The linear, two-dimensional stability of flows down an inclined plane has been examined at large Reynolds numbers. Both the surface and shear wave modes have been numerically investigated, involving changes in angle of inclination, surface tension, and form factor.

The problem of oscillatory viscous flow in a tube with rigid sinusoidal walls of large amplitude is solved numerically, for Reynolds numbers up to 300 and Strouhal numbers in the range 10−4–1. Flow visualization photographs have confirmed qualitatively many of the predictions. Results analogous to those of Sobey (1980, 1983) for the two-dimensional problem have been obtained for regions of the parameter space studied in detail by that author. However, new flow structures are found in the previously neglected Strouhal number range of 0.02–0.1. These flows are characterized by significant interaction of flow events in successive half-cycles, due to the persistence of strong shed vortices. Bifurcation of the solution structure can then occur for Strouhal numbers between about 0.025 and 0.045, with the development of time-asymmetric flows: thus the velocity field at some instant of a positive-flow half-cycle may not be equal to minus the velocity field at the corresponding instant of a negative-flow half-cycle.

Modulatory heat-transfer enhancement in grooved channels is investigated by direct numerical simulation of the Navier–Stokes and energy equations using the spectral element method. It is shown that oscillatory perturbation of the flow at the frequency of the least-stable mode of the linearized system results in subcritical resonant excitation and associated transport enhancement as the critical Reynolds number of the flow is approached. The Tollmien–Schlichting frequency theory that was presented in Part 1 of this paper is shown to accurately predict the optimal frequency for transport augmentation for small values of the modulatory amplitude, and the effect of the excited travelling-wave channel modes on the resulting temperature distribution is described. The importance of (non-trivial) geometry in the forced response of a flow is discussed, and grooved-channel flow is compared to (straight-channel) plane Poiseuille flow, for which no resonance excitation occurs owing to a zero projection of the forcing inhomogeneity on the dangerous modes of the system. For the particular grooved-channel geometry investigated, resonant oscillatory forcing at modulatory amplitudes as small as 20% of the mean flow results in a doubling of transport as measured by a time, space-averaged Nusselt number.