The nonlinear evolution of deep-water wave groups, which are initiated by unstable three-wave systems, have been observed in a large wave tank (50 m long, 4.2 m wide, 2.1 m deep), equipped with a programmable, high-resolution wave generator. A large number of experiments were conducted (over 80 cases) for waves 1.0–4.0 m long, initial steepness ε=0.10–0.28, and normalized sideband frequency differences, δω=δω, 0.2–1.4. Using an array of eight high-resolution wave wires distributed in range (up to 43 m fetch), spectral evolution was studied in detail including the effect of background disturbances on the evolution. Minimizing those, new observations were made which extend the pioneering work of Lake et al. (1977) and of Melville (1982). Foremost, near recurrence without downshifting was observed without breaking, despite a significant but reversible energy transfer to the lower sideband at peak modulation; complete recurrence was prevented by the spreading of discretized energy to higher frequencies. Strong breaking was found to increase the transfer of energy from the higher to the lower sideband and to render that transfer irreversible. The end state of the evolution following strong breaking is an effective downshifting of the spectral energy, where the lower and the carrier wave amplitudes nearly coincide; the further evolution of this almost two-wave system was not studied here. Breaking during strong modulation was observed not only for the fastest growing initial condition, but over a wide parameter range. An explanation of the sideband behaviour in both the breaking and non-breaking case was given based on wave energy and momentum considerations, including the separate effects of energy and momentum loss due to breaking, and transfer to discretized higher frequencies throughout the spectra. Attention was drawn to the latter, which was almost universally observed.

The dynamics of two-dimensional uniform wavetrains on the interface between a viscoelastic compliant coating and a boundary-layer flow are explored theoretically. The coating is treated as a single-layer isotropic Voigt material of finite thickness that is bonded to a rigid half-space. The flow is modelled first by potential theory and then modified to incorporate pressure phase shifts and magnitudes found in boundary-layer flow over wavy walls. The consideration of viscoelastic effects has led to an important dimensionless damping parameter γt = Ct τt/d (where τt is the strain relaxation time, Ct is the elastic shear-wave speed and d is the layer depth) that seems to have been overlooked by experimentalists. The flow and the damping are found to have dramatic effects on wave propagation. Using flow pressure and material-damping parameters typical of experiments, the results show that both upstream- and downstream-propagating waves exist at low flow speeds. At higher flow speeds, shorter waves can no longer propagate upstream. At still higher velocities, two instabilities, ‘static divergence’ and ‘flutter’, are found. Static divergence occurs for flow speeds above 2.86Ct and consists of slow waves moving with speeds of about 0.02Ct. These results compare fairly well with published experimental data. Static divergence is found to be a damping instability for these coating systems. When the flow speed is increased further, the flutter instability appears consisting of waves with phase speeds about equal to Ct.

SUMMARYAn efficient 2D non-linear numerical wave tank called LONGTANK has been developed based on a multisubdomain (MSD) approach combined with the conventional boundary element method (BEM). The multisubdomain approach aims at optimized matrix diagonalhation, thus minimizing the computing time and reserved storage. The CPU per time step in LONGTANK simulations is found to increase only linearly with the number of surface nodes, which makes LONGTANK highly efficient especially when simulating long-time wave evolutions in space.Appropriate treatment of special points on the boundary ensures high resolution in LONGTANK simulation beyond initial deformation and breaking, which allows detailed study of breaking criterion, breaker morphology, breaking dissipation, vorticity generation, etc.Detailed numerical implementation has been given with demonstration of LONGTANK simulations.

A linearized theory is developed for steady, two-dimensional cavity flows about slender symmetric bodies. The theory is applied to the cases of zero and nonzero (positive) cavitation numbers. It is shown that, for the case of finite cavities, the linearized theory avoids the necessity for choosing an artificial cavitation model as must be done in any exact theory attempts. The problem of calculating cavity shapes and drags for arbitrary slender bodies is reduced to one of quadratures. As an example, calculations are made for the family of wedge profiles and results are shown to be in good agreement with "exact" theory results for sufficiently slender bodies. In particular, the example demonstrates that the linearized theory is a valid first order theory.