The use of steady, normal and oblique shock configurations is explored in calculating the pressure and deformation produced by the impact of a liquid mass on a plane solid surface. Since pressures generated are very large, the change in bulk modulus of the liquid (water) is accounted for by using an equation of state following Field, Lesser & Davies (1979). The impact of a plane-ended liquid mass is analysed using a normal shock for the cases of a rigid surface and a perfectly plastic surface. For the former, it is found that pressures somewhat in excess of the ‘water-hammer’ pressure of linear acoustic theory are predicted, and for the latter there is a critical impact velocity below which no deformation occurs. Above this velocity the surface deforms at a constant rate, producing a pit with maximum depth at the centre.

If the liquid mass is wedge-shaped then an oblique shock is formed, which is attached to the contact point provided that the impact Mach number is large enough, as originally shown by Heymann (1969). Pressure and deformation velocity can again be calculated for the cases of rigid and perfectly plastic surfaces respectively. For a rigid surface it is confirmed that pressures considerably in excess of the plane-ended case are produced at shock detachment. For the plastic surface, it is found that there is no critical impact velocity and deformation can occur at any velocity as shock detachment is approached. For a cylindrical liquid mass with a conical tip, the pit produced again has maximum depth at the centre, but with a considerably increased value. The possible use of these models for pitting caused by microjets associated with cavitation bubbles and by impact of liquid drops is discussed.

Boundary-layer flow past an impulsively started cylinder is studied by extending the Blasius time-series expansion to many terms. The ordinary differential equations that result from this expansion are solved using an O(h6)-accurate numerical method. The validity of the simple series expansions for the wall shear, displacement thickness and viscous displacement velocity is extended by recasting the series using rational functions. The solutions so obtained are in good agreement with previous authors’ work. In particular, an examination of the poles and zeros of the rational functions confirms that a singularity develops within a finite time. The analytic structure of the singularity is found to be in agreement with the asymptotic expansion proposed by van Dommelen & Shen.

We argue that the universality and statistical nature of the deep-ocean internal gravity-wave spectrum results from a strange attractor in the driven, dissipative internal-wave field. To explore this we construct a model which injects energy into the oceanic surface at a constant rate. A two-dimensional version of the model is explored analytically and numerically. For the numerical work we restrict our considerations to a few of the longest-wavelength modes. This few-mode system exhibits bifurcation into limit cycles, period doubling of the limit cycles, and chaotic, non-periodic behaviour associated with a strange attractor. In an appendix we present some discussion of the three-dimensional version of the model.